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BEGIN:VEVENT
SUMMARY:David Williams (Penn State University)
DTSTART;VALUE=DATE-TIME:20221104T223000Z
DTEND;VALUE=DATE-TIME:20221104T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/2
DESCRIPTION:Title: Space-Time Finite Element Methods: Challenges and Perspectives\nby
David Williams (Penn State University) as part of SFU Mathematics of Comp
utation\, Application and Data ("MOCAD") Seminar\n\nLecture held in K9509.
\n\nAbstract\nSpace-time finite element methods (FEMs) are likely to grow
in popularity due to the ongoing growth in the size\, speed\, and parallel
ism of modern computing platforms. The allure of space-time FEMs is both i
ntuitive and practical. From the intuitive standpoint\, there is considera
ble elegance and simplicity in accommodating both space and time using the
same numerical discretization strategy. From the practical standpoint\, t
here are considerable advantages in efficiency and accuracy that can be ga
ined from space-time mesh adaptation: i.e. adapting the mesh in both space
and time to resolve important solution features. However\, despite these
considerable advantages\, there are numerous challenges that must be overc
ome before space-time FEMs can realize their full potential. These challen
ges are primarily associated with four-dimensional geometric obstacles (hy
persurface and hypervolume mesh generation)\, four-dimensional approximati
on theory (basis functions and quadrature rules)\, four-dimensional bounda
ry condition enforcement (well-posed\, moving boundary conditions)\, and i
terative-solution techniques for large-scale linear systems. In this prese
ntation\, we will provide a brief overview of space-time FEMs\, and discus
s some of the latest research developments and ongoing issues.\n\nDavid M.
Williams is an assistant professor at The Pennsylvania State University i
n the Mechanical Engineering Department. He came to Penn State from the Fl
ight Sciences division of Boeing Commercial Airplanes and Boeing Research
and Technology\, where he worked for several years as a computational flui
d dynamics engineer. Williams received his M.S. and Ph. D. in Aeronautics
and Astronautics at Stanford University. He holds a B.S.E. in Aerospace En
gineering from the University of Michigan. He has made significant advance
s in the design of numerical algorithms for computational fluid dynamic si
mulations. Currently\, his research focuses on employing high-order Finite
Element schemes to more accurately predict unsteady flows.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Messenger (University of Colorado Boulder)
DTSTART;VALUE=DATE-TIME:20221007T223000Z
DTEND;VALUE=DATE-TIME:20221007T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/4
DESCRIPTION:Title: Weak-form sparse identification of differential equations from noisy m
easurements\nby Daniel Messenger (University of Colorado Boulder) as p
art of SFU Mathematics of Computation\, Application and Data ("MOCAD") Sem
inar\n\nLecture held in K9509.\n\nAbstract\nData-driven modeling refers to
the use of measurement data to infer the parameters and structure of a ma
thematical model\, or to aid in forward simulations of a partially known m
athematical model. Motivated by problems in collective cell biology\, this
talk will explore algorithms which automate the map from experimental dat
a to governing differential equations\, specifically using weak formulatio
ns of the dynamics. We will show that the weak form is an ideal framework
for identifying models from data if the performance criteria are robustnes
s to data corruptions\, highly accurate model recovery when corruption lev
els are low\, and computational efficiency. We will first demonstrate the
advantages of the resulting weak-form sparse identification for nonlinear
dynamics algorithm (WSINDy) in the discovery of correct underlying model e
quations across several key modeling paradigms\, including ordinary differ
ential equations (ODEs)\, partial differential equations (PDEs)\, and inte
racting particle systems (IPS). We will then discuss more recent extension
s of this framework\, including weak-form identification of PDEs from stre
aming data\, enabling identification of time-varying coefficients\, and th
e use of weak-form model selection as a classifier to determine species me
mbership in a heterogeneous population of initially unlabeled cells. We wi
ll conclude with an overview of possible next directions\, including open
questions related to numerical analysis and theoretical recovery guarantee
s.\n\nPasscode 696604\n
LOCATION:https://researchseminars.org/talk/AppliedMath/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hansol Park (SFU)
DTSTART;VALUE=DATE-TIME:20221014T223000Z
DTEND;VALUE=DATE-TIME:20221014T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/5
DESCRIPTION:Title: The Watanabe-Strogatz transform and constant of motion functionals for
kinetic vector models\nby Hansol Park (SFU) as part of SFU Mathematic
s of Computation\, Application and Data ("MOCAD") Seminar\n\n\nAbstract\nW
e present a kinetic version of the Watanabe-Strogatz (WS) transform for ve
ctor models in this paper. From the generalized WS-transform\, we can redu
ce the kinetic vector model into an ODE system. We also obtain the cross-r
atio type constant of motion functionals for kinetic vector models under s
uitable conditions. We present the sufficient and necessary conditions for
the existence of the suggested constant of motion functionals. As an appl
ication of the constant of motion functional\, we provide the instability
of bipolar states of the kinetic swarm sphere model. We also provide the W
S-transform and constant of motion functionals for non-identical kinetic v
ector models.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Solomon (MIT)
DTSTART;VALUE=DATE-TIME:20221021T220000Z
DTEND;VALUE=DATE-TIME:20221021T230000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/6
DESCRIPTION:Title: Volumetric Methods for Modeling\, Deformation\, and Correspondence
\nby Justin Solomon (MIT) as part of SFU Mathematics of Computation\, Appl
ication and Data ("MOCAD") Seminar\n\n\nAbstract\nIn 3D modeling\, medical
imaging\, and other disciplines\, popular techniques for geometry process
ing often rely on mathematical models for surface geometry\, viewing shape
s as thin sheets embedded in $\\mathbb{R}^3$\; this construction neglects
the fact that many of these surfaces are "boundary representations\," inte
nded to represent boundaries of volumes. As an alternative\, in this talk
we will explore how calculations on the extrinsic space around a surface
can benefit geometry processing applications---as well as the mathematical
\, numerical\, and computational challenges of this extension to three dim
ensions. Our algorithms for these problems will build on machinery from d
ifferential geometry\, geometric measure theory\, vector field design\, an
d machine learning.\n\n(Joint work with several members of the MIT Geometr
ic Data Processing Group.)\n
LOCATION:https://researchseminars.org/talk/AppliedMath/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Wiedemann (Universitaet Augsburg)
DTSTART;VALUE=DATE-TIME:20220916T223000Z
DTEND;VALUE=DATE-TIME:20220917T000000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/11
DESCRIPTION:Title: Homogenization in evolving porous media\nby David Wiedemann (Univ
ersitaet Augsburg) as part of SFU Mathematics of Computation\, Application
and Data ("MOCAD") Seminar\n\n\nAbstract\nNumerical simulations of physic
al or chemical processes in heterogeneous \nmedia require a resolution of
the heterogeneous structure. If\, however\, \nthis heterogeneity is micros
copically small while the object under \nconsideration is large\, a dimens
ional mismatch occurs and classical \nnumerical methods become infeasible.
\n\nAt this point\, analytical homogenization provides effective homogeneo
us \nsubstitute models\, which can be simulated numerically much more easi
ly. \nOne class of problems that can be treated are processes in porous me
dia. \nIn many biological or chemical applications\, the pore structure ev
olves \nin time\, which impedes classical homogenization. By means of the
\ntwo-scale transformation method\, we can overcome this difficulty and \n
derive new effective models for problems in evolving heterogeneous media.\
n
LOCATION:https://researchseminars.org/talk/AppliedMath/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingwei Hu (University of Washington)
DTSTART;VALUE=DATE-TIME:20220923T223000Z
DTEND;VALUE=DATE-TIME:20220924T000000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/12
DESCRIPTION:Title: Dynamical low-rank methods for high-dimensional collisional kinetic e
quations\nby Jingwei Hu (University of Washington) as part of SFU Math
ematics of Computation\, Application and Data ("MOCAD") Seminar\n\n\nAbstr
act\nKinetic equations describe the nonequilibrium dynamics of a complex s
ystem using a probability density function. Despite of their important rol
e in multiscale modeling to bridge microscopic and macroscopic scales\, nu
merically solving kinetic equations is computationally demanding as they l
ie in the six-dimensional phase space. Dynamical low-rank method is a dime
nsion-reduction technique that has been recently applied to kinetic theory
\, yet most of the endeavor is devoted to linear or collisionless problems
. In this talk\, we introduce efficient dynamical low-rank methods for Bol
tzmann type collisional kinetic equations\, building on certain prior know
ledge about the low-rank structure of the solution.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Iwen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20221207T233000Z
DTEND;VALUE=DATE-TIME:20221208T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/15
DESCRIPTION:Title: Low-Distortion Embeddings of Submanifolds of $R^n$: Lower Bounds\, Fa
ster Realizations\, and Applications\nby Mark Iwen (Michigan State Uni
versity) as part of SFU Mathematics of Computation\, Application and Data
("MOCAD") Seminar\n\nLecture held in ASB10908.\n\nAbstract\nLet M be a smo
oth submanifold of R^n equipped with the Euclidean(chordal) metric. This t
alk will consider the smallest dimension\, m\, for which there exists a bi
-Lipschitz function f:M →R^m with bi-Lipschitz constants close to one. W
e will begin by presenting a bound for the embedding dimension m from belo
w in terms of the bi-Lipschitz constants of f and the reach\, volume\, dia
meter\, and dimension of M. We will then discuss how this lower bound can
be applied to show that prior upper bounds by Eftekhari and Wakin on the m
inimal low-distortion embedding dimension of such manifolds using random m
atrices achieve near-optimal dependence on dimension\, reach\, and volume
(even when compared against nonlinear competitors). Next\, we will discuss
a new class of linear maps for embedding arbitrary (infinite) subsets of
R^n with sufficiently small Gaussian width which can both (i) achieve near
-optimal embedding dimensions of submanifolds\, and (ii) be multiplied by
vectors in faster than FFT-time. When applied to d-dimensional submanifold
s of R^n we will see that these new constructions improve on prior fast em
bedding matrices in terms of both runtime and embedding dimension when d i
s sufficiently small. Time permitting\, we will then conclude with a discu
ssion of non-linear so-called “terminal embeddings” of manifolds which
allow for extensions of the famous Johnson-Lindenstrauss Lemma beyond wha
t any linear map can achieve.\n\nThis talk will draw on joint work with va
rious subsets of Mark Roach (MSU)\, Benjamin Schmidt (MSU)\, and Arman Tav
akoli (MSU).\n
LOCATION:https://researchseminars.org/talk/AppliedMath/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Corless (University of Western Ontario)
DTSTART;VALUE=DATE-TIME:20221012T223000Z
DTEND;VALUE=DATE-TIME:20221012T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/16
DESCRIPTION:Title: Compact cubic splines and compact finite differences\nby Robert C
orless (University of Western Ontario) as part of SFU Mathematics of Compu
tation\, Application and Data ("MOCAD") Seminar\n\nLecture held in K9509.\
n\nAbstract\nIn this paper we introduce an apparently new spline-like inte
rpolant that we call a compact cubic interpolant or compact cubic spline\;
this is similar to a cubic spline introduced in 1972 by Swartz and Varga\
, but has higher order accuracy at the edges. We argue that for nearly uni
form meshes the compact cubic approach offers some potential advantages\,
and offers a simple way to treat the edge conditions\, relieving the user
of the burden of deciding to use one of the three standard options: free (
natural)\, complete (clamped)\, or “not-a-knot” conditions. Finally\,
we establish that the matrices defining the compact cubic splines (equival
ently\, the fourth-order compact finite difference formulæ) are totally n
onnegative\, if all mesh widths are the same sign\, for instance if the me
sh is real and nodes are numbered in increasing order.\n\nThe talk will be
in-person and use chalk\, in the wonderful multi-board room that SFU has
for the purpose. The YouTube version linked above was a computer version
of the same talk\, with slides\, which has some advantages (run it at doub
le speed!). But the chalk version offers a chance to slow down and apprec
iate more of the "big picture". The topic will be accessible if the liste
ner has heard what a "spline" is\, but the main point is to prove total no
nnegativity of a certain tridiagonal matrix. I'll also make a connection
to the (very useful) subject of compact finite differences.\n\nThis is joi
nt work with Dr. Leili Rafiee Sevyeri (CS University of Waterloo)\n
LOCATION:https://researchseminars.org/talk/AppliedMath/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20230106T233000Z
DTEND;VALUE=DATE-TIME:20230107T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/18
DESCRIPTION:by TBA as part of SFU Mathematics of Computation\, Application
and Data ("MOCAD") Seminar\n\nLecture held in K9509.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruiwen Shu (University of Georgia)
DTSTART;VALUE=DATE-TIME:20230120T233000Z
DTEND;VALUE=DATE-TIME:20230121T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/19
DESCRIPTION:Title: Global Minimizers of a Large Class of Anisotropic Attractive-Repulsiv
e Interaction Energies in 2D\nby Ruiwen Shu (University of Georgia) as
part of SFU Mathematics of Computation\, Application and Data ("MOCAD") S
eminar\n\n\nAbstract\nI will discuss my joint work with José Carrillo on
a large family of Riesz-type singular interaction potentials with anisotro
py in two dimensions. Their associated global energy minimizers are given
by explicit formulas whose supports are determined by ellipses under certa
in assumptions. More precisely\, by parameterizing the strength of the ani
sotropic part we characterize the sharp range in which these explicit elli
pse-supported configurations are the global minimizers based on linear con
vexity arguments. Moreover\, for certain anisotropic parts\, we prove that
for large values of the parameter the global minimizer is only given by v
ertically concentrated measures corresponding to one dimensional minimizer
s. We also show that these ellipse-supported configurations generically do
not collapse to a vertically concentrated measure at the critical value f
or convexity\, leading to an interesting gap of the parameters in between.
In this intermediate range\, we conclude by infinitesimal concavity that
any superlevel set of any local minimizer in a suitable sense does not hav
e interior points. Furthermore\, for certain anisotropic parts\, their sup
port cannot contain any vertical segment for a restricted range of paramet
ers\, and moreover the global minimizers are expected to exhibit a zigzag
behavior. All these results hold for the limiting case of the logarithmic
repulsive potential\, extending and generalizing previous results in the l
iterature.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matias Delgadino (UT Austin)
DTSTART;VALUE=DATE-TIME:20230217T233000Z
DTEND;VALUE=DATE-TIME:20230218T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/24
DESCRIPTION:Title: Phase transitions and log Sobolev inequalities\nby Matias Delgadi
no (UT Austin) as part of SFU Mathematics of Computation\, Application and
Data ("MOCAD") Seminar\n\nLecture held in Remote.\n\nAbstract\nIn this ta
lk\, we will study the mean field limit of weakly interacting diffusions f
or confining and interaction potentials that are not necessarily convex. W
e explore the relationship between the large N limit of the constant in th
e logarithmic Sobolev inequality (LSI) for the N-particle system\, and the
presence or absence of phase transitions for the mean field limit. The no
n-degeneracy of the LSI constant will be shown to have far reaching conseq
uences\, especially in the context of uniform-in-time propagation of chaos
and the behaviour of equilibrium fluctuations. This will be done by emplo
ying techniques from the theory of gradient flows in the 2-Wasserstein dis
tance\, specifically the Riemannian calculus on the space of probability m
easures.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Pia Gualdani (UT Austin)
DTSTART;VALUE=DATE-TIME:20230314T223000Z
DTEND;VALUE=DATE-TIME:20230314T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/27
DESCRIPTION:Title: Recent progresses in kinetic equations.\nby Maria Pia Gualdani (U
T Austin) as part of SFU Mathematics of Computation\, Application and Data
("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\nWe will discuss
recent mathematical results for the Landau and Boltzmann equation. Kineti
c equations are used to describe evolution of interacting particles. The m
ost famous kinetic equation is the Boltzmann equation: formulated by Ludwi
g Boltzmann in 1872\, this equation describes motion of a large class of g
ases. Later\, in 1936\, Lev Landau derived a new mathematical model for mo
tion of plasma. This latter equation was named the Landau equation. While
many important questions are still partially unanswered due to their mathe
matical complexity\, many others have been solved thanks to novel combinat
ions of analytical techniques\, in particular the ones developed by Hoerma
nder\, J. Nash\, E. De Giorgi and Moser.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan King (The Cheriton School of Computer Science\, University
of Waterloo)
DTSTART;VALUE=DATE-TIME:20230324T223000Z
DTEND;VALUE=DATE-TIME:20230324T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/28
DESCRIPTION:Title: A Closest Point Method with Interior Boundary Conditions for Geometry
Processing\nby Nathan King (The Cheriton School of Computer Science\,
University of Waterloo) as part of SFU Mathematics of Computation\, Appli
cation and Data ("MOCAD") Seminar\n\nLecture held in AQ5008.\n\nAbstract\n
Many geometry processing tasks can be performed by solving partial differe
ntial equations (PDEs) on surfaces. These PDEs usually involve boundary co
nditions (e.g.\, Dirichlet or Neumann) defined anywhere on the surface\, n
ot just on the physical (exterior) boundary of an open surface. This talk
discusses how to handle BCs on the interior of a surface while solving PDE
s with the closest point method (CPM).\n\nThe CPM is an embedding method\,
i.e.\, it solves the surface PDE by solving a PDE defined in a space surr
ounding the surface. The PDE is commonly solved using standard Cartesian n
umerical methods (e.g.\, finite-differences and Lagrange interpolation). C
omplex surfaces with high-curvatures and/or thin regions impose restrictio
ns on the size of the embedding space. Therefore\, for complex surfaces\,
fine resolution grids must be used to fit within the embedding space. We d
evelop a matrix-free solver that can scale to millions of degrees of freed
om to allow for PDEs to be solved on complex shapes.\n\nOur use of a close
st point surface representation provides a general framework to handle any
surface that allows closest point computation\, e.g.\, parametrizations\,
point clouds\, level-sets\, neural implicits\, etc. The surface can be op
en or closed\, orientable or not\, of any codimension\, and even mixed-cod
imension. Therefore\, the approach presented provides a general framework
for geometry processing on complex surfaces given by general surface repre
sentations.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleks Donev (Courant Institute\, NYU)
DTSTART;VALUE=DATE-TIME:20230519T223000Z
DTEND;VALUE=DATE-TIME:20230519T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/32
DESCRIPTION:Title: Hydrodynamics and rheology of fluctuating\, semiflexible\, inextensib
le\, and slender filaments in Stokes flow\nby Aleks Donev (Courant Ins
titute\, NYU) as part of SFU Mathematics of Computation\, Application and
Data ("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\nEvery animal
cell is filled with a cytoskeleton\, a dynamic gel made of inextensible f
ilaments / bio-polymers\, such as microtubules\, actin filaments\, and int
ermediate filaments\, all suspended in a viscous fluid. Similar suspension
s of elastic filaments or polymers are widely used in materials processing
. Numerical simulation of such gels is challenging because the filament as
pect ratios are very large.\n\nWe have recently developed new methods for
rapidly computing the dynamics of non-Brownian and Brownian inextensible s
lender filaments in periodically-sheared Stokes flow [1\,2\,4]. We apply o
ur formulation to a permanently1 and dynamically cross-linked actin mesh3
in a background oscillatory shear flow. We find that nonlocal hydrodynamic
s can change the visco-elastic moduli by as much as 40% at certain frequen
cies\, especially in partially bundled networks [3\,4].\n\nI will focus on
accounting for bending thermal fluctuations of the filaments by first est
ablishing a mathematical formulation and numerical methods for simulating
the dynamics of stiff but not rigid Brownian fibers in Stokes flow [4]. I
will emphasize open questions for the community such as whether there is a
continuum limit of the Brownian contribution to the stress tensor from th
e filaments.\n\nThis is joint work with Ondrej Maxian and Brennan Sprinkle
.\n\nReferences:\n\n1. O. Maxian et al\, Integral-based spectral method fo
r inextensible slender fibers in Stokes flow\,. Phys. Rev. Fluids\, 6:0141
02\, 2021\n2. O. Maxian et al\,. Hydrodynamics of a twisting\, bending\, i
nextensible fiber in Stokes flow\, Phys. Rev. Fluids\, 7:074101\, 2022\n3.
O. Maxian et al\, Interplay between Brownian motion and cross-linking con
trols bundling dynamics in actin networks\, Biophysical J.\, 121:1230–12
45\, 2022.\n4. O. Maxian et al.\, Bending fluctuations in semiflexible\, i
nextensible\, slender filaments in Stokes flow: towards a spectral discret
ization\, ArXiv:2301.11123\, to appear in J. Chem. Phys.\, 2023.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anotida Madzvamuse (UBC)
DTSTART;VALUE=DATE-TIME:20230922T223000Z
DTEND;VALUE=DATE-TIME:20230922T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/33
DESCRIPTION:Title: Image-based modelling using geometric surface PDEs for single and col
lective cell migration\nby Anotida Madzvamuse (UBC) as part of SFU Mat
hematics of Computation\, Application and Data ("MOCAD") Seminar\n\nLectur
e held in K9509.\n\nAbstract\nIn this lecture\, I will focus on formulatin
g a dynamical geometric surface partial differential equation for modellin
g static images during the process of single or collective\ncell migration
. In the absence of detailed experimental molecular and mechanical observa
tions\,\na question asked by experimentalists is: Given a sequence of imag
es following\nsingle or collective cell migration\, is there an optimal dy
namic mathematical model that evolves static images at one time point into
static images at a later time point? I will employ both sharp- and diffus
e-interface formulations based on phase-fields for geometric surface parti
al differential equations to derive a dynamical spatiotemporal model for t
he migration of cells in 2- and 3-D. The model is solved efficiently using
novel high performance computing techniques based on finite differences\,
and multi-grid methods. Such an approach\nallows us to solve in realistic
times\, 2- and 3-D computations which are otherwise unfeasible\nwithout s
uch innovative numerical analysis computing strategies. To demonstrate the
\napplicability of the computational algorithm\, cell migration forces suc
h as polarisation\nwill be exhibited. A by-product of the computational al
gorithm is its ability to quantify\nautomatically cell proliferation rates
which are generally obtained through cumbersome\nand error-prone manual c
ounting.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miranda Holmes-Cerfon (UBC)
DTSTART;VALUE=DATE-TIME:20231027T223000Z
DTEND;VALUE=DATE-TIME:20231027T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/34
DESCRIPTION:Title: Numerically simulating particles with short-ranged interactions\n
by Miranda Holmes-Cerfon (UBC) as part of SFU Mathematics of Computation\,
Application and Data ("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstr
act\nParticles with diameters of nanometres to micrometres form the buildi
ng blocks of many of the materials around us\, and can be designed in a mu
ltitude of ways to form new ones. Such particles commonly live in fluids\,
where they jiggle about randomly because of thermal fluctuations in the f
luid\, and interact with each other via numerous mechanisms. One challenge
in simulating such particles is that the range over which they interact a
ttractively is often much shorter than their diameters\, so the equations
describing the particles’ dynamics are stiff\, requiring timesteps much
smaller than the timescales of interest. I will introduce methods to accel
erate these simulations\, which instead solve the limiting equations as th
e range of the attractive interaction goes to zero. In this limit a system
of particles is described by a diffusion process on a collection of manif
olds of different dimensions\, connected by “sticky” boundary conditio
ns. I will describe our progress in simulating low-dimensional sticky diff
usion processes\, explain how these algorithms give us insight into sticky
diffusions’ unusual mathematical properties\, and then discuss some ong
oing challenges such as extending these methods to high dimensions\, incor
porating friction and hydrodynamic interactions\, and capturing the anomal
ous diffusion that is sometimes observed experimentally.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blaise Bourdin (McMaster University)
DTSTART;VALUE=DATE-TIME:20231103T223000Z
DTEND;VALUE=DATE-TIME:20231103T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/35
DESCRIPTION:Title: Recent developments in variational and phase-field models of brittle
fracture\nby Blaise Bourdin (McMaster University) as part of SFU Mathe
matics of Computation\, Application and Data ("MOCAD") Seminar\n\nLecture
held in K9509.\n\nAbstract\nVariational phase-field models of fracture hav
e been at the center of a multidisciplinary effort involving a large commu
nity of mathematicians\, mechanicians\, engineers\, and computational scie
ntists over the last 25 years or so. I will start with a modern interpreta
tion of Griffith's classical criterion as a variational principle for a fr
ee discontinuity energy and will recall some of the milestones in its anal
ysis. Then\, I will introduce the phase-field approximation per se and des
cribe its numerical implementation. I illustrate how phase-field models ha
ve led to major breakthroughs in the predictive simulation of fracture in
complex situations. I then will turn my attention to current issues\, incl
uding crack nucleation in nominally brittle materials\, fracture of hetero
geneous materials\, and inverse problems.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Smith (Yale-NUS College)
DTSTART;VALUE=DATE-TIME:20230929T223000Z
DTEND;VALUE=DATE-TIME:20230929T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/36
DESCRIPTION:Title: Fokas Diagonalization\nby David Smith (Yale-NUS College) as part
of SFU Mathematics of Computation\, Application and Data ("MOCAD") Seminar
\n\nLecture held in K9509.\n\nAbstract\nWe describe a new form of diagonal
ization for linear two point constant coefficient differential operators w
ith arbitrary linear boundary conditions. Although the diagonalization is
in a weaker sense than that usually employed to solve initial boundary val
ue problems (IBVP)\, we show that it is sufficient to solve IBVP whose spa
tial parts are described by such operators. We argue that the method descr
ibed may be viewed as a reimplementation of the Fokas transform method for
linear evolution equations on the finite interval. The results are extend
ed to multipoint and interface operators\, including operators defined on
networks of finite intervals\, in which the coefficients of the differenti
al operator may vary between subintervals\, and arbitrary interface and bo
undary conditions may be imposed\; differential operators with piecewise c
onstant coefficients are thus included.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Argyrios Petras (Johann Radon Institute for Computational and Appl
ied Mathematics)
DTSTART;VALUE=DATE-TIME:20231011T223000Z
DTEND;VALUE=DATE-TIME:20231011T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/37
DESCRIPTION:Title: Numerical methods for the solution of PDEs on static and moving surfa
ces\nby Argyrios Petras (Johann Radon Institute for Computational and
Applied Mathematics) as part of SFU Mathematics of Computation\, Applicati
on and Data ("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\nParti
al differential equations (PDEs) on surfaces arise throughout the natural
and applied sciences. The solution of such equations poses a big challenge
for rather general surfaces\, where no parametrization is possible. In th
is talk\, we will give an overview of some methods that are based on the c
losest point concept and use finite difference stencils based on radial ba
sis functions (RBF-FD).\n
LOCATION:https://researchseminars.org/talk/AppliedMath/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephanie Ross (University of Calgary)
DTSTART;VALUE=DATE-TIME:20231020T223000Z
DTEND;VALUE=DATE-TIME:20231020T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/38
DESCRIPTION:Title: A multimodal approach to understanding skeletal muscle mechanics in h
ealth and disease\nby Stephanie Ross (University of Calgary) as part o
f SFU Mathematics of Computation\, Application and Data ("MOCAD") Seminar\
n\nLecture held in K9509.\n\nAbstract\nSkeletal muscle is the motor that d
rives human and animal movement\; however\, our understanding of how muscl
e performs this function is limited because of challenges in directly meas
uring muscle deformation and force output in living beings. In this talk\,
I will share my previous work using continuum models of muscle and comple
mentary experimental measures to determine the mechanisms underlying skele
tal muscle function. I will then present my current research that extends
on this fundamental work to probe how changes in the material properties o
f muscle with diseases such as stroke and cerebral palsy impact muscle fun
ction and mobility.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Ortner (UBC)
DTSTART;VALUE=DATE-TIME:20231006T223000Z
DTEND;VALUE=DATE-TIME:20231006T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/39
DESCRIPTION:Title: Geometric Shallow Learning with the Atomic Cluster Expansion (or\, Ef
ficient Parameterization of Many-body Interaction)\nby Christoph Ortne
r (UBC) as part of SFU Mathematics of Computation\, Application and Data (
"MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\nAlthough my talk i
s arguably about machine-learning\, I will use mostly ideas and language f
rom mathematical modelling and numerical analysis. I will introduce a natu
ral geometric learning framework\, the atomic cluster expansion (ACE)\, w
hich focuses on linear and shallow models\, and adds a new dimension to th
e design space of geometric deep learning. ACE is particularly well-suited
for parameterising surrogate models of particle systems where it is impor
tant to incorporate symmetries and geometric priors into models without sa
crificing systematic improvability.\nMy main focus will be on “learning
” interatomic potentials (or\, force fields): in this context\, ACE mode
ls arise naturally from a few systematic modelling and approximation theor
etic steps that can be made reasonably rigorous.\nHowever\, the applicabil
ity is much broader and\, time permitting\, I will also show how the ACE f
ramework can be adapted to other contexts such as electronic structure (pa
rameterising Hamiltonians)\, quantum chemistry (wave functions)\, or eleme
ntary particle physics (e.g.\, jet tagging).\n
LOCATION:https://researchseminars.org/talk/AppliedMath/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Stechmann (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20240306T233000Z
DTEND;VALUE=DATE-TIME:20240307T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/40
DESCRIPTION:Title: Element learning: a systematic approach of accelerating finite elemen
t-type methods via machine learning\nby Sam Stechmann (University of W
isconsin-Madison) as part of SFU Mathematics of Computation\, Application
and Data ("MOCAD") Seminar\n\nLecture held in SFU K9509.\n\nAbstract\nIn t
he past decade\, (artificial) neural networks and machine learning tools h
ave surfaced as game changing technologies across numerous fields\, resolv
ing an array of challenging problems. Even for the numerical solution of p
artial differential equations (PDEs) or other scientific computing problem
s\, results have shown that machine learning can speed up some computation
s. However\, many machine learning approaches tend to lose some of the adv
antageous features of traditional numerical PDE methods\, such as interpre
tability and applicability to general domains with complex geometry.\n\nIn
this talk\, we introduce a systematic approach (which we call element lea
rning) with the goal of accelerating finite element-type methods via machi
ne learning\, while also retaining the desirable features of finite elemen
t methods. The derivation of this new approach is closely related to hybri
dizable discontinuous Galerkin (HDG) methods in the sense that the local s
olvers of HDG are replaced by machine learning approaches. Numerical tests
are presented for an example PDE\, the radiative transfer equation\, in a
variety of scenarios with idealized or realistic cloud fields\, with smoo
th or sharp gradient in the cloud boundary transition. Comparisons are set
up with either a fixed number of degrees of freedom or a fixed accuracy l
evel of $10^{-3}$ in the relative $L^2$ error\, and we observe a significa
nt speed-up with element learning compared to a classical finite element-t
ype method.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Cheung (NVIDIA)
DTSTART;VALUE=DATE-TIME:20231023T223000Z
DTEND;VALUE=DATE-TIME:20231023T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/41
DESCRIPTION:Title: Generative AI and AI for Science and Mathematics\nby Charles Cheu
ng (NVIDIA) as part of SFU Mathematics of Computation\, Application and Da
ta ("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\nIn this talk\,
I will talk about a few directions and use cases of recent Generative AI
development for metaverse and science. In the second part of the talk\, I
will talk about PINNs and neural operator that have been used for solving
many engineering problems that involves differential equations with neural
network. We will walk through the basic concept of PINNs and neural opera
tor and introduce NVIDIA modulus\, an SDK for training PINNs and neural op
erator.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chunyi Gai (UBC)
DTSTART;VALUE=DATE-TIME:20231121T233000Z
DTEND;VALUE=DATE-TIME:20231122T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/42
DESCRIPTION:Title: Pattern formation and Spike Dynamics in the Presence of Noise\nby
Chunyi Gai (UBC) as part of SFU Mathematics of Computation\, Application
and Data ("MOCAD") Seminar\n\nLecture held in ASB10908.\n\nAbstract\nNoise
plays a crucial role in the formation and evolution of spatial patterns i
n various reaction-diffusion systems in mathematical biology and ecology.
In this talk\, I give two examples where noise significantly influences sp
atial patterning. The first example describes how patterned states can pr
ovide a refuge and prevent extinction under stressed conditions. It also i
llustrates the importance of not only the absolute level of climate change
\, but also the speed with which it occurs. The second example studies the
effect of noise on dynamics of a single spike pattern for the classical G
ierer--Meinhardt model on a finite interval.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liam Madden (UBC)
DTSTART;VALUE=DATE-TIME:20240126T233000Z
DTEND;VALUE=DATE-TIME:20240127T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/43
DESCRIPTION:Title: Memory capacity of two-layer neural networks\nby Liam Madden (UBC
) as part of SFU Mathematics of Computation\, Application and Data ("MOCAD
") Seminar\n\nLecture held in K9509.\n\nAbstract\nThe memory capacity of a
statistical model is the largest size of generic data that the model can
memorize and has important implications for both training and generalizati
on. In this talk\, we will prove a tight memory capacity result for two-la
yer neural networks with general activations. In order to do so\, we will
use tools from linear algebra\, combinatorics\, differential topology\, an
d the theory of real analytic functions of several variables. In particula
r\, we will show how to get memorization if the model is a local submersio
n and we will show that the Jacobian has generically full rank. The perspe
ctive that is developed also opens up a path towards deeper architectures\
, alternative models\, and training.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hansol Park (SFU)
DTSTART;VALUE=DATE-TIME:20231201T233000Z
DTEND;VALUE=DATE-TIME:20231202T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/44
DESCRIPTION:Title: Emergent behavior of mathematical models on manifolds\nby Hansol
Park (SFU) as part of SFU Mathematics of Computation\, Application and Dat
a ("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\nIn this talk\,
I introduce several first- and second-order models for self-collective beh
aviour on general manifolds and discuss their emergent behaviors. For the
first-order model\, we consider attractive-repulsive and purely attractive
interaction potentials\, and investigate the equilibria and the asymptoti
c behaviour of the solutions. In particular\, we quantify the approach to
asymptotic consensus in terms of the convergence rate of the diameter of t
he solution’s support. For the second-order model (known as the Cucker-S
male model)\, velocity alignment interactions are considered. To analyze t
he emergent behaviors of the two models\, the LaSalle invariance principle
is used. Also\, various geometric tools used to analyze the aggregation m
odels on manifolds are presented.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Fraser (University of Toronto)
DTSTART;VALUE=DATE-TIME:20231211T230000Z
DTEND;VALUE=DATE-TIME:20231212T000000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/45
DESCRIPTION:Title: The Clebsch-Mayer Theory of the Second Variation in the Calculus of V
ariations: A Case Study in the Influence of Dynamical Analysis on Pure Mat
hematics\nby Craig Fraser (University of Toronto) as part of SFU Mathe
matics of Computation\, Application and Data ("MOCAD") Seminar\n\nLecture
held in SFU AQ5025.\n\nAbstract\nCarl Jacobi worked in the 1830s at the Un
iversity of Königsberg on what became known as Hamilton-Jacobi theory\, a
nd also on the theory of the second variation in the calculus of variation
s. The first was a subject in dynamical analysis\, while the second was a
subject in pure mathematics. Insofar as the calculus of variations was con
cerned\, Jacobi’s contributions were seminal and highly original but pre
sented in an incomplete and programmatic form. Together his writings stimu
lated active but independent traditions of research in both subjects. In t
he late 1850s and 1860s Alfred Clebsch and Adolph Mayer – mathematicians
associated with the Königsberg school - established a new approach to th
e investigation of sufficient conditions in the calculus of variations by
bringing methods from Hamilton-Jacobi theory to bear on the transformation
of the second variation. In doing so they established the basis for resea
rch on the subject that was eventually codified in writings around 1900 of
Camille Jordan\, Gustav von Escherich and Oskar Bolza.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timon S. Gutleb (UBC)
DTSTART;VALUE=DATE-TIME:20240216T233000Z
DTEND;VALUE=DATE-TIME:20240217T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/46
DESCRIPTION:Title: A frame approach for equations involving the fractional Laplacian
\nby Timon S. Gutleb (UBC) as part of SFU Mathematics of Computation\, App
lication and Data ("MOCAD") Seminar\n\nLecture held in K9509.\n\nAbstract\
nI will be presenting a frame approach for computing solutions of differen
tial equations inspired by recent progress in frame theory and sparse spec
tral methods. The primary case study for our method will be a very general
family of equations involving the fractional Laplacian.\n\nThis is joint
work with I. Papadopoulos\, J.A. Carrillo and S. Olver.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lisa Kreusser (University of Bath)
DTSTART;VALUE=DATE-TIME:20240226T233000Z
DTEND;VALUE=DATE-TIME:20240227T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/47
DESCRIPTION:Title: Unlocking the Full Potential of Data: From Applied Analysis and Optim
isation to Applications\nby Lisa Kreusser (University of Bath) as part
of SFU Mathematics of Computation\, Application and Data ("MOCAD") Semina
r\n\nLecture held in K9509.\n\nAbstract\nRecent and rapid breakthroughs in
contemporary biology\, climate science\, and data science have unveiled a
spectrum of intricate mathematical challenges which can be tackled throug
h the fusion of applied and numerical analysis\, as well as optimisation.
In this talk\, I will begin by delving into a class of interacting particl
e models with anisotropic interaction forces and their corresponding conti
nuum limit. These models find their inspiration in the simulation of finge
rprint patterns\, which play a critical role in databases in forensic scie
nce and biometric applications. I will showcase our recent findings\, incl
uding the development of a mean-field optimal control algorithm to tackle
an inverse problem arising in parameter identification. Transitioning from
interaction-focused models to the realm of transport networks\, I will in
troduce an optimization approach tailored for a unique coupling of differe
ntial equations that arises in the context of biological network formation
. Additionally\, I will provide insights into my recent research in data s
cience\, encompassing topics such as image segmentation\, non-convex optim
isation algorithms for machine learning\, Wasserstein Generative Adversari
al Networks (WGANs)\, score-based diffusion models and semi-supervised lea
rning techniques.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silas Polani
DTSTART;VALUE=DATE-TIME:20240318T223000Z
DTEND;VALUE=DATE-TIME:20240318T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/48
DESCRIPTION:Title: Intraguild Predation in homogeneous and heterogeneous landscapes\
nby Silas Polani as part of SFU Mathematics of Computation\, Application a
nd Data ("MOCAD") Seminar\n\nLecture held in K9509 and Hybrid.\n\nAbstract
\nIntraguild predation (IGP) consists of two (or more) consumers of the sa
me shared resource exhibiting a predator-prey relation among themselves\,
and is a very present phenomena in terrestrial\, freshwater and marine ec
ological systems. Theoretical works show that IGP allows for coexistence b
etween two consumers of the same guild\, as long as IG prey is a more effe
ctive consumer than IG predator\, revealing an important mechanism for con
sumer coexistence in food chains. Here we explore biological invasions for
ming IGP communities\, by either introducing IG prey or IG predator to est
ablished (single) Consumer-Resource populations in homogeneous and heterog
eneous landscapes. We use reaction-diffusion equations as our modeling fra
mework\, and explore them through numerical simulations and homogenization
techniques. In homogeneous landscapes\, we find that asymptotic spreading
speeds are linearly determinate and also that the formation of traveling
wave solutions and dynamical stabilization regimes are possible. On hetero
geneous landscapes\, we find that coexistence regimes in highly heterogene
ous landscapes can occur regardless of IG-Prey being the least effective c
onsumer\, or be hindered even when IG-Prey remains as the dominant competi
tor\, depending on habitat preferences of each of the species involved. We
provide some conclusions of the work and venues of future research.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siting Liu (University of California\, Los Angeles)
DTSTART;VALUE=DATE-TIME:20240308T233000Z
DTEND;VALUE=DATE-TIME:20240309T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/49
DESCRIPTION:Title: An inverse problem in mean field game from partial boundary measureme
nt\nby Siting Liu (University of California\, Los Angeles) as part of
SFU Mathematics of Computation\, Application and Data ("MOCAD") Seminar\n\
nLecture held in K9509 and Hybrid.\n\nAbstract\nMean-field game (MFG) syst
ems provide a powerful framework for modeling the collective behavior of m
ulti-agent systems with diverse applications. However\, unknown parameters
pose challenges. In this work\, we tackle an inverse problem\, recovering
MFG parameters from limited\, noisy boundary observations. Despite the pr
oblem's ill-posed nature\, we aim to efficiently retrieve these parameters
to understand population dynamics. Our focus is on recovering running cos
t and interaction energy in MFG equations from boundary measurements. We f
ormalize the problem as a constrained optimization problem with L1 regular
ization. We then develop a fast and robust operator splitting algorithm to
solve the optimization using techniques\, including harmonic extensions\,
a three-operator splitting scheme\, and the primal-dual hybrid gradient m
ethod. Numerical experiments illustrate the effectiveness and robustness o
f the algorithm. This is joint work with Yat Tin Chow (UCR)\, Samy Wu Fung
(Colorado School of Mines)\, Levon Nurbekyan (Emory)\, and Stanley J. Osh
er (UCLA).\n
LOCATION:https://researchseminars.org/talk/AppliedMath/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolas Boullé (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20241108T230000Z
DTEND;VALUE=DATE-TIME:20241109T003000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/50
DESCRIPTION:by Nicolas Boullé (University of Cambridge) as part of SFU Ma
thematics of Computation\, Application and Data ("MOCAD") Seminar\n\nLectu
re held in K9509 and Hybrid.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregor Maier (University of Bonn)
DTSTART;VALUE=DATE-TIME:20240524T223000Z
DTEND;VALUE=DATE-TIME:20240524T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/51
DESCRIPTION:Title: On the Approximation of Gaussian Lipschitz Functionals\nby Gregor
Maier (University of Bonn) as part of SFU Mathematics of Computation\, Ap
plication and Data ("MOCAD") Seminar\n\nLecture held in K9509 and Hybrid.\
n\nAbstract\nOver the past few years\, operator learning – the approxima
tion of mappings between infinite-dimensional function spaces using ideas
from machine learning – has attracted increased research attention. Appr
oximate operators\, learned from data\, hold promise to serve as efficient
surrogate models for problems in scientific computing. Multiple model des
igns have been proposed so far and their efficiency has been demonstrated
in various practical applications.\nThe empirical findings are supported b
y a (slowly) growing body of theoretical approximation garantuees. The lat
ter focus to a large extent on linear and holomorphic operators. However\,
far less is known about the approximation of (nonlinear) operators which
are merely Lipschitz continuous. \n\nIn this talk\, I will focus on (scala
r-valued) Lipschitz functionals in a Gaussian setting. I will first consid
er their polynomial approximation by Hermite polynomials and present lower
and upper bounds on the best $s$-term error. This will be followed by a d
iscussion on the approximation of Lipschitz functionals by arbitrary (adap
tive) sampling algorithms\, which will result in sharp error bounds. Final
ly\, I will conclude by also addressing the problem of recovering Lipschit
z functionals from i.i.d. pointwise samples.\n\nThis is joint work with Be
n Adcock (SFU).\n
LOCATION:https://researchseminars.org/talk/AppliedMath/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Williams (Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20240718T223000Z
DTEND;VALUE=DATE-TIME:20240718T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/52
DESCRIPTION:Title: Finite element exterior calculus in four-dimensional space\nby Da
vid Williams (Pennsylvania State University) as part of SFU Mathematics of
Computation\, Application and Data ("MOCAD") Seminar\n\nLecture held in K
9509 and Hybrid.\n\nAbstract\nThe purpose of this talk is to explain the k
ey differences between standard finite element methods for 3D applications
\, and space-time finite element methods for 4D applications. These differ
ences are elucidated through the lens of finite element exterior calculus
(FEEC). Through FEEC\, we can leverage the language of differential geomet
ry and algebraic topology to construct finite element spaces in any number
of dimensions. In this work\, we use techniques from FEEC to construct de
rivative operators in 3D and 4D space. We explain the differences between
these operators\, and the associated Sobolev spaces. Thereafter\, we const
ruct conforming\, high-order\, finite element spaces on the tesseract\, pe
ntatope\, and tetrahedral prism in 4D. These shapes are fundamental geomet
ric quantities in 4D\, as they correspond to the four-dimensional analogs
of the cube\, tetrahedron\, and triangular prism\, respectively.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuefeng Liu (Tokyo Woman's Christian University)
DTSTART;VALUE=DATE-TIME:20240906T220000Z
DTEND;VALUE=DATE-TIME:20240906T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/53
DESCRIPTION:Title: Rigorous evaluation of the Hadamard derivative for shape optimization
problems\nby Xuefeng Liu (Tokyo Woman's Christian University) as part
of SFU Mathematics of Computation\, Application and Data ("MOCAD") Semina
r\n\nLecture held in TBA.\n\nAbstract\nThis talk introduces a newly develo
ped computational method for rigorously evaluating the Hadamard derivative
of Laplacian eigenvalues\, which plays an important role in studying shap
e optimization problems.\n\nTo evaluate the Hadamard derivative\, this met
hod employs state-of-the-art algorithms for eigenvalues and eigenfunctions
via the finite element method (Liu'2013\,2015\; Liu-Vejchodsky'2022)\, ef
fectively handling cases of repeated or closely spaced eigenvalues.\n\nWe
also present a computer-assisted proof for the optimization and simplicity
of Laplacian eigenvalues over triangular domains (Endo-Liu'2023\,2024)\,
demonstrating the impact of these computational advancements in spectral g
eometry.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isaac Harris (Purdue University)
DTSTART;VALUE=DATE-TIME:20240913T220000Z
DTEND;VALUE=DATE-TIME:20240913T233000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044127Z
UID:AppliedMath/54
DESCRIPTION:by Isaac Harris (Purdue University) as part of SFU Mathematics
of Computation\, Application and Data ("MOCAD") Seminar\n\nLecture held i
n TBA.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/54/
END:VEVENT
END:VCALENDAR