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*'''When:''' Fridays at 2:25pm (except as otherwise indicated)
*'''When:''' Fridays at 2:25pm (except as otherwise indicated)
*'''Where:''' B119 <strike> 901</strike> Van Vleck Hall
*'''Where:''' 901 Van Vleck Hall
*'''Organizers:''' [https://people.math.wisc.edu/~lzepeda/ Leonardo Zepeda-Núñez], [http://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie] and [http://www.math.wisc.edu/~jeanluc Jean-Luc Thiffeault]
*'''Organizers:''' [https://math.wisc.edu/staff/fabien-maurice/ Maurice Fabien], [https://people.math.wisc.edu/~rycroft/ Chris Rycroft], and [https://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie],
*'''To join the ACMS mailing list:''' Send mail to [mailto:acms+join@g-groups.wisc.edu acms+join@g-groups.wisc.edu].
*'''To join the ACMS mailing list:''' Send mail to [mailto:acms+join@g-groups.wisc.edu acms+join@g-groups.wisc.edu].


<br>
<br>  


== Fall 2021 ==
== Fall 2023 ==
    
    
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
!align="left" | date
!align="left" | virtual/in-person
!align="left" | speaker
!align="left" | speaker
!align="left" | title
!align="left" | title
!align="left" | host(s)
!align="left" | host(s)
|-
|-
| Sept 10
| Sep 8
| Virtual
|[https://webspace.clarkson.edu/~ebollt/ Erik Bollt] (Clarkson University)
|[https://www.math.tamu.edu/~jhu/ Jiuhua Hu] (Texas A&M / UW)
|A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions
|''[[Applied/ACMS/absF21#Jiuhua Hu (Texas A&M / UW)|Wavelet-based Edge Multiscale Parareal Algorithm for Parabolic Equations with Heterogeneous Coefficients]]''
| Chen
|Chen and Stechmann
|-
|-
| Sept 17
| Sep 15  '''4:00pm B239'''
|
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)
|[https://math.berkeley.edu/~difang/ Di Fang] (Berkeley)
| Nonlocal PDEs and Quantum Optics
|''[[Applied/ACMS/absF21#Di Fang (Berkeley)|Time-dependent unbounded Hamiltonian simulation with vector norm scaling]]''
| Li
|Li
|-
|-
| Sept 24
|Sep 22
| Virtual
|[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)
|[https://www.pnnl.gov/people/lai-yung-ruby-leung/ Ruby Leung] (PNNL)
|Oscillatory mass-action systems
|''[[Applied/ACMS/absF21#Ruby Leung  (PNNL)|Mesoscale convective systems in observations and a hierarchy of models]]''
|Craciun
|Chen and Stechmann
|-
|-
| Oct 1
| Sep 29
| Virtual
|[https://data-assimilation-causality-oceanography.atmos.colostate.edu/ Peter Jan van Leeuwen] (Colorado State University)
|[https://gauss.math.yale.edu/~ya248/ Yariv Aizenbud] (Yale)
|Nonlinear Causal Discovery, with applications to atmospheric science
|''[[Applied/ACMS/absF21#Yariv Aizenbud (Yale)|Non-parametric estimation of manifolds from noisy data]]'' [https://uwmadison.box.com/s/afbfx1u0h129bdwgal4qxm1c8bz1sid1 (Link to recorded talk)]
| Chen
|Saverio, Shamgar
|-
|-
| Oct 8
| '''Wed Oct 4'''
|VV B119
|[https://www.damtp.cam.ac.uk/person/est42/ Edriss Titi] (Cambridge/Texas A&M)
|[https://mathematics.stanford.edu/people/yuhua-zhu Yuhua Zhu] (Stanford)
|''[[Applied/ACMS/absF23#Edriss Titi (Cambridge/Texas A&M)|Distringuished Lecture Series]]''
|''[[Applied/ACMS/absF21#Yuhua Zhu (Stanford)|Fokker-Planck Equations and Machine Learning]]''
| Smith, Stechmann
|Zepeda-Núñez
|-
|-
| '''Oct 8, 4-5pm'''
| Oct 6
|Virtual
| No Friday seminar
|[https://www.maths.ox.ac.uk/people/jon.chapman Jon Chapman] (Oxford)
| Distinguished lecture this week on Wednesday
|'''Wasow Lecture''': ''[https://hilbert.math.wisc.edu/wiki/index.php/Colloquia#Fall_2021 Asymptotics beyond all orders: the devil's invention?]''
|
|Jean-Luc
|-
|-
| Oct 15
| Oct 13
|VV B119
| [https://geosci.uchicago.edu/people/da-yang/ Da Yang] (University of Chicago)
||[https://sites.google.com/site/enkeleidalushi/home Enkeleida Lushi] (NJIT)
|
|''[[Applied/ACMS/absF21#Enkeleida Lushi (NJIT)|Aligning active particles in confinement]]''
|Smith
|Saverio and Jean-Luc
|-
|-
| Oct 22
| Oct 20
| Virtual
|[https://www.stat.uchicago.edu/~ykhoo/ Yuehaw Khoo] (University of Chicago)
||[https://www.rjh.io Russell Hewett] (Virginia Tech)
|''[[Applied/ACMS/absF21#Russell Hewett (Virginia Tech)|TBA]]''
|Zepeda-Núñez
|
|
|Li
|-
| Oct 27
| [https://shukaidu.github.io/ Shukai Du] (UW)
| Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer
| Stechmann
|-
|-
| Oct 29
| Nov 3
|[https://www.math.arizona.edu/~lmig/ Lise-Marie Imbert-Gérard] (University of Arizona)
|
|
|TBA
|Rycroft
|TBA
|-
| Nov 10
| [https://as.tufts.edu/physics/people/faculty/timothy-atherton Timothy Atherton] (Tufts)
|
|
|Chandler, Spagnolie
|-
|-
| Nov 5
| Nov 17
|Virtual
|[https://klotsagroup.wixsite.com/home Daphne Klotsa]
|[https://people.maths.ox.ac.uk/vella/ Dominic Vella] (Oxford)
|
|''[[Applied/ACMS/absF21#Dominic Vella (Oxford)|TBA]]''
|Rycroft
|Saverio
|-
|-
| Nov 12
| Nov 24
|Virtual
| Thanksgiving break
|[https://www.mfarazmand.com/ Mohammad Farazmand] (NCSU)
|
|''[[Applied/ACMS/absF21#Mohammad Farazmand (NCSU)|TBA]]''
|Chen
|
|
|-
|-
| Nov 19
| Dec 1
|maybe in-person
|[https://scholar.google.ca/citations?user=CRlA-sEAAAAJ&hl=en&oi=sra Adam Stinchcombe] (University of Toronto)
|[https://bamdadhosseini.org/ Bamdad Hosseini] (Caltech and UW-Seattle)
|
|''[[Applied/ACMS/absF21#Bamdad Hosseini (Caltech and UW-Seattle)|TBA]]''
|Cochran
|Li
|-
|-
| Nov 26
| Dec 8
|
|
|Thanksgiving
|
|
|
|
|-
|-
| Dec 3
|Pending
|Virtual
|Invite sent to Talea Mayo
|[https://scholar.google.com/citations?user=LlBckhUAAAAJ&hl=en Aseel Farhat] (Florida State University)
|
|''[[Applied/ACMS/absF21#Aseel Farhat (Florida State University)|TBA]]''
|Fabien
|Smith
|-
| Dec 10
|Virtual
|[https://www.colorado.edu/amath/grooms Ian Grooms] (University of Colorado-Boulder)
|''[[Applied/ACMS/absF21#Ian Grooms (University of Colorado-Boulder)|TBA]]''
|Smith
|}
|}
== Abstracts ==
'''[https://webspace.clarkson.edu/~ebollt/ Erik Bollt] (Clarkson University)'''
''A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions''
Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of non- linear dynamic behavior (e.g. through normal forms). In this presentation we will argue that the use of the Koopman operator and its spectrum are particularly well suited for this endeavor, both in theory, but also especially in view of recent data-driven machine learning algorithmic developments. Recall that the Koopman operator describes the dynamics of observation functions along a flow or map, and it is formally the adjoint of the Frobenius-Perrron operator that describes evolution of densities of ensembles of initial conditions. The Koopman operator has a long theoretical tradition but it has recently become extremely popular through numerical methods such as dynamic mode decomposition (DMD) and variants, for applied problems such as coherence and also in control theory. We demonstrate through illustrative examples that we can nontrivially extend the applicability of the Koopman spectral theoretical and computational machinery beyond modeling and prediction, towards a systematic discovery of rectifying integrability coordinate transformations.
'''[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)'''
''Nonlocal PDEs and Quantum Optics''
Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.
'''[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)'''
''Oscillatory mass-action systems''
Mass-action differential equations are probably the most common mathematical models in biochemistry, cell biology, and population dynamics. Since oscillatory behavior is ubiquitous in nature, there are several papers (starting with Alfred Lotka) that deal with showing the existence of periodic solutions in mass-action systems. The standard way of proving the existence of a limit cycle in a high-dimensional system is via Andronov-Hopf bifurcation. In this talk, we recall some specific oscillatory models (like glycolysis or phosphorylation), as well as more recent results that aim to systematically classify small mass-action reaction networks that admit an Andronov-Hopf bifurcation.
'''[https://shukaidu.github.io/ Shukai Du] (UW)'''
''Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer''
In the past decade, (artificial) neural networks and machine learning tools have surfaced as game changing technologies across numerous fields, resolving an array of challenging problems. Even for the numerical solution of partial differential equations (PDEs) or other scientific computing problems, results have shown that machine learning can speed up some computations. However, many machine learning approaches tend to lose some of the advantageous features of traditional numerical PDE methods, such as interpretability and applicability to general domains with complex geometry.
In this talk, we introduce a systematic approach (which we call element learning) with the goal of accelerating finite element-type methods via machine learning, while also retaining the desirable features of finite element methods. The derivation of this new approach is closely related to hybridizable discontinuous Galerkin (HDG) methods in the sense that the local solvers 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 smooth 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 level of $10^{-3}$ in the relative $L^2$ error, and we observe a significant speed-up with element learning compared to a classical finite element-type method. Reference: [https://arxiv.org/abs/2308.02467 arxiv: 2308.02467]


== Future semesters ==
== Future semesters ==


*[[Applied/ACMS/Spring2022|Spring 2022]]
*[[Applied/ACMS/Spring2024|Spring 2024]]




Line 121: Line 138:
== Archived semesters ==
== Archived semesters ==


*[[Applied/ACMS/Spring2023|Spring 2023]]
*[[Applied/ACMS/Fall2022|Fall 2022]]
*[[Applied/ACMS/Spring2022|Spring 2022]]
*[[Applied/ACMS/Fall2021|Fall 2021]]
*[[Applied/ACMS/Spring2021|Spring 2021]]
*[[Applied/ACMS/Spring2021|Spring 2021]]
*[[Applied/ACMS/Fall2020|Fall 2020]]
*[[Applied/ACMS/Fall2020|Fall 2020]]

Latest revision as of 17:10, 22 September 2023


Applied and Computational Mathematics Seminar


Fall 2023

date speaker title host(s)
Sep 8 Erik Bollt (Clarkson University) A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions Chen
Sep 15 4:00pm B239 John Schotland (Yale University) Nonlocal PDEs and Quantum Optics Li
Sep 22 Balazs Boros (U Vienna) Oscillatory mass-action systems Craciun
Sep 29 Peter Jan van Leeuwen (Colorado State University) Nonlinear Causal Discovery, with applications to atmospheric science Chen
Wed Oct 4 Edriss Titi (Cambridge/Texas A&M) Distringuished Lecture Series Smith, Stechmann
Oct 6 No Friday seminar Distinguished lecture this week on Wednesday
Oct 13 Da Yang (University of Chicago) Smith
Oct 20 Yuehaw Khoo (University of Chicago) Li
Oct 27 Shukai Du (UW) Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer Stechmann
Nov 3 Lise-Marie Imbert-Gérard (University of Arizona) Rycroft
Nov 10 Timothy Atherton (Tufts) Chandler, Spagnolie
Nov 17 Daphne Klotsa Rycroft
Nov 24 Thanksgiving break
Dec 1 Adam Stinchcombe (University of Toronto) Cochran
Dec 8
Pending Invite sent to Talea Mayo Fabien

Abstracts

Erik Bollt (Clarkson University)

A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions

Matching dynamical systems, through different forms of conjugacies and equivalences, has long been a fundamental concept, and a powerful tool, in the study and classification of non- linear dynamic behavior (e.g. through normal forms). In this presentation we will argue that the use of the Koopman operator and its spectrum are particularly well suited for this endeavor, both in theory, but also especially in view of recent data-driven machine learning algorithmic developments. Recall that the Koopman operator describes the dynamics of observation functions along a flow or map, and it is formally the adjoint of the Frobenius-Perrron operator that describes evolution of densities of ensembles of initial conditions. The Koopman operator has a long theoretical tradition but it has recently become extremely popular through numerical methods such as dynamic mode decomposition (DMD) and variants, for applied problems such as coherence and also in control theory. We demonstrate through illustrative examples that we can nontrivially extend the applicability of the Koopman spectral theoretical and computational machinery beyond modeling and prediction, towards a systematic discovery of rectifying integrability coordinate transformations.


John Schotland (Yale University)

Nonlocal PDEs and Quantum Optics

Quantum optics is the quantum theory of the interaction of light and matter. In this talk, I will describe a real-space formulation of quantum electrodynamics with applications to many body problems. The goal is to understand the transport of nonclassical states of light in random media. In this setting, there is a close relation to kinetic equations for nonlocal PDEs with random coefficients.


Balazs Boros (U Vienna)

Oscillatory mass-action systems

Mass-action differential equations are probably the most common mathematical models in biochemistry, cell biology, and population dynamics. Since oscillatory behavior is ubiquitous in nature, there are several papers (starting with Alfred Lotka) that deal with showing the existence of periodic solutions in mass-action systems. The standard way of proving the existence of a limit cycle in a high-dimensional system is via Andronov-Hopf bifurcation. In this talk, we recall some specific oscillatory models (like glycolysis or phosphorylation), as well as more recent results that aim to systematically classify small mass-action reaction networks that admit an Andronov-Hopf bifurcation.


Shukai Du (UW)

Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer

In the past decade, (artificial) neural networks and machine learning tools have surfaced as game changing technologies across numerous fields, resolving an array of challenging problems. Even for the numerical solution of partial differential equations (PDEs) or other scientific computing problems, results have shown that machine learning can speed up some computations. However, many machine learning approaches tend to lose some of the advantageous features of traditional numerical PDE methods, such as interpretability and applicability to general domains with complex geometry.

In this talk, we introduce a systematic approach (which we call element learning) with the goal of accelerating finite element-type methods via machine learning, while also retaining the desirable features of finite element methods. The derivation of this new approach is closely related to hybridizable discontinuous Galerkin (HDG) methods in the sense that the local solvers 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 smooth 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 level of $10^{-3}$ in the relative $L^2$ error, and we observe a significant speed-up with element learning compared to a classical finite element-type method. Reference: arxiv: 2308.02467

Future semesters


Archived semesters


Return to the Applied Mathematics Group Page

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