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BEGIN:VEVENT
SUMMARY:Lexing Ying (Stanford University)
DTSTART;VALUE=DATE-TIME:20200408T231000Z
DTEND;VALUE=DATE-TIME:20200409T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/1
DESCRIPTION:Title: Solving inverse problems with deep learning\nby Lexing Ying (S
tanford University) as part of Berkeley applied mathematics seminar\n\n\nA
bstract\nThis talk is about some recent progress on solving inverse proble
ms using deep learning. Compared to traditional machine learning problems\
, inverse problems are often limited by the size of the training data set.
We show how to overcome this issue by incorporating mathematical analysis
and physics into the design of neural network architectures. We first des
cribe neural network representations of pseudodifferential operators and F
ourier integral operators. We then continue to discuss applications includ
ing electric impedance tomography\, optical tomography\, inverse acoustic/
EM scattering\, and travel-time tomography.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Mahoney (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200422T231000Z
DTEND;VALUE=DATE-TIME:20200423T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/2
DESCRIPTION:Title: Determinantal point processes and randomized numerical linear alge
bra\nby Michael Mahoney (UC Berkeley) as part of Berkeley applied math
ematics seminar\n\n\nAbstract\nRandomized Numerical Linear Algebra (RandNL
A) is an area which uses randomness\, most notably random sampling and ran
dom projection methods\, to develop improved algorithms for ubiquitous mat
rix problems\, such as those that arise in scientific computing\, data sci
ence\, machine learning\, etc. A seemingly different topic\, but one which
has a long history in pure and applied mathematics\, is that of Determina
ntal Point Processes (DPPs)\, which are stochastic point processes\, the p
robability distribution of which is characterized by sub-determinants of s
ome matrix. Recent work has uncovered deep and fruitful connections betwee
n DPPs and RandNLA. For example\, random sampling with a DPP leads to new
kinds of unbiased estimators for classical RandNLA tasks\, enabling more r
efined statistical and inferential understanding of RandNLA algorithms\; a
DPP is\, in some sense\, an optimal randomized method for many RandNLA pr
oblems\; and a standard RandNLA technique\, called leverage score sampling
\, can be derived as the marginal distribution of a DPP. This work will be
reviewed\, as will recent algorithmic developments\, illustrating that\,
while not quite as efficient as simply applying a random projection\, thes
e DPP-based algorithms are only moderately more expensive. Joint work with
Michal Derezinski.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Kamrin (MIT)
DTSTART;VALUE=DATE-TIME:20200429T231000Z
DTEND;VALUE=DATE-TIME:20200430T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/3
DESCRIPTION:Title: Toward reduced-order models for flowing grains: Surprising complex
ity meets surprising simplicity\nby Ken Kamrin (MIT) as part of Berkel
ey applied mathematics seminar\n\n\nAbstract\nDespite the commonality of g
ranular materials in day-to-day life\, modeling systems of millions or mor
e flowing particles has proven historically difficult. This has direct rea
l-world ramifications owing to the prominent role granular media play in m
ultiple industries and in terrain dynamics. One can attempt to track every
grain with discrete particle methods\, but realistic systems are often to
o large for this approach and a continuum model is desired. However\, gran
ular media display unusual behaviors that complicate the continuum treatme
nt: they can behave like solid\, flow like liquid\, or separate into a “
gas”\, and the rheology of the flowing state displays remarkable subtlet
ies.\n\nTo address these challenges\, in this talk we develop a family of
continuum models and solvers\, permitting quantitative modeling capabiliti
es. We discuss a variety of applications\, ranging from general problems t
o specific techniques for problems of intrusion\, impact\, driving\, and l
ocomotion in granular media. To calculate flows in general cases\, a rathe
r significant nonlocal effect is evident\, which is well-described with ou
r recent nonlocal model accounting for grain cooperativity within the flow
rule. On the other hand\, to model only intrusion forces on submerged obj
ects\, we will show\, and explain why\, many of the experimentally observe
d results can be captured from a much simpler tension-free frictional plas
ticity model. This approach gives way to some surprisingly simple general
tools\, including the granular Resistive Force Theory\, and a broad set of
scaling laws inherent to the problem of granular locomotion. These scalin
gs are validated directly and suggest a new down-scaled paradigm for granu
lar locomotive design\, on earth and beyond\, to be used much like scaling
laws in fluid mechanics.\n\nWe close with a brief discussion of ongoing m
odeling efforts for wet granular systems\, including those with non-trivia
l grain-grain interactions and those with highly deformable particles.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kolda (Sandia National Laboratory)
DTSTART;VALUE=DATE-TIME:20200506T231000Z
DTEND;VALUE=DATE-TIME:20200507T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/4
DESCRIPTION:Title: Practical leverage-based sampling for low-rank tensor decompositio
n\nby Tamara Kolda (Sandia National Laboratory) as part of Berkeley ap
plied mathematics seminar\n\n\nAbstract\nConventional algorithms for findi
ng low-rank canonical polyadic (CP) tensor decompositions are unwieldy for
large sparse tensors. The CP decomposition can be computed by solving a s
equence of overdetermined least problems with special Khatri-Rao structure
. In this work\, we present an application of randomized algorithms to fit
ting the CP decomposition of sparse tensors\, solving a significantly smal
ler sampled least squares problem at each iteration with probabilistic gua
rantees on the approximation errors. Prior work has shown that sketching i
s effective in the dense case\, but the prior approach cannot be applied t
o the sparse case because a fast Johnson-Lindenstrauss transform (e.g.\, u
sing a fast Fourier transform) must be applied in each mode\, causing the
sparse tensor to become dense. Instead\, we perform sketching through leve
rage score sampling\, crucially relying on the fact that the structure of
the Khatri-Rao product allows sampling from overestimates of the leverage
scores without forming the full product or the corresponding probabilities
. Naïve application of leverage score sampling is infective because we of
ten have cases where a few scores are quite large\, so we propose a novel
hybrid of deterministic and random leverage-score sampling which is more e
fficient and effective. Numerical results on real-world large-scale tensor
s show the method is faster than competing methods without sacrificing acc
uracy. This is joint work with Brett Larsen at Stanford University.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linfeng Zhang (Princeton University)
DTSTART;VALUE=DATE-TIME:20200513T231000Z
DTEND;VALUE=DATE-TIME:20200514T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/5
DESCRIPTION:Title: Symmetry preserving neural network models for molecular modelling<
/a>\nby Linfeng Zhang (Princeton University) as part of Berkeley applied m
athematics seminar\n\n\nAbstract\nWe discuss how to leverage the fitting a
bility of neural networks to accurately and efficiently represent two type
s of maps in molecular modelling problems. The first type takes as input t
he coordinates of atoms and their associated chemical species\, and output
s physical observables such as the interatomic potential energy (a scalar)
\, the electric polarization (a vector) and polarizability (a tensor)\, an
d the charge density (a field). The second type\, like post–Hartree–Fo
ck methods\, uses the ground-state electronic orbitals as the input\, and
predicts the energy difference between results of highly accurate models s
uch as the coupled-cluster method and low accuracy models such as the Hart
ree-Fock (HF) method. Special attentions are paid to how the neural networ
k models take care of physical properties like symmetry and locality\, so
that models trained with small-size systems can be transferred to differen
t and large-size ones\; and how they are made end-to-end\, so that little
human intervention is required for various complex tasks. This is joint wo
rk with Yixiao Chen\, Han Wang\, and Weinan E.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanhe Huang (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200818T231000Z
DTEND;VALUE=DATE-TIME:20200819T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/6
DESCRIPTION:Title: Axisymmetric bubbles rising in 3D and a new accurate algorithm for
evaluating orthogonal polynomials\nby Yanhe Huang (UC Berkeley) as pa
rt of Berkeley applied mathematics seminar\n\n\nAbstract\nn the high Reyno
lds number regime\, under what conditions do there exist steadily rising b
ubbles? This question has been studied extensively both experimentally and
numerically\, but current mathematical models and numerical discretizatio
ns suffer from large numerical errors that make the results less convincin
g. In the first part of this talk\, we build an inviscid model for the ste
ady rising problem and find different solution branches of bubble shapes c
haracterized by the number of humps. These only exist when there is no gra
vity. When there is gravity\, viscous potential flow is used to find diffe
rent steady shapes. The corresponding dynamic problem is also studied. Tec
hniques such as axisymmetric potential theory\, Hou-Lowengrub-Shelley fram
ework\, and weak/hyper-singularity removal are applied to guarantee spectr
al accuracy.\n\nDue to the importance of accurate evaluation of orthogonal
polynomials in the boundary integral method used in the first part\, in t
he second part of the talk I will introduce a new way to evaluate orthogon
al polynomials more accurately near the endpoints of the integration inter
val. An associated family of orthogonal polynomials is evaluated at interi
or points to determine the values of the original polynomials near endpoin
ts. The new method can achieve round-off error accuracy even for end-point
evaluation of generic high-degree Jacobi polynomials and generalized Lagu
erre polynomials. More accurate quadrature abscissas and weights can be ac
hieved accordingly.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART;VALUE=DATE-TIME:20200826T231000Z
DTEND;VALUE=DATE-TIME:20200827T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/7
DESCRIPTION:Title: Solving Linear Systems of Equations via Randomized Kaczmarz/Stocha
stic Gradient Descent\nby Stefan Steinerberger (University of Washingt
on) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nThe Ran
domized Kaczmarz method is a classical iterative method to solve linear sy
stems: the solution of a system Ax = b is simply the point of intersection
of several hyperplanes. The Kaczmarz method (also known as the Projection
Onto Convex Sets Method) proceeds by simply starting with a point and the
n iteratively projecting it on these hyperplanes. If the hyperplanes (=row
s of the matrix) are picked in random order\, the algorithm was analyzed b
y Strohmer & Vershynin and has linear convergence. We show that the method
\, as a byproduct\, also computes small singular vectors and\, in fact\, t
he iterates tend to approach the true solution from the direction of the s
mallest singular vector in a meta-stable way. This also explains why the a
lgorithm has such wonderful regularization properties. The arguments are a
ll fairly self-contained\, elementary and nicely geometric. This gives a p
retty clear picture – the question is: can this picture be used to impro
ve the method?\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Ma (Stanford University)
DTSTART;VALUE=DATE-TIME:20200902T231000Z
DTEND;VALUE=DATE-TIME:20200903T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/8
DESCRIPTION:Title: The Slow Deterioration of the Generalization Error of the Random F
eature Model\nby Chao Ma (Stanford University) as part of Berkeley app
lied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weile Jia (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200909T231000Z
DTEND;VALUE=DATE-TIME:20200910T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/9
DESCRIPTION:Title: HPC+AI: pushing ab initio MD to 100 million atoms on the Summit su
percomputer\nby Weile Jia (UC Berkeley) as part of Berkeley applied ma
thematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Townsend (Cornell University)
DTSTART;VALUE=DATE-TIME:20200916T231000Z
DTEND;VALUE=DATE-TIME:20200917T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/10
DESCRIPTION:Title: The ultraspherical spectral method\nby Alex Townsend (Cornell
University) as part of Berkeley applied mathematics seminar\n\n\nAbstract
\nPseudospectral methods\, based on high degree polynomials\, have spectra
l accuracy when solving differential equations but typically lead to dense
and ill-conditioned matrices. The ultraspherical spectral method is a num
erical technique to solve ordinary and partial differential equations\, le
ading to almost banded well-conditioned linear systems while maintaining s
pectral accuracy. In this talk\, we introduce the ultraspherical spectral
method and develop it into a spectral element method using a modification
to a hierarchical Poincare-Steklov domain decomposition method.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martina Bukac (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20200923T231000Z
DTEND;VALUE=DATE-TIME:20200924T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/11
DESCRIPTION:Title: A computational framework for fluid-structure interaction problem
s\nby Martina Bukac (University of Notre Dame) as part of Berkeley app
lied mathematics seminar\n\n\nAbstract\nFluid-structure interaction (FSI)
problems arise in many applications\, such as aerodynamics\, geomechanics
and hemodynamics. They are moving domain\, multiphysics problems character
ized by nonlinear coupling between a fluid and structure. As a result\, FS
I problems are challenging to numerically solve and analyze. A popular app
roach is to solve the fluid and structure sub-problems in a partitioned ma
nner\, allowing the use of solvers specifically designed for the physics o
f each subproblem. However\, stability issues often arise as a result of F
SI coupling unless the design and implementation of a partitioned scheme i
s carefully developed. We will present a family of partitioned numerical s
chemes for the interaction between an incompressible\, viscous fluid and a
n elastic structure. We will consider cases where the structure is thick\,
i.e.\, described using the same number of spatial dimensions as the fluid
\, and when the structure is thin\, i.e.\, described using a lower-dimensi
onal model. We will present stability and convergence results\, as well as
numerical examples where the presented methods are compared to other meth
ods in the literature.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Childs (University of Maryland)
DTSTART;VALUE=DATE-TIME:20200930T231000Z
DTEND;VALUE=DATE-TIME:20201001T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/12
DESCRIPTION:Title: Symmetries\, graph properties\, and quantum speedups\nby Andr
ew Childs (University of Maryland) as part of Berkeley applied mathematics
seminar\n\n\nAbstract\nAaronson and Ambainis (2009) and Chailloux (2018)
showed that fully symmetric (partial) functions do not admit exponential q
uantum query speedups. This raises a natural question: how symmetric must
a function be before it cannot exhibit a large quantum speedup?\n\nIn this
work\, we prove that hypergraph symmetries in the adjacency matrix model
allow at most a polynomial separation between randomized and quantum query
complexities. We also show that\, remarkably\, permutation groups constru
cted out of these symmetries are essentially the only permutation groups t
hat prevent super-polynomial quantum speedups. We prove this by fully char
acterizing the primitive permutation groups that allow super-polynomial qu
antum speedups.\n\nIn contrast\, in the adjacency list model for bounded-d
egree graphs (where graph symmetry is manifested differently)\, we exhibit
a property testing problem that shows an exponential quantum speedup. The
se results resolve open questions posed by Ambainis\, Childs\, and Liu (20
10) and Montanaro and de Wolf (2013).\n\nThis is joint work with Shalev Be
n-David\, András Gilyén\, William Kretschmer\, Supartha Podder\, and Dao
chen Wang. https://arxiv.org/abs/2006.12760\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franziska Weber (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20201014T231000Z
DTEND;VALUE=DATE-TIME:20201015T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/13
DESCRIPTION:Title: Numerical approximation of statistical solutions of hyperbolic sy
stems of conservation laws\nby Franziska Weber (Carnegie Mellon Univer
sity) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nStati
stical solutions are time-parameterized probability measures on spaces of
integrable functions\, which have been proposed recently as a framework fo
r global solutions for multi-dimensional hyperbolic systems of conservatio
n laws. We develop a numerical algorithm to approximate statistical soluti
ons of conservation laws and show that under the assumption of ‘weak sta
tistical scaling’\, which is inspired by Kolmogorov’s 1941 turbulence
theory\, the approximations converge in an appropriate topology to statist
ical solutions. Numerical experiments confirm that the assumption might ho
ld true.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rolando Somma (Los Alamos National Laboratory)
DTSTART;VALUE=DATE-TIME:20201021T231000Z
DTEND;VALUE=DATE-TIME:20201022T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/14
DESCRIPTION:Title: Quantum linear systems problem: solution and verification\nby
Rolando Somma (Los Alamos National Laboratory) as part of Berkeley applie
d mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dong An (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20201028T231000Z
DTEND;VALUE=DATE-TIME:20201029T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/15
DESCRIPTION:Title: Quantum adiabatic evolution and applications in computational phy
sics and quantum computing\nby Dong An (UC Berkeley) as part of Berkel
ey applied mathematics seminar\n\n\nAbstract\nOriginally discovered by Bor
n and Fock (1928)\, a quantum mechanical system almost remains in its inst
antaneous eigenstates if the Hamiltonian varies sufficiently slowly and th
ere is a gap between the eigenvalue and the rest of the Hamiltonian’s sp
ectrum. Such a system is said to be a quantum adiabatic evolution\, and ha
s become a powerful tool for analyzing quantum dynamics and designing fast
classical and quantum algorithms. In this talk\, I will first discuss the
mathematical formulation of quantum adiabatic evolutions\, namely quantum
adiabatic theorem. Several versions of the theorem will be discussed\, wi
th a focus on the factors that might significantly influence the adiabatic
ity. Then I will present two applications of the adiabatic evolutions and
adiabatic theorems. One is accelerating numerical simulation of Schrodinge
r equations on classical computers\, and the other is a quantum algorithm
for solving linear system of equations with near optimal complexity on a q
uantum computer.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaochuan Tian (UCSD)
DTSTART;VALUE=DATE-TIME:20201105T001000Z
DTEND;VALUE=DATE-TIME:20201105T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/16
DESCRIPTION:Title: Reproducing kernel collocation methods for nonlocal models: asymp
totic compatibility and numerical stability\nby Xiaochuan Tian (UCSD)
as part of Berkeley applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiequn Han (Princeton University)
DTSTART;VALUE=DATE-TIME:20201112T001000Z
DTEND;VALUE=DATE-TIME:20201112T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/17
DESCRIPTION:Title: Solving High-Dimensional PDEs\, Controls\, and Games with Deep Le
arning\nby Jiequn Han (Princeton University) as part of Berkeley appli
ed mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Webber (Courant Institute)
DTSTART;VALUE=DATE-TIME:20201203T001000Z
DTEND;VALUE=DATE-TIME:20201203T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/18
DESCRIPTION:Title: Monte Carlo methods for the Hermitian eigenvalue problem\nby
Robert Webber (Courant Institute) as part of Berkeley applied mathematics
seminar\n\n\nAbstract\nIn quantum mechanics and the analysis of Markov pro
cesses\, Monte Carlo methods are needed to identify low-lying eigenfunctio
ns of dynamical generators. The standard Monte Carlo approaches for identi
fying eigenfunctions\, however\, can be inaccurate or slow to converge. Wh
at limits the efficiency of the currently available spectral estimation me
thods\, and what is needed to build more efficient methods for the future?
Through numerical analysis and computational examples\, we begin to answe
r these questions. We present the first-ever convergence proof and error b
ounds for the variational approach to conformational dynamics (VAC)\, the
dominant method for estimating eigenfunctions used in biochemistry. Additi
onally\, we analyze and optimize variational Monte Carlo (VMC)\, which com
bines Monte Carlo with neural networks to accurately identify low-lying ei
genstates of quantum systems.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aditi Krishnapriyan (Lawrence Berkeley National Lab)
DTSTART;VALUE=DATE-TIME:20201007T231000Z
DTEND;VALUE=DATE-TIME:20201008T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/19
DESCRIPTION:Title: Persistent Homology Advances Interpretable Machine Learning for S
cientific Applications\nby Aditi Krishnapriyan (Lawrence Berkeley Nati
onal Lab) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nM
achine learning for scientific applications\, ranging from physics and mat
erials science to biology\, has emerged as a promising alternative to more
time-consuming experiments and simulations. The challenge with this appro
ach is the selection of features that enable universal and interpretable s
ystem representations across multiple prediction tasks. We use persistent
homology to construct holistic feature representations to describe the str
ucture of scientific systems\; for example\, material and protein structur
es. We show that these representations can also be augmented with other ge
neric features to capture further information. We demonstrate our approach
es on multiple scientific datasets by predicting a variety of different ta
rgets across different conditions. Our results show considerable improveme
nt in both accuracy and transferability across targets compared to models
constructed from commonly used manually curated features. A key advantage
of our approach is interpretability. For example\, in material structures\
, our persistent homology features allow us to identify the location and s
ize of pores in the structure that correlate best to different materials p
roperties\, contributing to understanding atomic level structure-property
relationships for materials design.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Stokes (Flatiron Institute)
DTSTART;VALUE=DATE-TIME:20201119T001000Z
DTEND;VALUE=DATE-TIME:20201119T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/20
DESCRIPTION:Title: First-quantized neural networks for lattice fermions\nby Jame
s Stokes (Flatiron Institute) as part of Berkeley applied mathematics semi
nar\n\n\nAbstract\nFirst-quantized deep neural network techniques are deve
loped for analyzing strongly coupled fermionic systems on the lattice. Usi
ng a Slater-Jastrow inspired ansatz which exploits deep residual networks
with convolutional residual blocks\, we approximately determine the ground
state of spinless fermions on a square lattice with nearest-neighbor inte
ractions. The flexibility of the neural-network ansatz results in a high l
evel of accuracy when compared to exact diagonalization results on small s
ystems\, both for energy and correlation functions. On large systems\, we
obtain accurate estimates of the boundaries between metallic and charge or
dered phases as a function of the interaction strength and the particle de
nsity.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongbin Xiu (The Ohio State University)
DTSTART;VALUE=DATE-TIME:20210211T001000Z
DTEND;VALUE=DATE-TIME:20210211T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/21
DESCRIPTION:by Dongbin Xiu (The Ohio State University) as part of Berkeley
applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seung-Yeal Ha (Seoul National University)
DTSTART;VALUE=DATE-TIME:20210428T231000Z
DTEND;VALUE=DATE-TIME:20210429T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/23
DESCRIPTION:Title: Emergent behaviors of Lohe tensor flocks\nby Seung-Yeal Ha (S
eoul National University) as part of Berkeley applied mathematics seminar\
n\n\nAbstract\nIn this talk\, we present a new aggregation model on the sp
ace of rank-m tensors with the same size\, and study emergent dynamics of
the proposed model. Our proposed aggregation model is general enough to in
clude Lohe type synchronization models such as the Kuramoto model\, the Lo
he sphere model and the Lohe matrix models for the ensemble of real rank-0
\, rank-1 and rank-2 tensors\, respectively. In this regard\, we call our
proposed model as the Lohe tensor model for rank-m tensors with the same s
ize. For the proposed model\, we present several sufficient frameworks lea
ding to the collective dynamics of the Lohe tensor model in terms of syste
m parameters and initial data\, and study existence of special solutions s
uch as completely separable solutions and quadratically separable solution
s. This is a joint work with Hansol Park (Seoul National Univ.) and Dohyu
n Kim (Sungshin Women’s Univ.)\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianfeng Lu (Duke University)
DTSTART;VALUE=DATE-TIME:20210204T001000Z
DTEND;VALUE=DATE-TIME:20210204T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/24
DESCRIPTION:Title: Towards solving high dimensional PDEs using neural networks\n
by Jianfeng Lu (Duke University) as part of Berkeley applied mathematics s
eminar\n\n\nAbstract\nNumerical solution to high dimensional PDEs has been
one of the central challenges in scientific computing due to curse of dim
ension. In recent years\, we have seen tremendous progress in applying neu
ral networks to solve high dimensional PDEs\, while the analysis for such
methods is still lacking. In this talk\, we will discuss some of these num
erical methods for high dimensional PDEs and also some initial attempts in
numerical analysis for high dimensional PDEs.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doron Levy (University of Maryland)
DTSTART;VALUE=DATE-TIME:20210304T001000Z
DTEND;VALUE=DATE-TIME:20210304T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/25
DESCRIPTION:Title: Fighting drug resistance with math\nby Doron Levy (University
of Maryland) as part of Berkeley applied mathematics seminar\n\n\nAbstrac
t\nThe emergence of drug-resistance is a major challenge in chemotherapy.
In this talk we will overview some of our recent mathematical models for d
escribing the dynamics of drug-resistance in solid tumors. These models fo
llow the dynamics of the tumor\, assuming that the cancer cell population
depends on a phenotype variable that corresponds to the resistance level t
o a cytotoxic drug. Under certain conditions\, our models predict that mu
ltiple resistant traits emerge at different locations within the tumor\, c
orresponding to heterogeneous tumors. We show that a higher drug dosage ma
y delay a relapse\, yet\, when this happens\, a more resistant trait emerg
es. We will show how mathematics can be used to propose an efficient drug
schedule aiming at minimizing the growth rate of the most resistant trait\
, and how such resistant cells can be eliminated.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruiwen Shu (University of Maryland\, College Park)
DTSTART;VALUE=DATE-TIME:20210128T001000Z
DTEND;VALUE=DATE-TIME:20210128T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/26
DESCRIPTION:Title: Linear interpolation convexity/concavity in the minimization of a
ttractive-repulsive energy\nby Ruiwen Shu (University of Maryland\, Co
llege Park) as part of Berkeley applied mathematics seminar\n\n\nAbstract\
nEnergy minimization problems of attractive-repulsive pairwise interaction
s are very important in the study of pattern formation in biological and s
ocial sciences. In this talk\, I will discuss some recent progress (joint
work with Jose Carrillo) on the study of Wasserstein-$\\infty$ local energ
y minimizers by using the method of linear interpolation convexity/concavi
ty. In the first part\, we prove the radial symmetry and uniqueness of loc
al minimizers for interaction potentials satisfying the 'linear interpolat
ion convexity'\, which generalizes the result of O. Lopes 17' for global m
inimizers. In the second part\, we show that the failure of linear interpo
lation convexity could lead to the formation of small scales in the suppor
t of local minimizers\, and construct interaction potentials whose local m
inimizers are supported on fractal sets. To our best knowledge\, this is t
he first time people observe fractal sets as the support of local minimize
rs.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mitchell Luskin (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20210331T231000Z
DTEND;VALUE=DATE-TIME:20210401T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/27
DESCRIPTION:Title: Mathematics and Physics at the Moiré Scale\nby Mitchell Lusk
in (University of Minnesota) as part of Berkeley applied mathematics semin
ar\n\n\nAbstract\nPlacing a two-dimensional lattice on another with a smal
l rotation gives rise to periodic “moire” patterns on a superlattice s
cale much larger than the original lattice. This effective large-scale fun
damental domain allows phenomena such as the fractal Hofstadter butterfly
in the spectrum of Harper’s equation to be observed in real crystals. Ex
perimentalists have more recently observed new correlated phases at the
“magic” twist angles predicted by theorists. \n\nWe will give mathemat
ical and computational models to predict and gain insight into new physica
l phenomena at the moiré scale including our recent mathematical and expe
rimental results for twisted trilayer graphene.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Horning (Cornell University)
DTSTART;VALUE=DATE-TIME:20210121T001000Z
DTEND;VALUE=DATE-TIME:20210121T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/28
DESCRIPTION:Title: Computing spectral properties of infinite-dimensional operators\nby Andrew Horning (Cornell University) as part of Berkeley applied mat
hematics seminar\n\n\nAbstract\nComputing the spectrum of a differential o
r integral operator is usually done in two steps: (1) discretize the opera
tor to obtain a matrix eigenvalue problem and (2) compute eigenvalues of t
he matrix with numerical linear algebra. This “discretize-then-solve”
paradigm is flexible and powerful\, but tension between spectral propertie
s of the operator and the matrix discretizations can lead to numerical art
ifacts that pollute computed spectra and degrade accuracy. Moreover\, it i
s unclear how to robustly capture infinite-dimensional phenomena\, like co
ntinuous spectra\, with “discretize-then-solve.” In this talk\, we int
roduce a new computational framework that extracts discrete and continuous
spectral properties of a broad class of operators by strategically sampli
ng the resolvent operator in the complex plane. The resulting algorithms r
espect key structure from the operator\, regardless of the underlying matr
ix discretizations used for computation. We illustrate the approach throug
h a range of examples\, including a Dirac operator and a magnetic tight-bi
nding model of graphene.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhewei Yao (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20210218T001000Z
DTEND;VALUE=DATE-TIME:20210218T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/29
DESCRIPTION:Title: Second Order Methods for Neural Network Analysis\, Training\, and
Inference\nby Zhewei Yao (University of California\, Berkeley) as par
t of Berkeley applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenning Cai (National University of Singapore)
DTSTART;VALUE=DATE-TIME:20210225T001000Z
DTEND;VALUE=DATE-TIME:20210225T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/30
DESCRIPTION:Title: On the method of complex Langevin\nby Zhenning Cai (National
University of Singapore) as part of Berkeley applied mathematics seminar\n
\n\nAbstract\nThe complex Langevin (CL) method is a numerical approach to
alleviate the numerical sign problem in the computation of path integrals
in lattice field theories. Mathematically\, it is a simple numerical tool
to compute a wide class of high-dimensional and oscillatory integrals with
the form of an ensemble average. The method was developed in 1980s. Howev
er\, after it was proposed\, it had very few applications due to its subtl
e nature. It is often observed that the CL method converges but the limiti
ng result is incorrect. Less than one decade ago\, the CL method was impro
ved by gauge cooling method and dynamical stabilization\, after which the
CL method acquired much more attention and was later successfully applied
to a number of fields including finite density quantum chromodynamics\, su
perstring theory\, and the spin-orbit coupling. In this talk\, I will take
the mathematical perspective to explain the basic idea of the CL method a
nd the reason of its failure. The current limitation of the method and the
possible remedies will also be discussed.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Casas (Universitat Jaume I\, Spain)
DTSTART;VALUE=DATE-TIME:20210311T001000Z
DTEND;VALUE=DATE-TIME:20210311T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/31
DESCRIPTION:Title: Symmetric-conjugate composition methods in the numerical integrat
ion of differential equations\nby Fernando Casas (Universitat Jaume I\
, Spain) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nIn
this talk I will analyze composition methods with complex coefficients ex
hibiting the so-called “symmetry-conjugate” pattern in their distribut
ion. In particular\, I will study their behavior with respect to preservat
ion of qualitative properties when projected on the real axis and how they
compare with the usual left-right palindromic compositions. New schemes w
ithin this family up to order 8 will be proposed and illustrated on severa
l examples. Some of the special features of this class of methods will als
o be reviewed.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuan Su (Caltech)
DTSTART;VALUE=DATE-TIME:20210319T171000Z
DTEND;VALUE=DATE-TIME:20210319T180000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/32
DESCRIPTION:Title: Nearly tight Trotterization of interacting electrons\nby Yuan
Su (Caltech) as part of Berkeley applied mathematics seminar\n\n\nAbstrac
t\nWe consider simulating quantum systems on digital quantum computers. We
show that the performance of quantum simulation can be improved by simult
aneously exploiting the commutativity of Hamiltonian\, the sparsity of int
eractions\, and the prior knowledge of initial state. We achieve this usin
g Trotterization for a class of interacting electrons that encompasses var
ious physical systems\, including the plane-wave-basis electronic structur
e and the Fermi-Hubbard model. We estimate the simulation error by taking
the transition amplitude of nested commutators of Hamiltonian terms within
the $\\eta$-electron manifold. We develop multiple techniques for boundin
g the transition amplitude and expectation of general fermionic operators\
, which may be of independent interest. We show that it suffices to use $\
\left(\\frac{n^{5/3}}{\\eta^{2/3}}+n^{4/3}\\eta^{2/3}\\right)n^{o(1)}$ gat
es to simulate electronic structure in the plane-wave basis with $n$ spin
orbitals and $\\eta$ electrons\, improving the best previous result in sec
ond quantization while outperforming the first-quantized simulation when $
n=\\eta^{2-o(1)}$. We also obtain an improvement for simulating the Fermi-
Hubbard model. We construct concrete examples for which our bounds are alm
ost saturated\, giving a nearly tight Trotterization of interacting electr
ons.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jimmy Xia (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20210407T231000Z
DTEND;VALUE=DATE-TIME:20210408T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/33
DESCRIPTION:Title: Mathematical modeling of human learning and decision making\n
by Jimmy Xia (University of California\, Berkeley) as part of Berkeley app
lied mathematics seminar\n\n\nAbstract\nReinforcement learning (RL) has be
en widely used to study and model human\, animal and artificial intelligen
ce. In this talk\, we focus on modeling human learning and decision making
\, and exemplify two ways that mathematical RL modeling adds to our existi
ng knowledge of human cognition: (1) as a powerful quantitative tool for p
arametrizing and compressing individual differences in human behavior\, an
d (2) as an important theoretical framework for complex human cognition. I
n the first study\, we use RL modeling to capture trial-by-trial learning
dynamics in a probabilistic task and to understand how learning changes du
ring puberty. In the second study\, we augment existing RL models to expla
in transfer and generalization effects in multi-step learning and decision
making tasks.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhennan Zhou (Peking University)
DTSTART;VALUE=DATE-TIME:20210414T231000Z
DTEND;VALUE=DATE-TIME:20210415T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/34
DESCRIPTION:Title: Efficient Sampling of Thermal Averages of Interacting Quantum Par
ticle Systems: preconditioning and simulation with random batches\nby
Zhennan Zhou (Peking University) as part of Berkeley applied mathematics s
eminar\n\n\nAbstract\nWe investigate the continuum limit that the number o
f beads goes to infinity in the ring polymer representation of thermal ave
rages. Studying the continuum limit of the trajectory sampling equation sh
eds light on possible preconditioning techniques for sampling ring polymer
configurations with large number of beads. In the case where the potentia
l is quadratic\, we show that the continuum limit of the preconditioned ma
ss modified Langevin dynamics converges to its equilibrium exponentially f
ast\, which suggests that the finite-dimensional counterpart has a dimensi
on-independent convergence rate. In the second part of the talk\, an effic
ient sampling method\, the pmmLang+RBM\, is proposed to compute the quantu
m thermal average in the interacting quantum particle system. Benefiting f
rom the random batch method (RBM)\, the pmmLang+RBM reduces the complexity
due to the interaction forces per timestep from O(NP^2) to O(NP)\, where
N is the number of beads and P is the number of particles. We also propose
an extension of the pmmLang+RBM\, which is based on the splitting Monte C
arlo method and is applicable when the interacting potential contains a si
ngular part.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phillip Colella (Lawrence Berkeley National Laboratory and UC Berk
eley)
DTSTART;VALUE=DATE-TIME:20210421T231000Z
DTEND;VALUE=DATE-TIME:20210422T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/35
DESCRIPTION:Title: Numerical Analysis of Particle-in-Cell Methods for Advection-Type
Partial Differential Equations\nby Phillip Colella (Lawrence Berkeley
National Laboratory and UC Berkeley) as part of Berkeley applied mathemat
ics seminar\n\n\nAbstract\nParticle-in-cell (PIC) methods for advection eq
uations use particles that move along integral curves of the advection vel
ocity to represent the primary dependent variables\, while using a structu
red grid to which the particle state has been interpolated to compute the
dependence of the velocities\, and forcing terms on the solution. PIC is
one of the oldest methods in numerical PDE\, dating back to the 1950s for
fluid dynamics\, and the 1960s for plasma physics\, and are still used ext
ensively today. Nonetheless\, there appears to be no mathematically-system
atic numerical analysis framework for understanding the error in PIC metho
ds. This is in contrast to traditional finite-difference\, finite element\
, and grid-free particle methods\, for which such framework exist and are
used very successfully to design methods for complex problems. In this tal
k\, we will present such a numerical analysis framework for both advection
and for kinetics problems. One of the principal results is that PIC metho
ds\, as they are currently used in scientific applications\, have an O(1)
contribution to the error\, relative to the number of particles\, that gro
ws exponentially in time. We will describe the source of this error\, and
strategies for controlling it.\n\nJoint work with Henry Boateng\, Bhavna S
ingh\, Erick Velez\, and Colin Wahl.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Hou (Caltech)
DTSTART;VALUE=DATE-TIME:20210901T231000Z
DTEND;VALUE=DATE-TIME:20210902T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/36
DESCRIPTION:Title: Potential singularity of 3D incompressible Euler equations and th
e nearly singular behavior of 3D Navier-Stokes equations\nby Thomas Ho
u (Caltech) as part of Berkeley applied mathematics seminar\n\n\nAbstract\
nWhether the 3D incompressible Euler and Navier-Stokes equations can devel
op a finite time singularity from smooth initial data is one of the most c
hallenging problems in nonlinear PDEs. In an effort to provide a rigorous
proof of the potential Euler singularity revealed by Luo-Hou's computation
\, we develop a novel method of analysis and prove that the original De Gr
egorio model and the Hou-Lou model develop a finite time singularity from
smooth initial data. Using this framework and some techniques from Elgindi
's recent work on the Euler singularity\, we prove the finite time blowup
of the 2D Boussinesq and 3D Euler equations with $C^{1\,\\alpha}$ initial
velocity and boundary. Further\, we present some new numerical evidence th
at the 3D incompressible Euler equations with smooth initial data develop
a potential finite time singularity at the origin\, which is quite differe
nt from the Luo-Hou scenario. Our study also shows that the 3D Navier-Stok
es equations develop nearly singular solutions with maximum vorticity incr
easing by a factor of $10^7$. However\, the viscous effect eventually domi
nates vortex stretching and the 3D Navier-Stokes equations narrowly escape
finite time blowup. Finally\, we present strong numerical evidence that t
he 3D Navier-Stokes equations with slowly decaying viscosity develop a fin
ite time singularity.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Kuan (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20210908T231000Z
DTEND;VALUE=DATE-TIME:20210909T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/37
DESCRIPTION:Title: A stochastic fluid-structure interaction problem describing Stoke
s flow interacting with a membrane\nby Jeffrey Kuan (UC Berkeley) as p
art of Berkeley applied mathematics seminar\n\n\nAbstract\nIn this talk\,
we present a well-posedness result for a stochastic fluid-structure intera
ction model. We study a fully coupled stochastic fluid-structure interacti
on problem\, with linear coupling between Stokes flow and an elastic struc
ture modeled by the wave equation\, and stochastic noise in time acting on
the structure. Such stochasticity is of interest in applications of fluid
-structure interaction\, in which there is random noise present which may
affect the dynamics and statistics of the full system. We construct a solu
tion by using a new splitting method for stochastic fluid-structure intera
ction\, and probabilistic methods. To the best of our knowledge\, this is
the first result on well-posedness for fully coupled stochastic fluid-stru
cture interaction. This is joint work with Sunčica Čanić (UC Berkeley).
\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Komarova (UC Irvine)
DTSTART;VALUE=DATE-TIME:20210915T231000Z
DTEND;VALUE=DATE-TIME:20210916T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/38
DESCRIPTION:Title: Mathematical methods in cancer dynamics\nby Natalia Komarova
(UC Irvine) as part of Berkeley applied mathematics seminar\n\n\nAbstract\
nEvolutionary dynamics are at the core of carcinogenesis. Mathematical met
hods can be used to study evolutionary processes\, such as selection and m
utation\, and to shed light onto cancer origins\, progression\, and mechan
isms of treatment. I will present two broad approaches to cancer modeling
that we have developed. One is concerned with near-equilibrium dynamics of
stem cells\, with the goal of figuring out how tissue cell turnover is or
chestrated\, and how control networks prevent “selfish” cell growth. T
he other direction is studying evolutionary dynamics of drug resistance in
cancer.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lindsey (Courant Institute)
DTSTART;VALUE=DATE-TIME:20210922T231000Z
DTEND;VALUE=DATE-TIME:20210923T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/39
DESCRIPTION:Title: Embedding approaches for classical and quantum statistical mechan
ics\nby Michael Lindsey (Courant Institute) as part of Berkeley applie
d mathematics seminar\n\n\nAbstract\nWe show how a synthesis of ideas from
graphical models\, tensor networks\, optimal transport\, and semidefinite
programming can be brought to bear on problems from classical and quantum
statistical mechanics\, broadly construed. Specifically\, we discuss appl
ications including classical and quantum spin systems on the lattice\, con
tinuous global optimization\, and electronic structure.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Becker (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20210929T231000Z
DTEND;VALUE=DATE-TIME:20210930T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/40
DESCRIPTION:Title: Mathematical properties of twisted bilayer graphene\nby Simon
Becker (University of Cambridge) as part of Berkeley applied mathematics
seminar\n\n\nAbstract\nTwistronics is the study of how the angle (the twis
t) between layers of two-dimensional materials can change their electronic
structure. When two sheets of graphene are twisted by those angles the re
sulting material exhibits flat bands which\, as argued in the physics lite
rature\, is related to superconductivity\, ferromagnetism\, and Mott-insul
ators. I will start with a very simple operator whose spectral properties
are supposed to determine which angles are magical and describe some of th
e mathematical challenges and results. Then\, I will introduce a method to
study the response of this material to an external magnetic field in a re
gime of large magnetic fields and explain some of the phenomena. Finally\,
I will move on to even simpler one-dimensional models\, that naturally ap
pear when strain is applied in one direction of the van der Waals material
to make it periodic in one spatial direction\, which allow for a more ref
ined mathematical analysis (Cantor spectrum and metal/insulator transition
s). If time permits\, I will briefly touch upon the connection between suc
h materials and topological insulators.\n\nThis is joint work with M Embre
e\, R Kim\, J Wittsten\, X Zhu\, M Zworski.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuel Gull (University of Michigan)
DTSTART;VALUE=DATE-TIME:20211020T231000Z
DTEND;VALUE=DATE-TIME:20211021T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/41
DESCRIPTION:Title: Nevanlinna Analytical Continuation\nby Emanuel Gull (Universi
ty of Michigan) as part of Berkeley applied mathematics seminar\n\n\nAbstr
act\nSimulations of finite temperature quantum systems provide imaginary f
requency Green’s functions that correspond one-to-one to experimentally
measurable real-frequency spectra. However\, due to the bad conditioning o
f the continuation transform from imaginary to real frequencies\, establis
hed methods tend to either wash out spectral features at high frequencies
or produce spectral functions with unphysical negative parts. Here\, we sh
ow that explicitly respecting the analytic ‘Nevanlinna' structure of the
Green’s function leads to intrinsically positive and normalized spectra
l functions and we present a continued fraction expansion that yields all
possible functions consistent with the analytic structure. Application to
synthetic trial data shows that sharp\, smooth\, and multi-peak data is re
solved accurately. Application to the band structure of silicon demonstrat
es that high energy features are resolved precisely. Continuations in a re
alistic correlated setup reveal additional features that were previously u
nresolved. By substantially increasing the resolution of the real frequenc
y calculations\, our work overcomes one of the main limitations of finite-
temperature quantum simulations.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Song Mei (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20211027T181000Z
DTEND;VALUE=DATE-TIME:20211027T190000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/42
DESCRIPTION:Title: The efficiency of kernel methods on structured datasets\nby S
ong Mei (UC Berkeley) as part of Berkeley applied mathematics seminar\n\n\
nAbstract\nInspired by the proposal of tangent kernels of neural networks
(NNs)\, a recent research line aims to design kernels with a better genera
lization performance on standard datasets. Indeed\, a few recent works sho
wed that certain kernel machines perform as well as NNs on certain dataset
s\, despite their separations in specific cases implied by theoretical res
ults. Furthermore\, it was shown that the induced kernels of convolutional
neural networks perform much better than any former handcrafted kernels.
These empirical results pose a theoretical challenge to understanding the
performance gaps in kernel machines and NNs in different scenarios.\n\nIn
this talk\, we show that data structures play an essential role in inducin
g these performance gaps. We consider a few natural data structures\, and
study their effects on the performance of these learning methods. Based on
a fine-grained high dimensional asymptotics framework of analyzing random
features models and kernel machines\, we show the following: 1) If the fe
ature vectors are nearly isotropic\, kernel methods suffer from the curse
of dimensionality\, while NNs can overcome it by learning the best low-dim
ensional representation\; 2) If the feature vectors display the same low-d
imensional structure as the target function (the spiked covariates model)\
, this curse of dimensionality becomes milder\, and the performance gap be
tween kernel methods and NNs become smaller\; 3) On datasets that display
some invariance structure (e.g.\, image dataset)\, there is a quantitative
performance gain of using invariant kernels (e.g.\, convolutional kernels
) over inner product kernels. Beyond explaining the performance gaps\, the
se theoretical results can further provide some intuitions towards designi
ng kernel methods with better performance.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Kaye (Flatiron institute)
DTSTART;VALUE=DATE-TIME:20211111T001000Z
DTEND;VALUE=DATE-TIME:20211111T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/43
DESCRIPTION:Title: Efficient numerical algorithms for simulating quantum dynamics\nby Jason Kaye (Flatiron institute) as part of Berkeley applied mathemat
ics seminar\n\n\nAbstract\nI will describe a few new algorithms which redu
ce computational bottlenecks in simulations of quantum many-body dynamics.
\n\nIn time-dependent density functional theory (TDDFT)\, the many-body wa
vefunction is approximated using a collection of single-particle wavefunct
ions\, which independently satisfy the Schrodinger equation and are couple
d through an effective potential. I will introduce a high-order\, FFT-base
d solver for free space (nonperiodic) problems in TDDFT which sidesteps th
e usual requirement of imposing artificial boundary conditions.\n\nMany-bo
dy Green's functions\, which describe correlations between quantum observa
bles\, enable practical simulations beyond the effective one-body picture
of TDDFT. The Green's functions satisfy history dependent Volterra integro
-differential equations with kernel nonlinearities. I will outline efficie
nt history integration algorithms which significantly extend feasible prop
agation times in both equilibrium and nonequilibrium calculations.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Chorin (UC Berkeley and LBNL)
DTSTART;VALUE=DATE-TIME:20211209T001000Z
DTEND;VALUE=DATE-TIME:20211209T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/44
DESCRIPTION:by Alexandre Chorin (UC Berkeley and LBNL) as part of Berkeley
applied mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yu Tong (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20211103T231000Z
DTEND;VALUE=DATE-TIME:20211104T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/45
DESCRIPTION:Title: Quantum eigenstate filtering and its applications\nby Yu Tong
(UC Berkeley) as part of Berkeley applied mathematics seminar\n\n\nAbstra
ct\nIn this talk I will introduce a quantum algorithmic technique called q
uantum eigenstate filtering\, which is based on approximation theory resul
ts and the quantum singular value transformation. I will discuss its appli
cations in preparing eigenstates\, solving quantum linear systems\, and es
timating the ground state energy. For these tasks this technique leads to
significantly better query complexities\, fewer ancilla qubits\, and does
so without requiring complex subroutines that may not be realistically imp
lementable. Besides these algorithmic applications\, the essential idea al
so leads to a useful proof technique for studying the ground state propert
y of quantum many-body systems.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Di Fang (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20211006T231000Z
DTEND;VALUE=DATE-TIME:20211007T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/46
DESCRIPTION:Title: Time-dependent unbounded Hamiltonian simulation with vector norm
scaling\nby Di Fang (UC Berkeley) as part of Berkeley applied mathemat
ics seminar\n\n\nAbstract\nHamiltonian simulation is a basic task in quant
um computation. The accuracy of such simulation is usually measured by the
error of the unitary evolution operator in the operator norm\, which in t
urn depends on certain norm of the Hamiltonian. For unbounded operators\,
after suitable discretization\, the norm of the Hamiltonian can be very la
rge\, which significantly increases the simulation cost. However\, the ope
rator norm measures the worst-case error of the quantum simulation\, while
practical simulation concerns the error with respect to a given initial v
ector at hand. We demonstrate that under suitable assumptions of the Hamil
tonian and the initial vector\, if the error is measured in terms of the v
ector norm\, the computational cost may not increase at all as the norm of
the Hamiltonian increases using Trotter type methods. In this sense\, our
result outperforms all previous error bounds in the quantum simulation li
terature. We also clarify the existence and the importance of commutator s
calings of Trotter and generalized Trotter methods for time-dependent Hami
ltonian simulations.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franziska Weber (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20211013T231000Z
DTEND;VALUE=DATE-TIME:20211014T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/47
DESCRIPTION:Title: A Convergent Numerical Method for a Model of Liquid Crystal Direc
tor Coupled to An Electric Field\nby Franziska Weber (Carnegie Mellon
University) as part of Berkeley applied mathematics seminar\n\n\nAbstract\
nStarting from the Oseen-Frank theory\, we derive a simple model for the d
ynamics of a nematic liquid crystal director field under the influence of
an electric field. The resulting nonlinear system of partial differential
equations consists of the electrostatics equations for the electric field
coupled with the damped wave map equation for the evolution of the liquid
crystal director field\, which is a normal vector pointing in the directio
n of the main orientation of the liquid crystal molecules. The liquid crys
tal director field enters the electrostatics equations in the constitutive
relations while the electric field enters the wave map equation in the fo
rm of a nonlinear source term. Since it is a normal vector\, the variable
for the liquid crystal director field has to satisfy the constraint that i
t takes values in the unit sphere. We derive an energy-stable and constrai
nt preserving numerical method for this system and prove convergence of a
subsequence of approximations to a weak solution of the system of partial
differential equations. In particular\, this implies the existence of weak
solutions for this model.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aditi Krishnapriyan (Lawrence Berkeley National Lab)
DTSTART;VALUE=DATE-TIME:20211202T001000Z
DTEND;VALUE=DATE-TIME:20211202T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/48
DESCRIPTION:Title: Integrating machine learning with physics-based spatial and tempo
ral modeling\nby Aditi Krishnapriyan (Lawrence Berkeley National Lab)
as part of Berkeley applied mathematics seminar\n\n\nAbstract\nDeep learni
ng has achieved great success in numerous areas\, and is also seeing incre
asing interest in scientific applications. However\, challenges still rema
in: scientific phenomena are difficult to model\, and can also be limited
by a lack of training data. As a result\, scientific machine learning appr
oaches are being developed by incorporating domain knowledge into the mach
ine learning process to enable more accurate and general predictions. One
such popular approach\, colloquially known as physics-informed neural netw
orks (PINNs)\, incorporates domain knowledge as soft constraints on an emp
irical loss function. I will discuss the challenges associated with such a
n approach\, and show that by changing the learning paradigm to curriculum
regularization or sequence-to-sequence learning\, we can achieve signific
antly lower error. Another approach\, colloquially known as ODE-Nets\, aim
s to couple dynamical systems/numerical methods with neural networks. I wi
ll discuss how exploiting techniques from numerical analysis for these sys
tems can enable learning continuous dynamics for scientific problems. This
method will be illustrated by showing that it can: resolve fine-scale fea
tures in a temporal solution despite training on coarse data\, successfull
y resolve fine-scale features in the temporal solution even when the train
ing data is irregularly spaced with non-uniform time intervals\, and learn
dynamics from image snapshots by generating super-resolution videos at hi
gher frame rates of the much finer solution.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No seminar
DTSTART;VALUE=DATE-TIME:20220127T001000Z
DTEND;VALUE=DATE-TIME:20220127T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/49
DESCRIPTION:by No seminar as part of Berkeley applied mathematics seminar\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Chertock (North Carolina State University)
DTSTART;VALUE=DATE-TIME:20220203T001000Z
DTEND;VALUE=DATE-TIME:20220203T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/50
DESCRIPTION:Title: Structure Preserving Numerical Methods for Hyperbolic Systems of
Conservation and Balance Laws\nby Alina Chertock (North Carolina State
University) as part of Berkeley applied mathematics seminar\n\n\nAbstract
\nMany physical models\, while quite different in nature\, can be describe
d by nonlinear hyperbolic systems of conservation and balance laws. The ma
in source of difficulties one comes across when numerically solving these
systems is lack of smoothness as solutions of hyperbolic conservation/bala
nce laws may develop very complicated nonlinear wave structures including
shocks\, rarefaction waves and contact discontinuities. The level of compl
exity may increase even further when solutions of the hyperbolic system re
veal a multiscale character and/or the system includes additional terms su
ch as friction terms\, geometrical terms\, nonconservative products\, etc.
\, which are needed to be taken into account in order to achieve a proper
description of the studied physical phenomena. In such cases\, it is extre
mely important to design a numerical method that is not only consistent wi
th the given PDEs\, but also preserves certain structural and asymptotic p
roperties of the underlying problem at the discrete level. While a variety
of numerical methods for such models have been successfully developed\, t
here are still many open problems\, for which the derivation of reliable h
igh-resolution numerical methods still remains to be an extremely challeng
ing task.\n\nIn this talk\, I will discuss recent advances in the developm
ent of two classes of structure preserving numerical methods for nonlinear
hyperbolic systems of conservation and balance laws. In particular\, I wi
ll present (i) well-balanced and positivity preserving numerical schemes\,
that is\, the methods which are capable of exactly preserving some steady
-state solutions as well as maintaining the positivity of the numerical qu
antities when it is required by the physical application\, and (ii) asympt
otic preserving schemes\, which provide accurate and efficient numerical s
olutions in certain stiff and/or asymptotic regimes of physical interest.\
n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunan Yang (ETH Zurich)
DTSTART;VALUE=DATE-TIME:20220209T181000Z
DTEND;VALUE=DATE-TIME:20220209T190000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/51
DESCRIPTION:Title: Adjoint DSMC Method for Boltzmann-Constrained Optimization Proble
ms\nby Yunan Yang (ETH Zurich) as part of Berkeley applied mathematics
seminar\n\n\nAbstract\nApplications for kinetic equations such as optimal
design and inverse problems often involve finding unknown parameters thro
ugh gradient-based optimization algorithms. Based on the adjoint-state met
hod\, we derive two different frameworks for approximating the gradient of
an objective functional constrained by the nonlinear Boltzmann equation.
While the forward problem can be solved by the Direct Simulation Monte Car
lo (DSMC) method\, it is difficult to efficiently solve the high-dimension
al continuous adjoint equation obtained by the "optimize-then-discretize"
approach. This challenge motivates us to propose an adjoint DSMC method fo
llowing the "discretize-then-optimize" approach for Boltzmann-constrained
optimization. We also analyze the properties of the two frameworks and the
ir connections. Several numerical examples are presented to demonstrate th
eir accuracy and efficiency.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andre Laestadius (Hylleraas Centre for Quantum Molecular Sciences)
DTSTART;VALUE=DATE-TIME:20220224T001000Z
DTEND;VALUE=DATE-TIME:20220224T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/52
DESCRIPTION:Title: Energy error estimate for coupled-cluster excited states\nby
Andre Laestadius (Hylleraas Centre for Quantum Molecular Sciences) as part
of Berkeley applied mathematics seminar\n\n\nAbstract\nIn our recent work
\, the nonlinear equations of the single-reference Coupled-Cluster method
have been analyzed using topological degree theory. This generalizes previ
ous work based on (local) strong monotonicity. We have established existen
ce results and qualitative information about the solutions of these equati
ons that also sheds light on some of the numerically observed behavior. In
particular\, to investigate truncation schemes within the Coupled-Cluster
method\, we have utilized the Kowalski-Piecuch homotopy. In this setting\
, we have derived an energy error bound for approximate eigenstates of the
Schrödinger equation\, i.e.\, for both ground and excited states.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Olivier (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220303T001000Z
DTEND;VALUE=DATE-TIME:20220303T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/53
DESCRIPTION:Title: High Order Finite Element Discretizations of the Variable Eddingt
on Factor Equations for Accelerating Radiation Transport Calculations on C
urved Meshes\nby Samuel Olivier (University of California\, Berkeley)
as part of Berkeley applied mathematics seminar\n\n\nAbstract\nThe Variabl
e Eddington Factor (VEF) method is one of the oldest techniques for solvin
g the radiation transport equation. In VEF\, the kinetic equation is itera
tively coupled to the moment equations through discrete closures. This mom
ent-based approach enables significant algorithmic flexibility and more ef
ficient multiphysics coupling. However\, despite considerable attention in
the literature\, VEF is rarely used in practice due to the lack of scalab
le iterative preconditioners for the discretized moment equations. In this
talk\, I present three classes of VEF methods with high-order accuracy on
curved meshes that can be efficiently and scalably solved. Discretization
and preconditioning techniques known to be effective on simpler model ell
iptic problems are extended to the VEF moment equations to derive Disconti
nuous Galerkin\, continuous finite element\, and mixed finite element VEF
methods. These methods are demonstrated to be effective on a proxy problem
from thermal radiative transfer in both outer transport iterations and in
ner preconditioned linear solver iterations and to scale out to 1152 proce
ssors and over 10 million scalar flux unknowns.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael I Weinstein (Columbia University)
DTSTART;VALUE=DATE-TIME:20220406T231000Z
DTEND;VALUE=DATE-TIME:20220407T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/54
DESCRIPTION:Title: Discrete honeycombs\, rational edges and edge states\nby Mich
ael I Weinstein (Columbia University) as part of Berkeley applied mathemat
ics seminar\n\n\nAbstract\nWe first discuss the derivation of tight bindin
g (discrete) Hamiltonians from an underlying continuum Schroedinger Hamilt
onians in both non-magnetic and strongly magnetic systems (joint works wit
h with CL Fefferman and J Shapiro).\n\nWe then present very recent work (w
ith CL Fefferman and S Fliss) on the tight binding model of graphene\, sha
rply terminated along a rational edge\, a line I parallel to a direction o
f translational symmetry of the underlying period lattice. We classify suc
h edges into those of "zigzag type" and those of "armchair type"\, general
izing the classical zigzag and armchair edges. Edge states are eigenstates
which are plane wave like in directions parallel to the edge and are loc
alized in directions transverse to the edge. We prove that zero energy/fla
t band edge states arise for edges of zigzag type\, but never for those of
armchair type. We exhibit explicit formulas for flat band edge states whe
n they exist. Finally\, we produce strong evidence for the existence of di
spersive (non flat) edge state curves of nonzero energy for most rational
edges.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Houman Owhadi (California Institute of Technology)
DTSTART;VALUE=DATE-TIME:20220427T231000Z
DTEND;VALUE=DATE-TIME:20220428T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/55
DESCRIPTION:Title: Computational Graph Completion\nby Houman Owhadi (California
Institute of Technology) as part of Berkeley applied mathematics seminar\n
\n\nAbstract\nWe present a framework for generating\, organizing\, and rea
soning with computational knowledge. It is motivated by the observation th
at most problems in Computational Sciences and Engineering (CSE) can be fo
rmulated as that of completing (from data) a computational graph (or hyper
graph) representing dependencies between functions and variables. Nodes re
present variables\, and edges represent functions. Functions and variables
may be known\, unknown\, or random. Data comes in the form of observation
s of distinct values of a finite number of subsets of the variables of the
graph (satisfying its functional dependencies). The underlying problem co
mbines a regression problem (approximating unknown functions) with a matr
ix completion problem (recovering unobserved variables in the data). Repla
cing unknown functions by Gaussian Processes (GPs) and conditioning on ob
served data provides a simple but efficient approach to completing such gr
aphs. Since this completion process can be reduced to an algorithm\, as on
e solves $\\sqrt{2}$ on a pocket calculator without thinking about it\, on
e could\, with the automation of the proposed framework\, solve a complex
CSE problem by drawing a diagram.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingwei Hu (University of Washington)
DTSTART;VALUE=DATE-TIME:20220217T001000Z
DTEND;VALUE=DATE-TIME:20220217T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/56
DESCRIPTION:Title: An efficient dynamical low-rank algorithm for the Boltzmann-BGK e
quation close to the compressible viscous flow regime\nby Jingwei Hu (
University of Washington) as part of Berkeley applied mathematics seminar\
n\n\nAbstract\nIt has recently been demonstrated that dynamical low-rank a
lgorithms can provide robust and efficient approximations to a range of ki
netic equations. This is true especially if the solution is close to some
asymptotic limit where it is known that the solution is low-rank. A partic
ularly interesting case is the fluid dynamic limit that is commonly obtain
ed in the limit of small Knudsen number. However\, in this case the Maxwel
lian which describes the corresponding equilibrium distribution is not nec
essarily low-rank\; because of this\, the methods known in the literature
are only applicable to the weakly compressible case. In this paper\, we pr
opose an efficient dynamical low-rank integrator that can capture the flui
d limit—the Navier–Stokes equations—of the Boltzmann-BGK model even
in the compressible regime. This is accomplished by writing the solution a
s f = Mg\, where M is the Maxwellian and the low-rank approximation is onl
y applied to g. To efficiently implement this decomposition within a low-r
ank framework requires\, in the isothermal case\, that certain coefficient
s are evaluated using convolutions\, for which fast algorithms are known.
Using the proposed decomposition also has the advantage that the rank requ
ired to obtain accurate results is significantly reduced compared to the p
revious state of the art. We demonstrate this by performing a number of nu
merical experiments and also show that our method is able to capture sharp
gradients/shock waves. This is joint work with Lukas Einkemmer (Innsbruck
) and Lexing Ying (Stanford).\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillaume Bal (University of Chicago)
DTSTART;VALUE=DATE-TIME:20220330T231000Z
DTEND;VALUE=DATE-TIME:20220331T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/57
DESCRIPTION:Title: Asymmetric transport and topological invariants\nby Guillaume
Bal (University of Chicago) as part of Berkeley applied mathematics semin
ar\n\n\nAbstract\nRobust asymmetric transport at the interface between two
-dimensional insulating bulks has been observed in many areas of (geo)phys
ical and materials sciences. The main practical appeal of this asymmetry i
s its immunity to large classes of perturbations. This stability is explai
ned by topological considerations.\n \nA physical observable\, a one-dimen
sional conductivity\, is assigned to the asymmetric transport. Interface H
amiltonians modeling the transition between the bulk phases are next intro
duced and classified by a topological charge\, the index of an appropriate
Fredholm operator. A general principle\, the bulk-edge correspondence\, t
hen states that the conductivity is quantized and equal to the topological
charge\, which may be interpreted as a difference of bulk topologies.\n \
nWhile ubiquitous in the physical and engineering literatures\, the bulk-e
dge correspondence remains difficult to establish mathematically or in fac
t even heuristically. This talk presents recent results on the derivation
of the correspondence for reasonably large algebras of (pseudo-)differenti
al operators that appear generically as low-energy large-wavelength models
in the applications. We use the correspondence to compute the asymmetry i
n several settings where a direct estimation seems hopeless\, with applica
tions\, e.g.\, in graphene-based Floquet topological insulators and topolo
gical properties of twisted bilayer graphene.\n \nTime permitting\, we wil
l contrast the above spectral properties with the practically more relevan
t temporal picture and\, for instance\, the propagation of semi-classical
wavepackets along curved interfaces.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eitan Tadmor (University of Maryland)
DTSTART;VALUE=DATE-TIME:20220316T231000Z
DTEND;VALUE=DATE-TIME:20220317T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/58
DESCRIPTION:Title: Hierarchical decomposition of images and the problem of Bourgain-
Brezis\nby Eitan Tadmor (University of Maryland) as part of Berkeley a
pplied mathematics seminar\n\n\nAbstract\nEdges are noticeable features in
images which can be extracted from noisy data using different variational
models. The analysis of such models leads to the question of expressing g
eneral L^2-data\, f\, as the divergence of uniformly bounded vector fields
\, div(U). We present a multi-scale approach to construct uniformly bounde
d solutions of div(U)=f for general f’s in the critical regularity space
L^d(T^d). The study of this equation and related problems was motivated b
y results of Bourgain & Brezis. The intriguing critical aspect here is tha
t although the problems are linear\, construction of their solution is not
. Our constructive solution for such problems is a special case of a rathe
r general framework for solving linear equations\, formulated as inverse p
roblems in critical regularity spaces. The solutions are realized in terms
of nonlinear hierarchical decomposition\, U=image001.png\, which we intro
duced earlier in the context of image processing\, and yield a multi-scale
decomposition of “objects” U.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dejan Slepcev (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20220413T231000Z
DTEND;VALUE=DATE-TIME:20220414T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/59
DESCRIPTION:Title: Proper regularizers for semi-supervised learning\nby Dejan Sl
epcev (Carnegie Mellon University) as part of Berkeley applied mathematics
seminar\n\n\nAbstract\nWe will discuss a standard problem of semi-supersi
sed learning: given a data set (considered as a point cloud in a euclidean
space) with a small number of labeled points the task is to extrapolate t
he label values to the whole data set. In order to utilize the geometry of
the dataset one creates a graph by connecting the nodes which are suffici
ently close. Many standard approaches rely on minimizing graph-based funct
ionals\, which reward the agreement with the labels and the regularity of
the estimator. Choosing a good regularization leads to questions about the
relations between discrete functionals in random setting and continuum no
nlocal and differential functionals. We will discuss how insights about th
is relation provide ways to properly choose the functionals for semi-supe
rvised learning and appropriately set the weights of the graph so that the
information is propagated in a desirable way from the labeled points. The
oretical results\, numerical illustrations and performance on standard tes
t data sets will be provided.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Minh Tran (MIT)
DTSTART;VALUE=DATE-TIME:20220420T231000Z
DTEND;VALUE=DATE-TIME:20220421T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/60
DESCRIPTION:Title: The propagation of information in power-law interacting systems\nby Minh Tran (MIT) as part of Berkeley applied mathematics seminar\n\n
\nAbstract\nMost physical many-body quantum systems are geometrically loca
l\; it takes time to propagate quantum information in the systems. Such lo
cality imposes fundamental limits on many quantum information processing t
asks. In this talk\, we will review the state-of-the-art speed limits for
the propagation of information in quantum systems with power-law interacti
ons. We discuss applications of the speed limits and\, in particular\, use
them to constrain the propagation of error and improve the performance of
quantum simulation algorithms. Inversely\, we also prove new speed limits
using quantum simulation algorithms\, suggesting a deep connection betwee
n the propagation of information and digital quantum simulation.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spring break. No seminar
DTSTART;VALUE=DATE-TIME:20220323T231000Z
DTEND;VALUE=DATE-TIME:20220324T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/61
DESCRIPTION:by Spring break. No seminar as part of Berkeley applied mathem
atics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Franco (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220310T001000Z
DTEND;VALUE=DATE-TIME:20220310T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/62
DESCRIPTION:Title: Relating high-order fluid flow problems to simpler subproblems to
create efficient preconditioners\nby Michael Franco (University of Ca
lifornia\, Berkeley) as part of Berkeley applied mathematics seminar\n\n\n
Abstract\nThis talk will focus on two solvers for high-order methods\, wit
h the common thread being that their efficiency derives from relating the
original problem to a simpler subproblem. First\, a matrix-free flow solve
r for high-order finite element discretizations of the incompressible Navi
er-Stokes and Stokes equations with GPU acceleration will be presented. Fo
r high polynomial degrees\, assembling the matrix for the linear systems r
esulting from the finite element discretization can be prohibitively expen
sive\, both in terms of computational complexity and memory. For this reas
on\, it is necessary to develop matrix-free operators and preconditioners\
, which can be used to efficiently solve these linear systems without acce
ss to the matrix entries themselves. Particular attention will be given to
the matrix-free operator evaluations that utilize GPU-accelerated sum-fac
torization techniques to minimize memory movement and maximize throughput.
I will also briefly introduce novel preconditioners based on a low-order
refined methodology with parallel subspace corrections. Second\, I will in
troduce a novel class of iterative subregion correction preconditioners fo
r solving flow problems with geometrically localized stiffness. Just as mu
ltigrid methods spend more effort on cheaper grids to apply a correction t
hat improves convergence on lower frequency components\, our subregion cor
rection preconditioners spend more effort on a subregion of the domain dem
onstrating slow convergence to improve overall convergence rates. Converge
nce theory and numerical results validating this theory will be presented.
\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Di Fang (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220225T001000Z
DTEND;VALUE=DATE-TIME:20220225T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/63
DESCRIPTION:Title: Mathematics Department Colloquium: Quantum algorithms for Hamilto
nian simulation with unbounded operators\nby Di Fang (University of Ca
lifornia\, Berkeley) as part of Berkeley applied mathematics seminar\n\nLe
cture held in 60 Evans Hall.\n\nAbstract\nRecent years have witnessed trem
endous progress in developing and analyzing quantum algorithms for quantum
dynamics simulation of bounded operators (Hamiltonian simulation). Howeve
r\, many scientific and engineering problems require the efficient treatme
nt of unbounded operators\, which frequently arise due to the discretizati
on of differential operators. Such applications include molecular dynamics
\, electronic structure theory\, quantum control and quantum differential
equations solver. We will introduce some recent advances in quantum algori
thms for efficient unbounded Hamiltonian simulation\, including Trotter-ty
pe splitting and the quantum highly oscillatory protocol (qHOP) in the int
eraction picture. The latter yields a surprising superconvergence result f
or regular potentials.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mo Zhou (Duke University)
DTSTART;VALUE=DATE-TIME:20220907T231000Z
DTEND;VALUE=DATE-TIME:20220908T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/64
DESCRIPTION:Title: Neural network approaches for high dimensional problems\nby M
o Zhou (Duke University) as part of Berkeley applied mathematics seminar\n
\n\nAbstract\nNeural networks are effective tools for solving high dimensi
onal problems. In this talk\, I will summarize the popular methods to solv
e high dimensional problems with neural networks. Then I will briefly intr
oduce two of my works based on the DeepBSDE method. In the first work\, we
solve the eigenvalue problem by transforming it into a fixed-point formul
ation\, which is a diffusion Monte Carlo like approach. In the second work
\, we leverage the actor-critic framework from reinforcement learning to s
olve the static Hamilton—Jacobi—Bellman equations. We propose a varian
ce reduced temporal difference method for the critic and apply an adaptive
step size algorithm for the actor to improve accuracy.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Wang (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20220921T231000Z
DTEND;VALUE=DATE-TIME:20220922T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/65
DESCRIPTION:Title: Variational methods for gradient flow\nby Li Wang (University
of Minnesota) as part of Berkeley applied mathematics seminar\n\n\nAbstra
ct\nIn this talk\, I will introduce a general variational framework for no
nlinear evolution equations with a gradient flow structure\, which arise i
n material science\, animal swarms\, chemotaxis\, and deep learning\, amon
g many others. Building upon this framework\, we develop numerical methods
that have built-in properties such as positivity preserving and entropy d
ecreasing\, and resolve stability issues due to the strong nonlinearity. T
wo specific applications will be discussed. One is the Wasserstein gradien
t flow\, where the major challenge is to compute the Wasserstein distance
and resulting optimization problem. I will show techniques to overcome the
se difficulties. The other is to simulate crystal surface evolution\, whic
h suffers from significant stiffness and therefore prevents simulation wit
h traditional methods on fine spatial grids. On the contrary\, our method
resolves this issue and is proved to converge at a rate independent of the
grid size.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Felix Leditzky (UIUC)
DTSTART;VALUE=DATE-TIME:20220928T231000Z
DTEND;VALUE=DATE-TIME:20220929T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/66
DESCRIPTION:Title: The platypus of the quantum channel zoo\nby Felix Leditzky (U
IUC) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nUnders
tanding quantum channels and the strange behavior of their capacities is a
key driver of quantum information theory. Despite having rigorous coding
theorems\, quantum capacities are poorly understood due to super-additivit
y effects. We will talk about a remarkably simple\, low-dimensional\, sing
le-parameter family of quantum channels with exotic quantum information-th
eoretic features. As the simplest example from this family\, we focus on a
qutrit-to-qutrit channel that is intuitively obtained by hybridizing toge
ther a simple degradable channel and a completely useless qubit channel. S
uch hybridizing makes this channel's capacities behave in a variety of int
eresting ways. For instance\, the private and classical capacity of this c
hannel coincide and can be explicitly calculated\, even though the channel
does not belong to any class for which the underlying information quantit
ies are known to be additive. Moreover\, the quantum capacity of the chann
el can be computed explicitly\, given a clear and compelling conjecture is
true. This "spin alignment conjecture\," which may be of independent inte
rest\, is proved in certain special cases and additional numerical evidenc
e for its validity is provided. We further show that this qutrit channel d
emonstrates superadditivity when transmitting quantum information jointly
with a variety of assisting channels\, in a manner unknown before. A highe
r-dimensional variant of this qutrit channel displays super-additivity of
quantum capacity together with an erasure channel. Subject to the spin-ali
gnment conjecture\, our results on super-additivity of quantum capacity ex
tend to lower-dimensional channels as well as larger parameter ranges. In
particular\, super-additivity occurs between two weakly additive channels
each with large capacity on their own\, in stark contrast to previous resu
lts. Remarkably\, a single\, novel transmission strategy achieves super-ad
ditivity in all examples. Our results show that super-additivity is much m
ore prevalent than previously thought. It can occur across a wide variety
of channels\, even when both participating channels have large quantum cap
acity.\n\nThis is joint work with Debbie Leung\, Vikesh Siddhu\, Graeme Sm
ith\, and John Smolin\, and based on the papers https://arxiv.org/abs/2202
.08380 and https://arxiv.org/abs/2202.08377.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Ma (Stanford University)
DTSTART;VALUE=DATE-TIME:20221005T231000Z
DTEND;VALUE=DATE-TIME:20221006T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/67
DESCRIPTION:Title: Implicit bias of optimization algorithms for neural networks and
their effects on generalization\nby Chao Ma (Stanford University) as p
art of Berkeley applied mathematics seminar\n\n\nAbstract\nModern neural n
etworks are usually over-parameterized—the number of parameters exceeds
the number of training data. In this case the loss functions tend to have
many (or even infinite) global minima\, which imposes an additional challe
nge of minima selection on optimization algorithms besides the convergence
. Specifically\, when training a neural network\, the algorithm not only h
as to find a global minimum\, but also needs to select minima with good ge
neralization among many other bad ones. In this talk\, I will share a seri
es of works studying the mechanisms that facilitate global minima selectio
n of optimization algorithms. First\, with a linear stability theory\, we
show that stochastic gradient descent (SGD) favors flat and uniform global
minima. Then\, we build a theoretical connection of flatness and generali
zation performance based on a special structure of neural networks. Next\,
we study the global minima selection dynamics—the process that an optim
izer leaves bad minima for good ones—in two settings. For a manifold of
minima around which the loss function grows quadratically\, we derive effe
ctive exploration dynamics on the manifold for SGD and Adam\, using a quas
istatic approach. For a manifold of minima around which the loss function
grows subquadratically\, we study the behavior and effective dynamics for
GD\, which also explains the edge of stability phenomenon.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Fornace (Caltech)
DTSTART;VALUE=DATE-TIME:20221012T231000Z
DTEND;VALUE=DATE-TIME:20221013T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/68
DESCRIPTION:Title: Theoretical methods for nucleic acid secondary structure thermody
namics and kinetics\nby Mark Fornace (Caltech) as part of Berkeley app
lied mathematics seminar\n\n\nAbstract\nNucleic acid secondary structure m
odels offer a simplified but powerful lens through which to view\, analyze
\, and design nucleic acid chemistry. Computational approaches based on su
ch models are central to current research directions across molecular prog
ramming and the life sciences more broadly. Considering only structures in
volving noncrossing partitions of nucleotides\, dynamic programming algori
thms can exactly compute equilibrium quantities (with respect to an approx
imate free energy model) in cubic complexity. I first show how such algori
thms may be improved in speed\, augmented in accuracy\, and unified across
a variety of physical quantities.\n\nWhile analysis and design paradigms
for nucleic acid thermodynamics are long-established in essence\, nucleic
acid kinetics have proved vexing for accurate and principled estimation al
gorithms. Past approaches have thus generally relied on stochastic simulat
ion of the respective continuous time Markov chains (an asymptotically cor
rect but computationally costly approach). In contrast\, I show how a prin
cipled Galerkin-type approach to the kinetics proves remarkably amenable t
o deterministic estimation by dynamic programming algorithms. While inexac
t\, the approach proves empirically accurate and is theoretically extensib
le to treatments of mass-action kinetics\, macrostate models\, and sequenc
e design.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Gao (University of Houston)
DTSTART;VALUE=DATE-TIME:20221019T231000Z
DTEND;VALUE=DATE-TIME:20221020T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/69
DESCRIPTION:Title: Logarithmic Sobolev inequalities for matrices and matrix-valued f
unctions\nby Li Gao (University of Houston) as part of Berkeley applie
d mathematics seminar\n\n\nAbstract\nLogarithmic Sobolev inequalities\, fi
rst introduced by Gross in 70s\, have rich connections to probability\, ge
ometry\, as well as information theory. In recent years\, logarithmic Sobo
lev inequalities for quantum Markov semigroups attracted a lot of attentio
ns for its applications in quantum information theory and quantum many-bod
y systems. In this talk\, I'll present a simple\, information-theoretic ap
proach to modified logarithmic Sobolev inequalities for both quantum Marko
v semigroup on matrices\, and classical Markov semigroup on matrix-valued
functions. In the classical setting\, our results implies every sub-Laplac
ian of a Hörmander system admits a uniform modified logarithmic Sobolev
constant for all its matrix valued functions. For quantum Markov semigroup
s\, we improve a previous result of Gao and Rouzé by replacing the dimens
ion constant by its logarithm. This talk is based on a joint work with Mar
ius Junge\, Nicholas\, LaRacunte\, and Haojian Li.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Colbrook (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20221024T231000Z
DTEND;VALUE=DATE-TIME:20221025T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/70
DESCRIPTION:Title: Residual Dynamic Mode Decomposition: Rigorous Data-Driven Computa
tion of Spectral Properties of Koopman Operators for Dynamical Systems
\nby Matthew Colbrook (University of Cambridge) as part of Berkeley applie
d mathematics seminar\n\n\nAbstract\nKoopman operators are infinite-dimens
ional operators that globally linearize\nnonlinear dynamical systems\, mak
ing their spectral information valuable for\nunderstanding dynamics. Howev
er\, Koopman operators can have continuous\nspectra\, can lack finite-dime
nsional invariant subspaces\, and approximations can\nsuffer from spectral
pollution (spurious modes). These issues make computing\nthe spectral pro
perties of Koopman operators a considerable challenge. This two-\npart tal
k will detail the first scheme (ResDMD) with convergence guarantees for\nc
omputing the spectra and pseudospectra of general Koopman operators from\n
snapshot data. Furthermore\, we use the resolvent operator and ResDMD to\n
compute smoothed approximations of spectral measures (including continuous
\nspectra)\, with explicit high-order convergence. ResDMD is similar to ex
tended\nDMD\, except it rigorously concurrently computes a residual from t
he same\nsnapshot data\, allowing practitioners to gain confidence in the
computed results.\nKernelized variants of our algorithms allow for dynamic
al systems with a high-\ndimensional state-space\, and the error control p
rovided by ResDMD allows a\nposteriori verification of learnt dictionaries
. We apply ResDMD to compute the\nspectral measure associated with the dyn
amics of a protein molecule (20\,046-dimensional state-space) and demonstr
ate several problems in fluid dynamics\n(with state-space dimensions > 100
\,000). For example\, we compare ResDMD\nand DMD for particle image veloci
metry data from turbulent wall-jet flow\, the\nacoustic signature of laser
-induced plasma\, and turbulent flow past a cascade of\naerofoils.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Lanthaler (Caltech)
DTSTART;VALUE=DATE-TIME:20221110T001000Z
DTEND;VALUE=DATE-TIME:20221110T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/71
DESCRIPTION:Title: Supervised learning in function space\nby Samuel Lanthaler (C
altech) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nNeu
ral networks have proven to be effective approximators of high dimensional
functions in a wide variety of applications. In scientific applications t
he goal is often to approximate an underlying operator\, which defines a m
apping between infinite-dimensional spaces of input and output functions.
Extensions of neural networks to this infinite-dimensional setting have be
en proposed in recent years\, giving rise to the rapidly emerging field of
operator learning. Despite their practical success\, our theoretical unde
rstanding of these approaches is still in its infancy. In this talk\, I wi
ll review some of the proposed operator learning architectures (deep opera
tor networks/neural operators)\, and present recent results on their appro
ximation theory and sample complexity. This work identifies basic mechanis
ms by which neural operators can avoid a curse of dimensionality in the un
derlying (very high- or even infinite-dimensional) approximation task\, th
us providing a first rationale for their practical success for concrete op
erators of interest. The analysis also reveals fundamental limitations of
some of these approaches.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Bouck (University of Maryland)
DTSTART;VALUE=DATE-TIME:20221117T001000Z
DTEND;VALUE=DATE-TIME:20221117T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/72
DESCRIPTION:Title: Finite Element Approximation of a Membrane Model for Liquid Cryst
al Polymeric Networks\nby Lucas Bouck (University of Maryland) as part
of Berkeley applied mathematics seminar\n\n\nAbstract\nLiquid crystal pol
ymeric networks are materials where a nematic liquid crystal is coupled wi
th a rubbery material. When actuated with heat or light\, the interaction
of the liquid crystal with the rubber creates complex shapes. Starting fro
m the classical 3D trace formula energy of Bladon\, Warner and Terentjev (
1994)\, we derive a 2D membrane energy as the formal asymptotic limit of t
he 3D energy. The derivation is similar to derivations in Ozenda\, Sonnet\
, and Virga (2020) and Cirak et. al. (2014). We characterize the zero ener
gy deformations and prove that the energy lacks certain convexity properti
es. We propose a finite element method to discretize the problem. To addre
ss the lack of convexity of the membrane energy\, we regularize with a ter
m that mimics a higher order bending energy. We prove that minimizers of t
he discrete energy converge to minimizers of the continuous energy. For mi
nimizing the discrete problem\, we employ a nonlinear gradient flow scheme
\, which is energy stable. Additionally\, we present computations showing
the geometric effects that arise from liquid crystal defects. Computations
of configurations from nonisometric origami are also presented.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No seminar. Happy thanksgiving.
DTSTART;VALUE=DATE-TIME:20221124T001000Z
DTEND;VALUE=DATE-TIME:20221124T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/73
DESCRIPTION:by No seminar. Happy thanksgiving. as part of Berkeley applied
mathematics seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sui Tang (UCSB)
DTSTART;VALUE=DATE-TIME:20221201T001000Z
DTEND;VALUE=DATE-TIME:20221201T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/74
DESCRIPTION:Title: Bridging the interacting particle models and data science via Gau
ssian process\nby Sui Tang (UCSB) as part of Berkeley applied mathemat
ics seminar\n\n\nAbstract\nSystem of interacting particles that display a
wide variety of collective behaviors are ubiquitous in science and enginee
ring\, such as self-propelled particles\, flocking of birds\, milling of f
ish. Modeling interacting particle systems by a system of differential equ
ations plays an essential role in exploring how individual behavior engend
ers collective behaviors\, which is one of the most fundamental and import
ant problems in various disciplines. Although the recent theoretical and
numerical study bring a flood of models that can reproduce many macroscopi
cal qualitative collective patterns of the observed dynamics\, the quantit
ative study towards matching the well-developed models to observational d
ata is scarce. \n\nWe consider the data-driven discovery of macroscopic pa
rticle models with latent interactions. We propose a learning approach tha
t models the latent interactions as Gaussian processes\, which provides an
uncertainty-aware modeling of interacting particle systems. We introduce
an operator-theoretic framework to provide a detailed analysis of recovera
bility conditions\, and establish statistical optimality of the proposed a
pproach. Numerical results on prototype systems and real data demonstrate
the effectiveness of the proposed approach.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krutika Tawri (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20220914T231000Z
DTEND;VALUE=DATE-TIME:20220915T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/75
DESCRIPTION:Title: On stochastic partial differential equations with a Ladyzenskaya-
Smagorinsky type nonlinearity\nby Krutika Tawri (University of Califor
nia\, Berkeley) as part of Berkeley applied mathematics seminar\n\nLecture
held in 939 Evans Hall.\n\nAbstract\nThe theory of monotone operators pla
ys a central role in many areas of nonlinear analysis. Monotone operators
often appear in fluid dynamics\, for example the p-Laplacian appears in a
non-Newtonian variant of the Navier-Stokes equations modeled by Ladyzenska
ya or in the Smagorinsky model of turbulence. In this talk\, we will discu
ss global existence results of both martingale and pathwise solutions of s
tochastic equations with a monotone operator\, of the Ladyzenskaya-Smagori
nsky type\, driven by a general Levy noise. The classical approach based o
n using directly the Galerkin approximation is not valid. In this talk we
will discuss how one can approximate a monotone operator by a family of mo
notone operators acting in a Hilbert space\, so as to recover certain usef
ul properties of the orthogonal projectors and overcome the challenges fac
ed while applying the Galerkin scheme.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yonah Borns-Weil (University of California\, Berkeley)
DTSTART;VALUE=DATE-TIME:20221102T231000Z
DTEND;VALUE=DATE-TIME:20221103T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/76
DESCRIPTION:Title: Observable Trotter error bounds in the semiclassical regime\n
by Yonah Borns-Weil (University of California\, Berkeley) as part of Berke
ley applied mathematics seminar\n\n\nAbstract\nThe Trotter product formula
is perhaps the oldest and most well-known method for computing Schröding
er propagators. We consider its application to the semiclassical Schroding
er equation where the parameter $h$ is taken to be very small. If one wish
es to do practical computations in such a regime\, they must take at least
$O(h^{-1})$ spatial grid points\, which gives the Hamiltonian terms and t
heir nested commutators to be of norm O(h^{-1}). This would appear to caus
e serious trouble for both Trotter and post-Trotter methods\, as their tim
e complexity depends on such norms.\n\nThe issue resolves itself when we c
onsider approximating the propagator in observable norm\, which measures h
ow much an observable propagated via the actual Hamiltonian differs from o
ne propagated by our Trotter approximation. By a simple argument using Ego
rov's theorem from semiclasscial analysis\, we show the error in this norm
to be uniform in the semiclassical parameter $h$. In addition\, we consid
er the discretized space case of interest in quantum computing\, and use d
iscrete microlocal analysis on the quantized torus to extend our results t
o this case without added error.\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Govind Menon (Brown University)
DTSTART;VALUE=DATE-TIME:20230121T001000Z
DTEND;VALUE=DATE-TIME:20230121T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/77
DESCRIPTION:Title: Stochastic Nash evolution\nby Govind Menon (Brown University)
as part of Berkeley applied mathematics seminar\n\n\nAbstract\nAbout ten
years ago\, De Lellis and Szekelyhidi made the surprising discovery that N
ash’s results on the isometric embedding problem for Riemannian manifold
scould be adapted to construct counterintuitive solutions to the Euler equ
ations for incompressible flow. Their work shed new light on turbulence an
d nonlinear PDE. We use this link in the other direction\, transferring id
eas from turbulence to geometry.\n\nA thermodynamic framework is introduce
d that connects two problems previously thought to be distinct: the isomet
ric embedding problem for Riemannian manifolds and the construction of Bro
wnian motion on Riemannian manifolds. This link is used to introduce a geo
metric stochastic flow that we term stochastic Nash evolution.\n\nThese id
eas will be explained in a (hopefully) elementary manner. My main goal is
to present the stochastic flows in a manner that is suited to implementati
ons by modifications of level set methods. The absence of numerical comput
ations of isometric embeddings is an important gap in our understanding.\n
\nThis is joint work with Dominik Inauen (University of Leipzig).\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anuj Kumar (UC Santa Cruz)
DTSTART;VALUE=DATE-TIME:20230126T001000Z
DTEND;VALUE=DATE-TIME:20230126T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/78
DESCRIPTION:Title: Application of branching flows to optimal scalar transport and a
result concerning the nonuniqueness of trajectories\nby Anuj Kumar (UC
Santa Cruz) as part of Berkeley applied mathematics seminar\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Albergo (New York University)
DTSTART;VALUE=DATE-TIME:20230223T001000Z
DTEND;VALUE=DATE-TIME:20230223T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/79
DESCRIPTION:by Michael Albergo (New York University) as part of Berkeley a
pplied mathematics seminar\n\nInteractive livestream: https://berkeley.zoo
m.us/j/186935273\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/79/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiantao Li (Penn State University)
DTSTART;VALUE=DATE-TIME:20230302T001000Z
DTEND;VALUE=DATE-TIME:20230302T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/80
DESCRIPTION:by Xiantao Li (Penn State University) as part of Berkeley appl
ied mathematics seminar\n\nInteractive livestream: https://berkeley.zoom.u
s/j/186935273\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/80/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fanhui Xu (Harvard University)
DTSTART;VALUE=DATE-TIME:20230315T231000Z
DTEND;VALUE=DATE-TIME:20230316T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/81
DESCRIPTION:by Fanhui Xu (Harvard University) as part of Berkeley applied
mathematics seminar\n\nInteractive livestream: https://berkeley.zoom.us/j/
186935273\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/81/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi-Fang Chen (Caltech)
DTSTART;VALUE=DATE-TIME:20230322T231000Z
DTEND;VALUE=DATE-TIME:20230323T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/82
DESCRIPTION:by Chi-Fang Chen (Caltech) as part of Berkeley applied mathema
tics seminar\n\nInteractive livestream: https://berkeley.zoom.us/j/1869352
73\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/82/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:no seminar. spring break
DTSTART;VALUE=DATE-TIME:20230329T231000Z
DTEND;VALUE=DATE-TIME:20230330T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/83
DESCRIPTION:by no seminar. spring break as part of Berkeley applied mathem
atics seminar\n\nInteractive livestream: https://berkeley.zoom.us/j/186935
273\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/83/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangwen Zhang (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20230405T231000Z
DTEND;VALUE=DATE-TIME:20230406T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/84
DESCRIPTION:by Yangwen Zhang (Carnegie Mellon University) as part of Berke
ley applied mathematics seminar\n\nInteractive livestream: https://berkele
y.zoom.us/j/186935273\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/84/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandeep Sharma (University of Colorado Boulder)
DTSTART;VALUE=DATE-TIME:20230412T231000Z
DTEND;VALUE=DATE-TIME:20230413T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/85
DESCRIPTION:by Sandeep Sharma (University of Colorado Boulder) as part of
Berkeley applied mathematics seminar\n\nInteractive livestream: https://be
rkeley.zoom.us/j/186935273\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/85/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeremy Hoskins (University of Chicago)
DTSTART;VALUE=DATE-TIME:20230419T231000Z
DTEND;VALUE=DATE-TIME:20230420T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/86
DESCRIPTION:by Jeremy Hoskins (University of Chicago) as part of Berkeley
applied mathematics seminar\n\nInteractive livestream: https://berkeley.zo
om.us/j/186935273\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/86/
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandar Donev (Courant Institute)
DTSTART;VALUE=DATE-TIME:20230317T231000Z
DTEND;VALUE=DATE-TIME:20230318T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/87
DESCRIPTION:Title: Hydrodynamics and rheology of fluctuating\, semiflexible\, inexte
nsible\, and slender filaments in Stokes flow\nby Aleksandar Donev (Co
urant Institute) as part of Berkeley applied mathematics seminar\n\nIntera
ctive livestream: https://berkeley.zoom.us/j/98667278310\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/87/
URL:https://berkeley.zoom.us/j/98667278310
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyan Ding (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20230209T001000Z
DTEND;VALUE=DATE-TIME:20230209T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/88
DESCRIPTION:by Zhiyan Ding (UC Berkeley) as part of Berkeley applied mathe
matics seminar\n\nInteractive livestream: https://berkeley.zoom.us/j/98667
278310\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/88/
URL:https://berkeley.zoom.us/j/98667278310
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uros Seljak (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20230216T001000Z
DTEND;VALUE=DATE-TIME:20230216T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/89
DESCRIPTION:by Uros Seljak (UC Berkeley) as part of Berkeley applied mathe
matics seminar\n\nInteractive livestream: https://berkeley.zoom.us/j/98667
278310\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/89/
URL:https://berkeley.zoom.us/j/98667278310
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julian Urban (MIT)
DTSTART;VALUE=DATE-TIME:20230309T001000Z
DTEND;VALUE=DATE-TIME:20230309T010000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/90
DESCRIPTION:by Julian Urban (MIT) as part of Berkeley applied mathematics
seminar\n\nInteractive livestream: https://berkeley.zoom.us/j/98667278310\
nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/90/
URL:https://berkeley.zoom.us/j/98667278310
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuehaw Khoo (University of Chicago)
DTSTART;VALUE=DATE-TIME:20230426T231000Z
DTEND;VALUE=DATE-TIME:20230427T000000Z
DTSTAMP;VALUE=DATE-TIME:20230205T210943Z
UID:BerekelyApplied/91
DESCRIPTION:by Yuehaw Khoo (University of Chicago) as part of Berkeley app
lied mathematics seminar\n\nInteractive livestream: https://berkeley.zoom.
us/j/98667278310\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BerekelyApplied/91/
URL:https://berkeley.zoom.us/j/98667278310
END:VEVENT
END:VCALENDAR