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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:20201031T050002Z
UID:BerekelyApplied/1
DESCRIPTION:Title: Solving inverse problems with deep learning\nby Lexing
Ying (Stanford University) as part of Berkeley applied mathematics seminar
\n\n\nAbstract\nThis talk is about some recent progress on solving inverse
problems using deep learning. Compared to traditional machine learning pr
oblems\, inverse problems are often limited by the size of the training da
ta set. We show how to overcome this issue by incorporating mathematical a
nalysis and physics into the design of neural network architectures. We fi
rst describe neural network representations of pseudodifferential operator
s and Fourier integral operators. We then continue to discuss applications
including electric impedance tomography\, optical tomography\, inverse ac
oustic/EM scattering\, and travel-time tomography.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Mahoney (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200422T231000Z
DTEND;VALUE=DATE-TIME:20200423T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/2
DESCRIPTION:Title: Determinantal point processes and randomized numerical
linear algebra\nby Michael Mahoney (UC Berkeley) as part of Berkeley appli
ed mathematics seminar\n\n\nAbstract\nRandomized Numerical Linear Algebra
(RandNLA) is an area which uses randomness\, most notably random sampling
and random projection methods\, to develop improved algorithms for ubiquit
ous matrix problems\, such as those that arise in scientific computing\, d
ata science\, machine learning\, etc. A seemingly different topic\, but on
e which has a long history in pure and applied mathematics\, is that of De
terminantal Point Processes (DPPs)\, which are stochastic point processes\
, the probability distribution of which is characterized by sub-determinan
ts of some matrix. Recent work has uncovered deep and fruitful connections
between DPPs and RandNLA. For example\, random sampling with a DPP leads
to new kinds of unbiased estimators for classical RandNLA tasks\, enabling
more refined statistical and inferential understanding of RandNLA algorit
hms\; a DPP is\, in some sense\, an optimal randomized method for many Ran
dNLA problems\; and a standard RandNLA technique\, called leverage score s
ampling\, 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
\, these DPP-based algorithms are only moderately more expensive. Joint wo
rk with Michal Derezinski.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ken Kamrin (MIT)
DTSTART;VALUE=DATE-TIME:20200429T231000Z
DTEND;VALUE=DATE-TIME:20200430T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/3
DESCRIPTION:Title: Toward reduced-order models for flowing grains: Surpris
ing complexity meets surprising simplicity\nby Ken Kamrin (MIT) as part of
Berkeley applied mathematics seminar\n\n\nAbstract\nDespite the commonali
ty of granular materials in day-to-day life\, modeling systems of millions
or more flowing particles has proven historically difficult. This has dir
ect real-world ramifications owing to the prominent role granular media pl
ay in multiple industries and in terrain dynamics. One can attempt to trac
k every grain with discrete particle methods\, but realistic systems are o
ften too large for this approach and a continuum model is desired. However
\, granular media display unusual behaviors that complicate the continuum
treatment: they can behave like solid\, flow like liquid\, or separate int
o a “gas”\, and the rheology of the flowing state displays remarkable
subtleties.\n\nTo address these challenges\, in this talk we develop a fam
ily of continuum models and solvers\, permitting quantitative modeling cap
abilities. We discuss a variety of applications\, ranging from general pro
blems to specific techniques for problems of intrusion\, impact\, driving\
, and locomotion in granular media. To calculate flows in general cases\,
a rather significant nonlocal effect is evident\, which is well-described
with our recent nonlocal model accounting for grain cooperativity within t
he flow rule. On the other hand\, to model only intrusion forces on submer
ged objects\, we will show\, and explain why\, many of the experimentally
observed results can be captured from a much simpler tension-free friction
al plasticity model. This approach gives way to some surprisingly simple g
eneral tools\, including the granular Resistive Force Theory\, and a broad
set of scaling laws inherent to the problem of granular locomotion. These
scalings are validated directly and suggest a new down-scaled paradigm fo
r granular locomotive design\, on earth and beyond\, to be used much like
scaling laws in fluid mechanics.\n\nWe close with a brief discussion of on
going modeling efforts for wet granular systems\, including those with non
-trivial grain-grain interactions and those with highly deformable particl
es.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamara Kolda (Sandia National Laboratory)
DTSTART;VALUE=DATE-TIME:20200506T231000Z
DTEND;VALUE=DATE-TIME:20200507T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/4
DESCRIPTION:Title: Practical leverage-based sampling for low-rank tensor d
ecomposition\nby Tamara Kolda (Sandia National Laboratory) as part of Berk
eley applied mathematics seminar\n\n\nAbstract\nConventional algorithms fo
r finding low-rank canonical polyadic (CP) tensor decompositions are unwie
ldy for large sparse tensors. The CP decomposition can be computed by solv
ing a sequence of overdetermined least problems with special Khatri-Rao st
ructure. In this work\, we present an application of randomized algorithms
to fitting the CP decomposition of sparse tensors\, solving a significant
ly smaller sampled least squares problem at each iteration with probabilis
tic guarantees on the approximation errors. Prior work has shown that sket
ching is effective in the dense case\, but the prior approach cannot be ap
plied to the sparse case because a fast Johnson-Lindenstrauss transform (e
.g.\, using a fast Fourier transform) must be applied in each mode\, causi
ng the sparse tensor to become dense. Instead\, we perform sketching throu
gh leverage score sampling\, crucially relying on the fact that the struct
ure of the Khatri-Rao product allows sampling from overestimates of the le
verage scores without forming the full product or the corresponding probab
ilities. Naïve application of leverage score sampling is infective becaus
e we often 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 efficient and effective. Numerical results on real-world large-scale
tensors show the method is faster than competing methods without sacrific
ing accuracy. This is joint work with Brett Larsen at Stanford University.
\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linfeng Zhang (Princeton University)
DTSTART;VALUE=DATE-TIME:20200513T231000Z
DTEND;VALUE=DATE-TIME:20200514T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/5
DESCRIPTION:Title: Symmetry preserving neural network models for molecular
modelling\nby Linfeng Zhang (Princeton University) as part of Berkeley ap
plied mathematics seminar\n\n\nAbstract\nWe discuss how to leverage the fi
tting ability of neural networks to accurately and efficiently represent t
wo types of maps in molecular modelling problems. The first type takes as
input the coordinates of atoms and their associated chemical species\, and
outputs physical observables such as the interatomic potential energy (a
scalar)\, the electric polarization (a vector) and polarizability (a tenso
r)\, and the charge density (a field). The second type\, like post–Hartr
ee–Fock methods\, uses the ground-state electronic orbitals as the input
\, and predicts the energy difference between results of highly accurate m
odels such as the coupled-cluster method and low accuracy models such as t
he Hartree-Fock (HF) method. Special attentions are paid to how the neural
network models take care of physical properties like symmetry and localit
y\, so that models trained with small-size systems can be transferred to d
ifferent 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 j
oint work with Yixiao Chen\, Han Wang\, and Weinan E.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanhe Huang (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200818T231000Z
DTEND;VALUE=DATE-TIME:20200819T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/6
DESCRIPTION:Title: Axisymmetric bubbles rising in 3D and a new accurate al
gorithm for evaluating orthogonal polynomials\nby Yanhe Huang (UC Berkeley
) as part of Berkeley applied mathematics seminar\n\n\nAbstract\nn the hig
h Reynolds number regime\, under what conditions do there exist steadily r
ising bubbles? This question has been studied extensively both experimenta
lly and numerically\, but current mathematical models and numerical discre
tizations suffer from large numerical errors that make the results less co
nvincing. In the first part of this talk\, we build an inviscid model for
the steady rising problem and find different solution branches of bubble s
hapes characterized by the number of humps. These only exist when there is
no gravity. When there is gravity\, viscous potential flow is used to fin
d different steady shapes. The corresponding dynamic problem is also studi
ed. Techniques such as axisymmetric potential theory\, Hou-Lowengrub-Shell
ey framework\, and weak/hyper-singularity removal are applied to guarantee
spectral accuracy.\n\nDue to the importance of accurate evaluation of ort
hogonal polynomials in the boundary integral method used in the first part
\, in the second part of the talk I will introduce a new way to evaluate o
rthogonal polynomials more accurately near the endpoints of the integratio
n interval. An associated family of orthogonal polynomials is evaluated at
interior points to determine the values of the original polynomials near
endpoints. The new method can achieve round-off error accuracy even for en
d-point evaluation of generic high-degree Jacobi polynomials and generaliz
ed Laguerre polynomials. More accurate quadrature abscissas and weights ca
n be achieved accordingly.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART;VALUE=DATE-TIME:20200826T231000Z
DTEND;VALUE=DATE-TIME:20200827T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/7
DESCRIPTION:Title: Solving Linear Systems of Equations via Randomized Kacz
marz/Stochastic Gradient Descent\nby Stefan Steinerberger (University of W
ashington) as part of Berkeley applied mathematics seminar\n\n\nAbstract\n
The Randomized Kaczmarz method is a classical iterative method to solve li
near systems: the solution of a system Ax = b is simply the point of inter
section of several hyperplanes. The Kaczmarz method (also known as the Pro
jection Onto Convex Sets Method) proceeds by simply starting with a point
and then iteratively projecting it on these hyperplanes. If the hyperplane
s (=rows of the matrix) are picked in random order\, the algorithm was ana
lyzed by Strohmer & Vershynin and has linear convergence. We show that the
method\, as a byproduct\, also computes small singular vectors and\, in f
act\, the iterates tend to approach the true solution from the direction o
f the smallest singular vector in a meta-stable way. This also explains wh
y the algorithm has such wonderful regularization properties. The argument
s are all fairly self-contained\, elementary and nicely geometric. This gi
ves a pretty clear picture – the question is: can this picture be used t
o improve the method?\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Ma (Stanford University)
DTSTART;VALUE=DATE-TIME:20200902T231000Z
DTEND;VALUE=DATE-TIME:20200903T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/8
DESCRIPTION:Title: The Slow Deterioration of the Generalization Error of t
he Random Feature Model\nby Chao Ma (Stanford University) as part of Berke
ley applied mathematics seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weile Jia (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20200909T231000Z
DTEND;VALUE=DATE-TIME:20200910T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/9
DESCRIPTION:Title: HPC+AI: pushing ab initio MD to 100 million atoms on th
e Summit supercomputer\nby Weile Jia (UC Berkeley) as part of Berkeley app
lied mathematics seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Townsend (Cornell University)
DTSTART;VALUE=DATE-TIME:20200916T231000Z
DTEND;VALUE=DATE-TIME:20200917T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/10
DESCRIPTION:Title: The ultraspherical spectral method\nby Alex Townsend (C
ornell University) as part of Berkeley applied mathematics seminar\n\n\nAb
stract\nPseudospectral methods\, based on high degree polynomials\, have s
pectral accuracy when solving differential equations but typically lead to
dense and ill-conditioned matrices. The ultraspherical spectral method is
a numerical technique to solve ordinary and partial differential equation
s\, leading to almost banded well-conditioned linear systems while maintai
ning spectral accuracy. In this talk\, we introduce the ultraspherical spe
ctral method and develop it into a spectral element method using a modific
ation to a hierarchical Poincare-Steklov domain decomposition method.\n
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:20201031T050002Z
UID:BerekelyApplied/11
DESCRIPTION:Title: A computational framework for fluid-structure interacti
on problems\nby Martina Bukac (University of Notre Dame) as part of Berkel
ey applied mathematics seminar\n\n\nAbstract\nFluid-structure interaction
(FSI) problems arise in many applications\, such as aerodynamics\, geomech
anics and hemodynamics. They are moving domain\, multiphysics problems cha
racterized by nonlinear coupling between a fluid and structure. As a resul
t\, FSI problems are challenging to numerically solve and analyze. A popul
ar approach is to solve the fluid and structure sub-problems in a partitio
ned manner\, allowing the use of solvers specifically designed for the phy
sics of each subproblem. However\, stability issues often arise as a resul
t of FSI coupling unless the design and implementation of a partitioned sc
heme is carefully developed. We will present a family of partitioned numer
ical schemes for the interaction between an incompressible\, viscous fluid
and an elastic structure. We will consider cases where the structure is t
hick\, 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-d
imensional model. We will present stability and convergence results\, as w
ell as numerical examples where the presented methods are compared to othe
r methods in the literature.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Childs (University of Maryland)
DTSTART;VALUE=DATE-TIME:20200930T231000Z
DTEND;VALUE=DATE-TIME:20201001T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/12
DESCRIPTION:Title: Symmetries\, graph properties\, and quantum speedups\nb
y Andrew Childs (University of Maryland) as part of Berkeley applied mathe
matics seminar\n\n\nAbstract\nAaronson and Ambainis (2009) and Chailloux (
2018) showed that fully symmetric (partial) functions do not admit exponen
tial quantum query speedups. This raises a natural question: how symmetric
must a function be before it cannot exhibit a large quantum speedup?\n\nI
n 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 c
onstructed out of these symmetries are essentially the only permutation gr
oups that prevent super-polynomial quantum speedups. We prove this by full
y characterizing the primitive permutation groups that allow super-polynom
ial quantum speedups.\n\nIn contrast\, in the adjacency list model for bou
nded-degree graphs (where graph symmetry is manifested differently)\, we e
xhibit a property testing problem that shows an exponential quantum speedu
p. These results resolve open questions posed by Ambainis\, Childs\, and L
iu (2010) and Montanaro and de Wolf (2013).\n\nThis is joint work with Sha
lev Ben-David\, András Gilyén\, William Kretschmer\, Supartha Podder\, a
nd Daochen Wang. https://arxiv.org/abs/2006.12760\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franziska Weber (Carnegie Mellon University)
DTSTART;VALUE=DATE-TIME:20201014T231000Z
DTEND;VALUE=DATE-TIME:20201015T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/13
DESCRIPTION:Title: Numerical approximation of statistical solutions of hyp
erbolic systems of conservation laws\nby Franziska Weber (Carnegie Mellon
University) as part of Berkeley applied mathematics seminar\n\n\nAbstract\
nStatistical solutions are time-parameterized probability measures on spac
es of integrable functions\, which have been proposed recently as a framew
ork for global solutions for multi-dimensional hyperbolic systems of conse
rvation laws. We develop a numerical algorithm to approximate statistical
solutions of conservation laws and show that under the assumption of ‘we
ak statistical scaling’\, which is inspired by Kolmogorov’s 1941 turbu
lence theory\, the approximations converge in an appropriate topology to s
tatistical solutions. Numerical experiments confirm that the assumption mi
ght hold true.\n
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:20201031T050002Z
UID:BerekelyApplied/14
DESCRIPTION:by Rolando Somma (Los Alamos National Laboratory) as part of B
erkeley applied mathematics seminar\n\nAbstract: TBA\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dong An (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20201028T231000Z
DTEND;VALUE=DATE-TIME:20201029T000000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/15
DESCRIPTION:by Dong An (UC Berkeley) as part of Berkeley applied mathemati
cs seminar\n\n\nAbstract\nOriginally discovered by Born and Fock (1928)\,
a quantum mechanical system almost remains in its instantaneous eigenstate
s if the Hamiltonian varies sufficiently slowly and there is a gap between
the eigenvalue and the rest of the Hamiltonian’s spectrum. Such a syste
m is said to be a quantum adiabatic evolution\, and has become a powerful
tool for analyzing quantum dynamics and designing fast classical and quant
um algorithms. In this talk\, I will first discuss the mathematical formul
ation of quantum adiabatic evolutions\, namely quantum adiabatic theorem.
Several versions of the theorem will be discussed\, with a focus on the fa
ctors that might significantly influence the adiabaticity. Then I will pre
sent two applications of the adiabatic evolutions and adiabatic theorems.
One is accelerating numerical simulation of Schrodinger equations on class
ical computers\, and the other is a quantum algorithm for solving linear s
ystem of equations with near optimal complexity on a quantum computer.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaochuan Tian (UCSD)
DTSTART;VALUE=DATE-TIME:20201105T001000Z
DTEND;VALUE=DATE-TIME:20201105T010000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/16
DESCRIPTION:by Xiaochuan Tian (UCSD) as part of Berkeley applied mathemati
cs seminar\n\nInteractive livestream: https://berkeley.zoom.us/j/186935273
\nAbstract: TBA\n
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiequn Han (Princeton University)
DTSTART;VALUE=DATE-TIME:20201112T001000Z
DTEND;VALUE=DATE-TIME:20201112T010000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/17
DESCRIPTION:by Jiequn Han (Princeton University) as part of Berkeley appli
ed mathematics seminar\n\nInteractive livestream: https://berkeley.zoom.us
/j/186935273\nAbstract: TBA\n
URL:https://berkeley.zoom.us/j/186935273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Webber (Courant Institute)
DTSTART;VALUE=DATE-TIME:20201203T001000Z
DTEND;VALUE=DATE-TIME:20201203T010000Z
DTSTAMP;VALUE=DATE-TIME:20201031T050002Z
UID:BerekelyApplied/18
DESCRIPTION:by Robert Webber (Courant Institute) as part of Berkeley appli
ed mathematics seminar\n\nInteractive livestream: https://berkeley.zoom.us
/j/186935273\nAbstract: TBA\n
URL:https://berkeley.zoom.us/j/186935273
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:20201031T050002Z
UID:BerekelyApplied/19
DESCRIPTION:Title: Persistent Homology Advances Interpretable Machine Lear
ning for Scientific Applications\nby Aditi Krishnapriyan (Lawrence Berkele
y National Lab) as part of Berkeley applied mathematics seminar\n\n\nAbstr
act\nMachine learning for scientific applications\, ranging from physics a
nd materials science to biology\, has emerged as a promising alternative t
o more time-consuming experiments and simulations. The challenge with this
approach is the selection of features that enable universal and interpret
able system representations across multiple prediction tasks. We use persi
stent homology to construct holistic feature representations to describe t
he structure of scientific systems\; for example\, material and protein st
ructures. We show that these representations can also be augmented with ot
her generic features to capture further information. We demonstrate our ap
proaches on multiple scientific datasets by predicting a variety of differ
ent targets across different conditions. Our results show considerable imp
rovement in both accuracy and transferability across targets compared to m
odels constructed from commonly used manually curated features. A key adva
ntage of our approach is interpretability. For example\, in material struc
tures\, our persistent homology features allow us to identify the location
and size of pores in the structure that correlate best to different mater
ials properties\, contributing to understanding atomic level structure-pro
perty relationships for materials design.\n
END:VEVENT
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