Applied/ACMS: Difference between revisions

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*'''Where:''' 901 Van Vleck Hall
*'''Where:''' 901 Van Vleck Hall
*'''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],  
*'''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+subscribe@g-groups.wisc.edu].


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== Fall 2023  ==
== '''Spring 2025''' ==
 
{| cellpadding="8"
{| cellpadding="8"
!align="left" | date
! align="left" |Date
!align="left" | speaker
! align="left" |Speaker
!align="left" | title
! align="left" |Title
!align="left" | host(s)
! align="left" |Host(s)
|-
|-
| Sep 8
|Sep 19
|[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'''
|Sep 26
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)
|
| Nonlocal PDEs and Quantum Optics
|
| Li
|
|-
|-
|Sep 22
|Oct 3
|[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)
|
|Oscillatory mass-action systems
|
|Craciun
|
|-
|-
| Sep 29
|Oct 10
|[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 Oct 4'''
|Oct 17
|[https://www.damtp.cam.ac.uk/person/est42/ Edriss Titi] (Cambridge/Texas A&M)
|
|''[[Applied/ACMS/absF23#Edriss Titi (Cambridge/Texas A&M)|Distringuished Lecture Series]]''
|
| Smith, Stechmann
|
|-
|-
| Oct 6
|Oct 24
| [https://sites.google.com/view/pollyyu Polly Yu] (Harvard)
|
| A Spatiotemporal Model of GPCR-G protein Interactions
|
|Craciun
|
|-
|-
| Oct 13
|Oct 31
| [https://geosci.uchicago.edu/people/da-yang/ Da Yang] (University of Chicago)
|
| The Incredible Lightness of Water Vapor
|
|Smith
|
|-
|-
| Oct 19 '''(*Thursday* *1:25pm*)'''
|Nov 7
|[https://sites.google.com/view/jiaxinjin/ Jiaxin Jin] (The Ohio State University)
|
| On the Dimension of the R-Disguised Toric Locus of a Reaction Network
|
|Craciun
|
|-
|-
| Oct 20
|Nov 14
|[https://www.stat.uchicago.edu/~ykhoo/ Yuehaw Khoo] (University of Chicago)
|
| Randomized tensor-network algorithms for random data in high-dimensions
|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://as.tufts.edu/physics/people/faculty/timothy-atherton Timothy Atherton] (Tufts)
|
|
|Chandler, Spagnolie
|-
|-
| Nov 17
|Nov 21
|[https://klotsagroup.wixsite.com/home Daphne Klotsa]
|
|
|Rycroft
|-
| Nov 24
| Thanksgiving break
|
|
|
|
|-
|-
| Dec 1
|Nov 28
|[https://scholar.google.ca/citations?user=CRlA-sEAAAAJ&hl=en&oi=sra Adam Stinchcombe] (University of Toronto)
|Thanksgiving
|
|
|
|Cochran
|-
|-
| Dec 8
|Dec 5
|
|
|
|
|
|
|-
|-
|Pending
|Dec 12
|Invite sent to Talea Mayo
|
|
|
|Fabien
|-
|Pending
|Invite sent to Tony Kearsley
|
|
|Fabien
|}
|}


== Abstracts ==
==Abstract==
'''[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.


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== Archived semesters ==


'''[https://data-assimilation-causality-oceanography.atmos.colostate.edu/ Peter Jan van Leeuwen] (Colorado State University)'''
*[[Applied/ACMS/Spring2025|Spring 2025]]
 
*[[Applied/ACMS/Fall2024|Fall 2024]]
''Nonlinear Causal Discovery, with applications to atmospheric science''
 
Understanding cause and effect relations in complex systems is one of the main goals of scientific research. Ideally, one sets up controlled experiments in which different potential drivers are varied to infer their influence on a target variable. However, this procedure is impossible in many systems, for example the atmosphere, where nature is doing one experiment for us. An alternative is to build a detailed computer model of the system, and perform controlled experiments in model world. An issue there is that one can only control external drivers, because controlling an internal variable would kill all feedbacks to that variable, resulting in a study of ‘a different planet’. Because many natural systems cannot be controlled, or only partially, we focus on causal discovery in systems that are non-intervenable. I will describe a non-linear causal discovery framework that is based on (conditional) mutual information. It will be shown that conventional analysis of causal relations via so-called Directed Acyclic Graphs (DAGs, se e.g. Pearl and others) is not suitable for nonlinear systems, and an extension is provided that allows for interacting drivers. I prove that the interacting contributions and interaction informations, and provide a solid interpretation of those, in terms of buffering, hampering, and positive feedbacks. Also ways to infer completeness of the causal networks will be discussed, as well as causal relations that are invisible to our framework. The framework will be applied to simple idealized cloud models, and to real very detailed ground-based remote-sensing observations of cloud properties, where we contrast the causal structure of precipitating and non-precipitation strato-cumulus clouds.
 
 
'''[https://sites.google.com/view/pollyyu Polly Yu] (Harvard)'''
 
''A Spatiotemporal Model of GPCR-G protein Interactions''
 
G-protein coupled receptors (GPCRs) is a class of transmembrane receptors important to many signalling pathways and a common drug target. As its name suggests, the receptor, once activated, binds to a G-protein. Recent experiments suggests that GPCRs form dense tiny clusters. What are the effects of these "hotspots" on signalling kinetics? I will introduce a semi-empirical spatiotemporal model for GPCR-G protein interactions, and present some numerical evidence for how these clusters might locally increase signalling speed.
 
 
'''[https://geosci.uchicago.edu/people/da-yang/ Da Yang] (University of Chicago)'''
 
''The Incredible Lightness of Water Vapor''
 
Conventional wisdom suggests that warm air rises while cold air sinks. However, recent satellite observations show that, on average, rising air is colder than sinking air in the tropical free troposphere. This is due to the buoyancy effect of water vapor: the molar mass of water vapor is less than that of dry air, making humid air lighter than dry air at the same temperature and pressure. Unfortunately, this vapor buoyancy effect has been considered negligibly small and thereby overlooked in large-scale climate dynamics. Here we use theory, reanalysis data, and a hierarchy of climate models to show that vapor buoyancy has a similar magnitude to thermal buoyancy in the tropical free troposphere. As a result, cold air rises in the tropical free troposphere. We further show that vapor buoyancy enhances thermal radiation, increases subtropical stratiform low clouds, favors convective aggregation, and stabilizes Earth’s climate. However, some state-of-the-art climate models fail to represent vapor buoyancy properly. This flaw leads to inaccurate simulations of cloud distributions—the largest uncertainty in predicting climate change. Implications of our results on paleoclimate and planetary habitability will also be discussed.
 
 
'''[https://sites.google.com/view/jiaxinjin/ Jiaxin Jin] (The Ohio State University)'''
 
''On the Dimension of the R-Disguised Toric Locus of a Reaction Network''
 
The properties of general polynomial dynamical systems can be very difficult to analyze, due to nonlinearity, bifurcations, and the possibility for chaotic dynamics. On the other hand, toric dynamical systems are polynomial dynamical systems that appear naturally as models of reaction networks and have very robust and stable properties. A ''disguised toric dynamical system'' is a polynomial dynamical system generated by a reaction network and some choice of positive parameters, such that it has a toric realization with respect to some other network. Disguised toric dynamical systems enjoy all the robust stability properties of toric dynamical systems. In this project, we study a larger set of dynamical systems where the rate constants are allowed to take both positive and negative values. More precisely, we analyze the R-disguised toric locus of a reaction network, i.e., the subset in the space rate constants (positive or negative) for which the corresponding polynomial dynamical system is disguised toric. In particular, we construct homeomorphisms to provide an exact bound on the dimension of the R-disguised toric locus.
 
 
 
'''[https://www.stat.uchicago.edu/~ykhoo/ Yuehaw Khoo] (Chicago)'''
 
''Randomized tensor-network algorithms for random data in high-dimensions''
 
Tensor-network ansatz has long been employed to solve the high-dimensional Schrödinger equation, demonstrating linear complexity scaling with respect to dimensionality. Recently, this ansatz has found applications in various machine learning scenarios, including supervised learning and generative modeling, where the data originates from a random process. In this talk, we present a new perspective on randomized linear algebra, showcasing its usage in estimating a density as a tensor-network from i.i.d. samples of a distribution, without the curse of dimensionality, and without the use of optimization techniques. Moreover, we illustrate how this concept can combine the strengths of particle and tensor-network methods for solving high-dimensional PDEs, resulting in enhanced flexibility for both approaches.
 
 
'''[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]]
*[[Applied/ACMS/Spring2024|Spring 2024]]
 
*[[Applied/ACMS/Fall2023|Fall 2023]]
 
----
 
== Archived semesters ==
 
*[[Applied/ACMS/Spring2023|Spring 2023]]
*[[Applied/ACMS/Spring2023|Spring 2023]]
*[[Applied/ACMS/Fall2022|Fall 2022]]
*[[Applied/ACMS/Fall2022|Fall 2022]]

Revision as of 22:59, 1 June 2025


Applied and Computational Mathematics Seminar


Spring 2025

Date Speaker Title Host(s)
Sep 19
Sep 26
Oct 3
Oct 10
Oct 17
Oct 24
Oct 31
Nov 7
Nov 14
Nov 21
Nov 28 Thanksgiving
Dec 5
Dec 12

Abstract

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