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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:''' [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].


<br>
<br>  
 
== Fall 2012 Semester ==


== Fall 2023  ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
!align="left" | date
Line 17: Line 18:
!align="left" | host(s)
!align="left" | host(s)
|-
|-
|Sept 14
| Sep 8
|[http://mechse.illinois.edu/research/dstn David Saintillan] (U. Illinois)
|[https://webspace.clarkson.edu/~ebollt/ Erik Bollt] (Clarkson University)
|''[[Applied/ACMS/absF12#David_Saintillan_(U._Illinois)|Living fluids: modeling and simulation of biologically active suspensions]]''
|A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions
|Jean-Luc, Saverio
| Chen
|-
|-
|'''<strike>Thu Sept 20, 4pm, B239</strike>'''
| Sep 15  '''4:00pm B239'''
|[http://www-stat.stanford.edu/~cgates/PERSI/ Persi Diaconis] (Stanford)
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)
|''CANCELLED''
| Nonlocal PDEs and Quantum Optics
|Jean-Luc
| Li
|-
|-
|Sept 21
|Sep 22
|[http://www.math.wisc.edu/~roch Sebastien Roch] (UW)
|[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)
|''[[Applied/ACMS/absF12#Sebastien_Roch_(UW)|Assembling the tree of life: theory beyond the substitution-only model of sequence evolution]]''
|Oscillatory mass-action systems
|local
|Craciun
|-
|-
|'''Sept 21, 4pm, B239'''
| Sep 29
|[http://eaton.math.rpi.edu/faculty/J.McLaughlin/mclauj.html Joyce McLaughlin] (RPI)
|[https://data-assimilation-causality-oceanography.atmos.colostate.edu/ Peter Jan van Leeuwen] (Colorado State University)
|''Mathematics for imaging biomechanical parameters in dynamic elastography''
|Nonlinear Causal Discovery, with applications to atmospheric science
|'''Colloquium'''
| Chen
|-
|-
|'''Sept 28, 1:20pm'''
| '''Wed Oct 4'''
|[http://engineering.purdue.edu/~mboutin/ Mireille Boutin] (Purdue)
|[https://www.damtp.cam.ac.uk/person/est42/ Edriss Titi] (Cambridge/Texas A&M)
|''[[Geometry_and_Topology_Seminar#Mirielle Boutin (Purdue)|The Pascal triangle of a discrete Image: definition, properties, and application to object segmentation]]''
|''[[Applied/ACMS/absF23#Edriss Titi (Cambridge/Texas A&M)|Distringuished Lecture Series]]''
|'''Geometry seminar'''
| Smith, Stechmann
|-
|-
|Sept 28
| Oct 6
|[http://caos.cims.nyu.edu/object/skeating Shane Keating] (NYU)
| [https://sites.google.com/view/pollyyu Polly Yu] (Harvard/UIUC)
|''[[Applied/ACMS/absF12#Shane_Keating_(NYU)|Models and measures of turbulent mixing in the ocean]]''
| TBA
|Jean-Luc
|Craciun
|-
|-
|Oct 5
| Oct 13
|[http://www.astro.wisc.edu/~zweibel Ellen Zweibel] (UW)
| [https://geosci.uchicago.edu/people/da-yang/ Da Yang] (University of Chicago)
|''[[Applied/ACMS/absF12#Ellen_Zweibel_(UW)|The fluid dynamics of stellar interiors]]''
|
|Jean-Luc
|Smith
|-
|-
|Oct 12
| Oct 20
|[http://m.njit.edu/~muratov Cyrill Muratov] (NJIT)
|[https://www.stat.uchicago.edu/~ykhoo/ Yuehaw Khoo] (University of Chicago)
|''[[Applied/ACMS/absF12#Cyrill_Muratov_(NJIT)|Gamma-convergence for pattern forming systems with competing interactions]]''
|
|Sasha Kiselev
|Li
|-
|-
|Oct 19
| Oct 27
|[http://www.math.cmu.edu/~gautam Gautam Iyer] (CMU)
| [https://shukaidu.github.io/ Shukai Du] (UW)
|''[[Applied/ACMS/absF12#Gautam_Iyer_(CMU)|Time discrete approximations to the Navier&ndash;Stokes equations:
| Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer
    Existence, stability and coercivity]]''
| Stechmann
|Sasha Kiselev
|-
|-
|Oct 26
| Nov 3
|[http://www.math.drexel.edu/~tyu Thomas Yu] (Drexel U.)
|[https://www.math.arizona.edu/~lmig/ Lise-Marie Imbert-Gérard] (University of Arizona)
|''[[Applied/ACMS/absF12#Thomas_Yu_(Drexel)|Subdivision methods in scientific computing]]''
|
|Shi Jin
|Rycroft
|-
|-
|'''Tues Oct 30, 4pm, B239'''
| Nov 10
|[http://www.math.nyu.edu/faculty/majda/ Andrew Majda] (Courant)
| [https://as.tufts.edu/physics/people/faculty/timothy-atherton Timothy Atherton] (Tufts)
|''[[Applied/ACMS/absF12#Andrew_Majda_(NYU)|Data driven methods for complex turbulent systems]]''
|
|Smith, Stechmann (Colloquium)
|Chandler, Spagnolie
|-
|-
|'''Thu Nov 1, 4pm, B239'''
| Nov 17
|[http://web.math.princeton.edu/~const Peter Constantin] (Princeton)
|[https://klotsagroup.wixsite.com/home Daphne Klotsa]
|''[[TBA]]''
|
|Distinguished Lecture (Colloquium)
|Rycroft
|-
| Nov 24
| Thanksgiving break
|
|
|-
|-
|'''Nov 2, 4pm, B239'''
| Dec 1
|[http://web.math.princeton.edu/~const Peter Constantin] (Princeton)
|[https://scholar.google.ca/citations?user=CRlA-sEAAAAJ&hl=en&oi=sra Adam Stinchcombe] (University of Toronto)
|''[[TBA]]''
|
|Distinguished Lecture (Colloquium)
|Cochran
|-
|-
|Nov 9
| Dec 8
|[http://www.biochem.wisc.edu/faculty/weibel Doug Weibel] (UW)
|
|''[[Applied/ACMS/absF12#xxxx|TBA]]''
|
|Jean-Luc, Saverio
|
|-
|-
|Nov 16
|Pending
|[http://www.math.colostate.edu/~yzhou Yongcheng Zhou] (Colorado State)
|Invite sent to Talea Mayo
|''[[Applied/ACMS/absF12#xxxx|Multiscale modeling and numerics for surface electrodiffusion]]''
|Julie
|
|
|Fabien
|}
|}


<br>
== 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.


== Spring 2013 Semester ==
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]


{| cellpadding="8"
== Future semesters ==
!align="left" | date
!align="left" | speaker
!align="left" | title
!align="left" | host(s)
|-
|
|}


<br>
*[[Applied/ACMS/Spring2024|Spring 2024]]


== How to join the ACMS mailing list ==
See [https://lists.math.wisc.edu/listinfo/acms mailing list] website


<br>
----


== 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/Spring2017|Spring 2017]]
*[[Applied/ACMS/Fall2016|Fall 2016]]
*[[Applied/ACMS/Spring2016|Spring 2016]]
*[[Applied/ACMS/Fall2015|Fall 2015]]
*[[Applied/ACMS/Spring2015|Spring 2015]]
*[[Applied/ACMS/Fall2014|Fall 2014]]
*[[Applied/ACMS/Spring2014|Spring 2014]]
*[[Applied/ACMS/Fall2013|Fall 2013]]
*[[Applied/ACMS/Spring2013|Spring 2013]]
*[[Applied/ACMS/Fall2012|Fall 2012]]
*[[Applied/ACMS/Spring2012|Spring 2012]]
*[[Applied/ACMS/Spring2012|Spring 2012]]
*[[Applied/ACMS/Fall2011|Fall 2011]]
*[[Applied/ACMS/Fall2011|Fall 2011]]

Latest revision as of 05:00, 25 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 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

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