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*'''When:''' Fridays at 2:25pm (except as otherwise indicated) | *'''When:''' Fridays at 2:25pm (except as otherwise indicated) | ||
*'''Where:''' 901 Van Vleck Hall | *'''Where:''' 901 Van Vleck Hall | ||
*'''Organizers:''' [ | *'''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:''' | *'''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 2023 == | ||
{| cellpadding="8" | {| cellpadding="8" | ||
Line 18: | Line 18: | ||
!align="left" | host(s) | !align="left" | host(s) | ||
|- | |- | ||
| | | Sep 8 | ||
|[https:// | |[https://webspace.clarkson.edu/~ebollt/ Erik Bollt] (Clarkson University) | ||
| | |A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions | ||
| | | Chen | ||
|- | |- | ||
| | | Sep 15 '''4:00pm B239''' | ||
|[https:// | |[https://math.yale.edu/people/john-schotland John Schotland] (Yale University) | ||
| | | Nonlocal PDEs and Quantum Optics | ||
| | | Li | ||
|- | |- | ||
| | |Sep 22 | ||
|[https:// | |[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna) | ||
| | |Oscillatory mass-action systems | ||
| | |Craciun | ||
|- | |- | ||
| | | Sep 29 | ||
|[https:// | |[https://data-assimilation-causality-oceanography.atmos.colostate.edu/ Peter Jan van Leeuwen] (Colorado State University) | ||
| | |Nonlinear Causal Discovery, with applications to atmospheric science | ||
| | | Chen | ||
|- | |- | ||
| ''' Wed | | '''Wed Oct 4''' | ||
|[ | |[https://www.damtp.cam.ac.uk/person/est42/ Edriss Titi] (Cambridge/Texas A&M) | ||
|''[[Applied/ACMS/ | |''[[Applied/ACMS/absF23#Edriss Titi (Cambridge/Texas A&M)|Distringuished Lecture Series]]'' | ||
| | | Smith, Stechmann | ||
|- | |- | ||
| | | Oct 6 | ||
|[ | | [https://sites.google.com/view/pollyyu Polly Yu] (Harvard/UIUC) | ||
| | | TBA | ||
| | |Craciun | ||
|- | |- | ||
| | | Oct 13 | ||
| [https://geosci.uchicago.edu/people/da-yang/ Da Yang] (University of Chicago) | |||
| | | | ||
|Smith | |||
|- | |||
| Oct 20 | |||
|[https://www.stat.uchicago.edu/~ykhoo/ Yuehaw Khoo] (University of Chicago) | |||
| | | | ||
|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 | |||
|- | |||
| Nov 3 | |||
|[https://www.math.arizona.edu/~lmig/ Lise-Marie Imbert-Gérard] (University of Arizona) | |||
| | | | ||
|Rycroft | |||
|- | |- | ||
| | | Nov 10 | ||
|[https:// | | [https://as.tufts.edu/physics/people/faculty/timothy-atherton Timothy Atherton] (Tufts) | ||
| | | | ||
| | |Chandler, Spagnolie | ||
|- | |- | ||
| | | Nov 17 | ||
|[https://klotsagroup.wixsite.com/home Daphne Klotsa] | |||
| | | | ||
|Rycroft | |||
|- | |||
| Nov 24 | |||
| Thanksgiving break | |||
| | | | ||
| | | | ||
|- | |- | ||
| | | Dec 1 | ||
| | |[https://scholar.google.ca/citations?user=CRlA-sEAAAAJ&hl=en&oi=sra Adam Stinchcombe] (University of Toronto) | ||
| | | | ||
| | |Cochran | ||
|- | |- | ||
| | | Dec 8 | ||
| | | | ||
| | | | ||
| | | | ||
|- | |- | ||
| | |Pending | ||
| | |Invite sent to Talea Mayo | ||
| | | | ||
| | |Fabien | ||
|} | |} | ||
== 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 == | |||
*[[Applied/ACMS/Spring2024|Spring 2024]] | |||
---- | |||
== 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/Fall2020|Fall 2020]] | |||
*[[Applied/ACMS/Spring2020|Spring 2020]] | |||
*[[Applied/ACMS/Fall2019|Fall 2019]] | |||
*[[Applied/ACMS/Spring2019|Spring 2019]] | |||
*[[Applied/ACMS/Fall2018|Fall 2018]] | |||
*[[Applied/ACMS/Spring2018|Spring 2018]] | |||
*[[Applied/ACMS/Fall2017|Fall 2017]] | *[[Applied/ACMS/Fall2017|Fall 2017]] | ||
*[[Applied/ACMS/Spring2017|Spring 2017]] | *[[Applied/ACMS/Spring2017|Spring 2017]] |
Latest revision as of 05:00, 25 September 2023
Applied and Computational Mathematics Seminar
- When: Fridays at 2:25pm (except as otherwise indicated)
- Where: 901 Van Vleck Hall
- Organizers: Maurice Fabien, Chris Rycroft, and Saverio Spagnolie,
- To join the ACMS mailing list: Send mail to acms+join@g-groups.wisc.edu.
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 | Polly Yu (Harvard/UIUC) | TBA | Craciun |
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
- Spring 2023
- Fall 2022
- Spring 2022
- Fall 2021
- Spring 2021
- Fall 2020
- Spring 2020
- Fall 2019
- Spring 2019
- Fall 2018
- Spring 2018
- Fall 2017
- Spring 2017
- Fall 2016
- Spring 2016
- Fall 2015
- Spring 2015
- Fall 2014
- Spring 2014
- Fall 2013
- Spring 2013
- Fall 2012
- Spring 2012
- Fall 2011
- Spring 2011
- Fall 2010
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