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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:''' [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://www.math.wisc.edu/~spagnolie/ Saverio Spagnolie], [https://people.math.wisc.edu/~rycroft/ Chris Rycroft], and [https://sites.google.com/view/laurel-ohm-math Laurel Ohm]  
*'''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].


<br>   
<br>   


== Fall 2023  ==
== '''Fall 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)
|[https://www.anl.gov/profile/zichao-di Zichao (Wendy) Di] (Argonne National Laboratory)
|A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions
|[[#Di|Multimodal Inverse Problems and Multilevel Optimization for X-ray Imaging Science]]
| Chen
|Rycroft/Li
|-
|-
| Sep 15  '''4:00pm B239'''
|Sep 26
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)
|[https://scholar.google.com/citations?user=Imuw5CMAAAAJ&hl=en&oi=ao Pouria Behnoudfar] (UW)
| Nonlocal PDEs and Quantum Optics
|[[#Behnoudfar|Bridging Conceptual and Operational Models: An Explainable AI Framework for Next-Generation Climate Emulators]]
| Li
|Spagnolie
|-
|-
|Sep 22
|Oct 3
|[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)
|''No seminar''
|Oscillatory mass-action systems
|
|Craciun
|
|-
|-
| Sep 29
|Oct 10*
|[https://data-assimilation-causality-oceanography.atmos.colostate.edu/ Peter Jan van Leeuwen] (Colorado State University)
|[https://www.alexandriavolkening.com Alexandria Volkening] (Purdue)
|Nonlinear Causal Discovery, with applications to atmospheric science
|Data-driven modeling of cell behavior in biological patterns
| Chen
|Rycroft
|-
|-
| '''Wed Oct 4'''
|Oct 17*
|[https://www.damtp.cam.ac.uk/person/est42/ Edriss Titi] (Cambridge/Texas A&M)
|[https://www.nickderr.me/ Nick Derr] (UW)
|''[[Applied/ACMS/absF23#Edriss Titi (Cambridge/Texas A&M)|Distringuished Lecture Series]]''
|TBD
| Smith, Stechmann
|Spagnolie
|-
|-
| Oct 6
|Oct 24
| [https://sites.google.com/view/pollyyu Polly Yu] (Harvard/UIUC)
|[https://cims.nyu.edu/~oneil/ Mike O'Neil] (Courant)
| A Spatiotemporal Model of GPCR-G protein Interactions
|TBD
|Craciun
|Spagnolie
|-
|-
| Oct 13
|Oct 31
| [https://geosci.uchicago.edu/people/da-yang/ Da Yang] (University of Chicago)
|[https://people.math.wisc.edu/~hhong78/ Hyukpyo Hong] (UW)
| The Incredible Lightness of Water Vapor
|TBD
|Smith
|Spagnolie
|-
| Oct 20
|[https://www.stat.uchicago.edu/~ykhoo/ Yuehaw Khoo] (University of Chicago)
|
|Li
|-
|-
| Oct 27
|Nov 7*
| [https://shukaidu.github.io/ Shukai Du] (UW)
|[https://thales.mit.edu/bush/ John Bush] (MIT)
| Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer
|TBD
| Stechmann
|Spagnolie
|-
|-
| Nov 3
|Nov 14
|[https://www.math.arizona.edu/~lmig/ Lise-Marie Imbert-Gérard] (University of Arizona)
|[https://sites.google.com/andrew.cmu.edu/yukunyue/home Yukun Yue] (UW)
|
|TBD
|Rycroft
|Spagnolie
|-
|-
| Nov 10
|Nov 21*
| [https://as.tufts.edu/physics/people/faculty/timothy-atherton Timothy Atherton] (Tufts)
|[https://jesnial.github.io/ Jessie Levillain] (CNES/INSA Toulouse)
|
|TBD
|Chandler, Spagnolie
|Ohm
|-
|-
| Nov 17
|Nov 24
|[https://klotsagroup.wixsite.com/home Daphne Klotsa]
|[https://people.maths.ox.ac.uk/trefethen/ Nick Trefethen] (Harvard/Oxford)
|
|TBD
|Rycroft
|Rycroft
|-
|-
| Nov 24
|Nov 28
| Thanksgiving break
|''Thanksgiving''
|
|
|
|
|-
|-
| Dec 1
|Dec 5
|[https://scholar.google.ca/citations?user=CRlA-sEAAAAJ&hl=en&oi=sra Adam Stinchcombe] (University of Toronto)
|[https://mesomod.weebly.com/ Jiamian Hu] (UW)
|
|TBD
|Cochran
|Chen
|-
|-
| Dec 8
|Dec 12
|
|[https://sites.google.com/a/brandeis.edu/tfai/home Thomas Fai] (Brandeis)
|
|TBD
|
|Rycroft
|-
|Pending
|Invite sent to Talea Mayo
|
|Fabien
|}
|}
''[Dates marked with an asterisk are close to weekends with a home game for the [https://uwbadgers.com/sports/football/schedule UW Badgers football team]. Hotel availability around these dates is often limited if booked on short notice.]''


== Abstracts ==
==Abstract==
'''[https://webspace.clarkson.edu/~ebollt/ Erik Bollt] (Clarkson University)'''


''A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions''
<div id="Di">
'''Zichao (Wendy) Di (Argonne National Laboratory)'''


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.
Title: Multimodal Inverse Problems and Multilevel Optimization for X-ray Imaging Science


X-ray imaging experiments generate vast datasets that are often incomplete or ill-posed when considered in isolation. One way forward is multimodal data analysis, where complementary measurement modalities are fused to reduce ambiguity and improve reconstructions. A key question, both mathematically and practically, is how to identify which modalities to combine and how best to integrate them within an inverse problem framework.


'''[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)'''
A second line of work focuses on the computational challenge: even for single-modality inverse problems, the resulting optimization problems are large-scale, nonlinear, and nonconvex. Here, I will discuss multilevel optimization and stochastic sampling strategies that accelerate convergence by exploiting hierarchical structure in both parameter and data spaces.


''Nonlocal PDEs and Quantum Optics''
Although developed separately, these two directions point toward a common goal: building scalable, optimization-based frameworks that make the best use of diverse data to enable new discoveries in X-ray imaging science.


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.
<div id="Behnoudfar">
'''Pouria Behnoudfar (UW Madison)'''


Title: Bridging Conceptual and Operational Models: An Explainable AI Framework for Next-Generation Climate Emulators


'''[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)'''
Computer models are indispensable tools for understanding and predicting the Earth system. While high-resolution operational models have achieved many successes, they exhibit persistent biases, particularly in simulating extreme events and statistical distributions. In contrast, coarse-grained conceptual models isolate fundamental processes and can be precisely calibrated to excel in characterizing specific dynamical and statistical features. Yet, different models often operate independently. By leveraging the complementary strengths of models of varying complexity, we develop a robust, explainable AI framework as a next-generation climate emulator. It bridges the model hierarchy through a reconfigured latent space data assimilation technique, uniquely suited to optimally exploit the sparse output from the conceptual models. The resulting bridging model inherits the high resolution and comprehensive variables of operational models while achieving global accuracy enhancements through targeted improvements from simpler models. Crucially, the AI's mechanism of inter-model communication provides a clear rationale for why each part of the bridging model is improved, moving beyond black-box correction to physically insightful understanding. This computationally efficient framework enables the creation of high-quality digital twins and advances uncertainty quantification for extreme events. We demonstrate its power by significantly correcting biases in CMIP6 simulations of El Ni\~no complexity using simpler, statistically accurate conceptual models.


''Oscillatory mass-action systems''
'''Alexandria Volkening (Purdue)'''


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.
Title: Data-driven modeling of cell behavior in biological patterns


Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Here I will focus on two examples of emergent behavior in biology, specifically cell interactions during pattern formation in zebrafish skin and gametophyte development in ferns. Different modeling approaches provide complementary insights into these systems and face different challenges. For example, vertex-based models describe cell shape, while more efficient agent-based models treat cells as particles. In both cases, it can be challenging to broadly characterize the behavior of these biologically detailed models or address questions about model uniqueness—even quantitatively judging messy, cell-based patterns is not straightforward. Continuum models, which track the evolution of cell densities, are more amenable to analysis, but it is often difficult to relate their few parameters to specific cell interactions. In this talk, I will overview our models of cell behavior in biological patterns and discuss our ongoing work combining Bayesian inference, topological data analysis, and other methods to more broadly characterize pattern systems and the relationship between different models.


'''[https://data-assimilation-causality-oceanography.atmos.colostate.edu/ Peter Jan van Leeuwen] (Colorado State University)'''
== Archived semesters ==
 
''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/UIUC)
 
''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://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/Spring2025|Spring 2025]]
*[[Applied/ACMS/Fall2024|Fall 2024]]
*[[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]]

Latest revision as of 21:39, 4 October 2025


Applied and Computational Mathematics Seminar


Fall 2025

Date Speaker Title Host(s)
Sep 19* Zichao (Wendy) Di (Argonne National Laboratory) Multimodal Inverse Problems and Multilevel Optimization for X-ray Imaging Science Rycroft/Li
Sep 26 Pouria Behnoudfar (UW) Bridging Conceptual and Operational Models: An Explainable AI Framework for Next-Generation Climate Emulators Spagnolie
Oct 3 No seminar
Oct 10* Alexandria Volkening (Purdue) Data-driven modeling of cell behavior in biological patterns Rycroft
Oct 17* Nick Derr (UW) TBD Spagnolie
Oct 24 Mike O'Neil (Courant) TBD Spagnolie
Oct 31 Hyukpyo Hong (UW) TBD Spagnolie
Nov 7* John Bush (MIT) TBD Spagnolie
Nov 14 Yukun Yue (UW) TBD Spagnolie
Nov 21* Jessie Levillain (CNES/INSA Toulouse) TBD Ohm
Nov 24 Nick Trefethen (Harvard/Oxford) TBD Rycroft
Nov 28 Thanksgiving
Dec 5 Jiamian Hu (UW) TBD Chen
Dec 12 Thomas Fai (Brandeis) TBD Rycroft

[Dates marked with an asterisk are close to weekends with a home game for the UW Badgers football team. Hotel availability around these dates is often limited if booked on short notice.]

Abstract

Zichao (Wendy) Di (Argonne National Laboratory)

Title: Multimodal Inverse Problems and Multilevel Optimization for X-ray Imaging Science

X-ray imaging experiments generate vast datasets that are often incomplete or ill-posed when considered in isolation. One way forward is multimodal data analysis, where complementary measurement modalities are fused to reduce ambiguity and improve reconstructions. A key question, both mathematically and practically, is how to identify which modalities to combine and how best to integrate them within an inverse problem framework.

A second line of work focuses on the computational challenge: even for single-modality inverse problems, the resulting optimization problems are large-scale, nonlinear, and nonconvex. Here, I will discuss multilevel optimization and stochastic sampling strategies that accelerate convergence by exploiting hierarchical structure in both parameter and data spaces.

Although developed separately, these two directions point toward a common goal: building scalable, optimization-based frameworks that make the best use of diverse data to enable new discoveries in X-ray imaging science.

Pouria Behnoudfar (UW Madison)

Title: Bridging Conceptual and Operational Models: An Explainable AI Framework for Next-Generation Climate Emulators

Computer models are indispensable tools for understanding and predicting the Earth system. While high-resolution operational models have achieved many successes, they exhibit persistent biases, particularly in simulating extreme events and statistical distributions. In contrast, coarse-grained conceptual models isolate fundamental processes and can be precisely calibrated to excel in characterizing specific dynamical and statistical features. Yet, different models often operate independently. By leveraging the complementary strengths of models of varying complexity, we develop a robust, explainable AI framework as a next-generation climate emulator. It bridges the model hierarchy through a reconfigured latent space data assimilation technique, uniquely suited to optimally exploit the sparse output from the conceptual models. The resulting bridging model inherits the high resolution and comprehensive variables of operational models while achieving global accuracy enhancements through targeted improvements from simpler models. Crucially, the AI's mechanism of inter-model communication provides a clear rationale for why each part of the bridging model is improved, moving beyond black-box correction to physically insightful understanding. This computationally efficient framework enables the creation of high-quality digital twins and advances uncertainty quantification for extreme events. We demonstrate its power by significantly correcting biases in CMIP6 simulations of El Ni\~no complexity using simpler, statistically accurate conceptual models.

Alexandria Volkening (Purdue)

Title: Data-driven modeling of cell behavior in biological patterns

Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, cells in a developing tissue, or locusts in a swarm. Here I will focus on two examples of emergent behavior in biology, specifically cell interactions during pattern formation in zebrafish skin and gametophyte development in ferns. Different modeling approaches provide complementary insights into these systems and face different challenges. For example, vertex-based models describe cell shape, while more efficient agent-based models treat cells as particles. In both cases, it can be challenging to broadly characterize the behavior of these biologically detailed models or address questions about model uniqueness—even quantitatively judging messy, cell-based patterns is not straightforward. Continuum models, which track the evolution of cell densities, are more amenable to analysis, but it is often difficult to relate their few parameters to specific cell interactions. In this talk, I will overview our models of cell behavior in biological patterns and discuss our ongoing work combining Bayesian inference, topological data analysis, and other methods to more broadly characterize pattern systems and the relationship between different models.

Archived semesters


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