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BEGIN:VEVENT
SUMMARY:ACMS#1
DTSTART;VALUE=DATE-TIME:20221028T223000Z
DTEND;VALUE=DATE-TIME:20221029T000000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
UID:AppliedMath/1
DESCRIPTION:by ACMS#1 as part of SFU Applied and Computational Math Semina
r\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Williams (Penn State University)
DTSTART;VALUE=DATE-TIME:20221104T223000Z
DTEND;VALUE=DATE-TIME:20221105T000000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
UID:AppliedMath/2
DESCRIPTION:Title: Space-Time Finite Element Methods: Challenges and Perspectives\nby
David Williams (Penn State University) as part of SFU Applied and Computa
tional Math Seminar\n\n\nAbstract\nSpace-time finite element methods (FEMs
) are likely to grow in popularity due to the ongoing growth in the size\,
speed\, and parallelism of modern computing platforms. The allure of spac
e-time FEMs is both intuitive and practical. From the intuitive standpoint
\, there is considerable elegance and simplicity in accommodating both spa
ce and time using the same numerical discretization strategy. From the pra
ctical standpoint\, there are considerable advantages in efficiency and ac
curacy that can be gained from space-time mesh adaptation: i.e. adapting t
he mesh in both space and time to resolve important solution features. How
ever\, despite these considerable advantages\, there are numerous challeng
es that must be overcome before space-time FEMs can realize their full pot
ential. These challenges are primarily associated with four-dimensional ge
ometric obstacles (hypersurface and hypervolume mesh generation)\, four-di
mensional approximation theory (basis functions and quadrature rules)\, fo
ur-dimensional boundary condition enforcement (well-posed\, moving boundar
y conditions)\, and iterative-solution techniques for large-scale linear s
ystems. In this presentation\, we will provide a brief overview of space-t
ime FEMs\, and discuss some of the latest research developments and ongoin
g issues.\n\nDavid M. Williams is an assistant professor at The Pennsylvan
ia State University in the Mechanical Engineering Department. He came to P
enn State from the Flight Sciences division of Boeing Commercial Airplanes
and Boeing Research and Technology\, where he worked for several years as
a computational fluid dynamics engineer. Williams received his M.S. and P
h. D. in Aeronautics and Astronautics at Stanford University. He holds a B
.S.E. in Aerospace Engineering from the University of Michigan. He has mad
e significant advances in the design of numerical algorithms for computati
onal fluid dynamic simulations. Currently\, his research focuses on employ
ing 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:20221008T000000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
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 Applied and Computational Math Seminar\n\n\nAbstract\nData-driv
en modeling refers to the use of measurement data to infer the parameters
and structure of a mathematical model\, or to aid in forward simulations o
f a partially known mathematical model. Motivated by problems in collectiv
e cell biology\, this talk will explore algorithms which automate the map
from experimental data to governing differential equations\, specifically
using weak formulations of the dynamics. We will show that the weak form i
s an ideal framework for identifying models from data if the performance c
riteria are robustness to data corruptions\, highly accurate model recover
y when corruption levels are low\, and computational efficiency. We will f
irst demonstrate the advantages of the resulting weak-form sparse identifi
cation for nonlinear dynamics algorithm (WSINDy) in the discovery of corre
ct underlying model equations across several key modeling paradigms\, incl
uding ordinary differential equations (ODEs)\, partial differential equati
ons (PDEs)\, and interacting particle systems (IPS). We will then discuss
more recent extensions of this framework\, including weak-form identificat
ion of PDEs from streaming data\, enabling identification of time-varying
coefficients\, and the use of weak-form model selection as a classifier to
determine species membership in a heterogeneous population of initially u
nlabeled cells. We will conclude with an overview of possible next directi
ons\, including open questions related to numerical analysis and theoretic
al recovery guarantees.\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:20221015T000000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
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 Applied an
d Computational Math Seminar\n\n\nAbstract\nWe present a kinetic version o
f the Watanabe-Strogatz (WS) transform for vector models in this paper. Fr
om the generalized WS-transform\, we can reduce the kinetic vector model i
nto an ODE system. We also obtain the cross-ratio type constant of motion
functionals for kinetic vector models under suitable conditions. We presen
t the sufficient and necessary conditions for the existence of the suggest
ed constant of motion functionals. As an application of the constant of mo
tion functional\, we provide the instability of bipolar states of the kine
tic swarm sphere model. We also provide the WS-transform and constant of m
otion functionals for non-identical kinetic vector models.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin Solomon (MIT)
DTSTART;VALUE=DATE-TIME:20221021T223000Z
DTEND;VALUE=DATE-TIME:20221022T000000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
UID:AppliedMath/6
DESCRIPTION:by Justin Solomon (MIT) as part of SFU Applied and Computation
al Math Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ACMS#2
DTSTART;VALUE=DATE-TIME:20221118T233000Z
DTEND;VALUE=DATE-TIME:20221119T010000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
UID:AppliedMath/8
DESCRIPTION:by ACMS#2 as part of SFU Applied and Computational Math Semina
r\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Wiedemann (Universitaet Augsburg)
DTSTART;VALUE=DATE-TIME:20220916T223000Z
DTEND;VALUE=DATE-TIME:20220917T000000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
UID:AppliedMath/11
DESCRIPTION:Title: Homogenization in evolving porous media\nby David Wiedemann (Univ
ersitaet Augsburg) as part of SFU Applied and Computational Math Seminar\n
\n\nAbstract\nNumerical simulations of physical or chemical processes in h
eterogeneous \nmedia require a resolution of the heterogeneous structure.
If\, however\, \nthis heterogeneity is microscopically small while the obj
ect under \nconsideration is large\, a dimensional mismatch occurs and cla
ssical \nnumerical methods become infeasible.\n\nAt this point\, analytica
l homogenization provides effective homogeneous \nsubstitute models\, whic
h can be simulated numerically much more easily. \nOne class of problems t
hat can be treated are processes in porous media. \nIn many biological or
chemical applications\, the pore structure evolves \nin time\, which imped
es classical homogenization. By means of the \ntwo-scale transformation me
thod\, we can overcome this difficulty and \nderive new effective models f
or 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:20220927T040111Z
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 Appl
ied and Computational Math Seminar\n\n\nAbstract\nKinetic equations descri
be the nonequilibrium dynamics of a complex system using a probability den
sity function. Despite of their important role in multiscale modeling to b
ridge microscopic and macroscopic scales\, numerically solving kinetic equ
ations is computationally demanding as they lie in the six-dimensional pha
se space. Dynamical low-rank method is a dimension-reduction technique tha
t has been recently applied to kinetic theory\, yet most of the endeavor i
s devoted to linear or collisionless problems. In this talk\, we introduce
efficient dynamical low-rank methods for Boltzmann type collisional kinet
ic equations\, building on certain prior knowledge about the low-rank stru
cture of the solution.\n
LOCATION:https://researchseminars.org/talk/AppliedMath/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ACMS#3
DTSTART;VALUE=DATE-TIME:20221125T233000Z
DTEND;VALUE=DATE-TIME:20221126T010000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
UID:AppliedMath/14
DESCRIPTION:by ACMS#3 as part of SFU Applied and Computational Math Semina
r\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AppliedMath/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Iwen (Michigan State University)
DTSTART;VALUE=DATE-TIME:20221207T233000Z
DTEND;VALUE=DATE-TIME:20221208T010000Z
DTSTAMP;VALUE=DATE-TIME:20220927T040111Z
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 Applied and Computational Math Seminar\n\n\nAbstra
ct\nLet M be a smooth submanifold of R^n equipped with the Euclidean(chord
al) metric. This talk will consider the smallest dimension\, m\, for which
there exists a bi-Lipschitz function f:M →R^m with bi-Lipschitz constan
ts close to one. We will begin by presenting a bound for the embedding dim
ension m from below in terms of the bi-Lipschitz constants of f and the re
ach\, volume\, diameter\, and dimension of M. We will then discuss how thi
s lower bound can be applied to show that prior upper bounds by Eftekhari
and Wakin on the minimal low-distortion embedding dimension of such manifo
lds using random matrices achieve near-optimal dependence on dimension\, r
each\, and volume (even when compared against nonlinear competitors). Next
\, we will discuss a new class of linear maps for embedding arbitrary (inf
inite) subsets of R^n with sufficiently small Gaussian width which can bot
h (i) achieve near-optimal embedding dimensions of submanifolds\, and (ii)
be multiplied by vectors in faster than FFT-time. When applied to d-dimen
sional submanifolds of R^n we will see that these new constructions improv
e on prior fast embedding matrices in terms of both runtime and embedding
dimension when d is sufficiently small. Time permitting\, we will then con
clude with a discussion of non-linear so-called “terminal embeddings”
of manifolds which allow for extensions of the famous Johnson-Lindenstraus
s Lemma beyond what any linear map can achieve.\n\nThis talk will draw on
joint work with various subsets of Mark Roach (MSU)\, Benjamin Schmidt (MS
U)\, and Arman Tavakoli (MSU).\n
LOCATION:https://researchseminars.org/talk/AppliedMath/15/
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