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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].


<br>   
<br>   


== 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
|Jan 31
|[https://webspace.clarkson.edu/~ebollt/ Erik Bollt] (Clarkson University)
|[https://people.math.wisc.edu/~tgchandler/ Thomas Chandler] (UW)
|A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions
|[[#Chandler|''Fluid–structure interactions in active complex fluids'']]
| Chen
|Spagnolie
|-
|-
| Sep 15  '''4:00pm B239'''
|Feb 7
|[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)
|[https://afraser3.github.io/ Adrian Fraser] (Colorado)
| Nonlocal PDEs and Quantum Optics
|[[#Fraser|''Destabilization of transverse waves by periodic shear flows'']]
| Li
|Spagnolie
|-
|-
|Sep 22
|Feb 14
|[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)
|[https://jrluedtke.github.io/ Jim Luedtke] (UW)
|Oscillatory mass-action systems
|[[#Luedtke|Using integer programming for verification of binarized neural networks]]
|Craciun
|Spagnolie
|-
|-
| Sep 29
|Feb 21
|[https://data-assimilation-causality-oceanography.atmos.colostate.edu/ Peter Jan van Leeuwen] (Colorado State University)
|[https://zhdankin.physics.wisc.edu/ Vladimir Zhdankin] (UW)
|Nonlinear Causal Discovery, with applications to atmospheric science
|[[#Zhdankin|Exploring astrophysical plasma turbulence with particle-in-cell methods]]
| Chen
|Spagnolie
|-
|-
| '''Wed Oct 4'''
|Feb 28
|[https://www.damtp.cam.ac.uk/person/est42/ Edriss Titi] (Cambridge/Texas A&M)
|[https://nmboffi.github.io/ Nick Boffi] (CMU)
|''[[Applied/ACMS/absF23#Edriss Titi (Cambridge/Texas A&M)|Distringuished Lecture Series]]''
|[[#Boffi|Generative modeling with stochastic interpolants]]
| Smith, Stechmann
|Li, Rycroft
|-
|-
| Oct 6
|Mar 7
| [https://sites.google.com/view/pollyyu Polly Yu] (Harvard/UIUC)
|[https://sites.lsa.umich.edu/shankar-lab/ Suraj Shankar] (Michigan)
| TBA
|[[#Shankar|Designer active matter]]
|Craciun
|Spagnolie
|-
|-
| Oct 13
|Mar 10
| [https://geosci.uchicago.edu/people/da-yang/ Da Yang] (University of Chicago)
|[https://www.math.kit.edu/csmm/~loevbak/en Emil Loevbak] (KIT)
|
|[[#Loevbak|Discrete adjoint Monte Carlo for kinetic equations with reversible pseudorandom generators]]
|Smith
|Li
|-
|-
| Oct 20
|Mar 14
|[https://www.stat.uchicago.edu/~ykhoo/ Yuehaw Khoo] (University of Chicago)
|[https://lu.seas.harvard.edu/ Yue Lu] (Harvard) '''[Colloquium]'''
|
|[[#Lu|Nonlinear Random Matrices in Estimation and Learning: Equivalence Principles and Applications]]
|Li
|Li
|-
|-
| Oct 27
|Mar 21
| [https://shukaidu.github.io/ Shukai Du] (UW)
|[https://people.llnl.gov/vogman1 Genia Vogman] (LLNL)
| Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer
|[[#Vogman|TBA]]
| Stechmann
|Li
|-
|-
| Nov 3
|Mar 28
|[https://www.math.arizona.edu/~lmig/ Lise-Marie Imbert-Gérard] (University of Arizona)
|''Spring Break''
|
|
|Rycroft
|-
| Nov 10
| [https://as.tufts.edu/physics/people/faculty/timothy-atherton Timothy Atherton] (Tufts)
|
|
|Chandler, Spagnolie
|-
|-
| Nov 17
|Apr 4
|[https://klotsagroup.wixsite.com/home Daphne Klotsa]
|[https://mathsci.kaist.ac.kr/~donghwankim/ Donghwan Kim] (KAIST)
|
|TBA
|Rycroft
|Lyu
|-
|-
| Nov 24
|Apr 11
| Thanksgiving break
|[https://meche.mit.edu/people/faculty/pierrel@mit.edu Pierre Lermusiaux] (MIT)
|
|[[#Lermusiaux|TBA]]
|
|Chen
|-
|-
| Dec 1
|Apr 18
|[https://scholar.google.ca/citations?user=CRlA-sEAAAAJ&hl=en&oi=sra Adam Stinchcombe] (University of Toronto)
|[https://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine) '''[Colloquium]'''
|[[#Xin|TBA]]
|
|
|Cochran
|-
|-
| Dec 8
|Apr 25
|
|[https://www-users.cse.umn.edu/~bcockbur/ Bernardo Cockburn] (Minnesota)
|
|[[#Cockburn|''Transforming stabilization into spaces'']]
|
| Stechmann, Fabien
|-
|-
|Pending
|May 2
|Invite sent to Talea Mayo
|[https://sylviaherbert.com/ Sylvia Herbert] (UCSD)
|
|[[#Herbert|TBA]]
|Fabien
|Chen
|}
|}


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


''A New View on Integrability: On Matching Dynamical Systems through Koopman Operator Eigenfunctions''
<div id="Chandler">
====Thomas G. J. Chandler (UW)====
Title: Fluid-structure interactions in active complex fluids


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.
Fluid anisotropy is central to many biological systems, from rod-like bacteria that self-assemble into dense swarms that function as fluids, to the cell cytoskeleton where the active alignment of stiff biofilaments is crucial to cell division. Nematic liquid crystals provide a powerful model for studying these complex environments. However, large immersed bodies elastically frustrate these fluids, leading to intricate interactions. This frustration can be alleviated through body deformations, at the cost of introducing internal stresses. Additionally, active stresses, arising from particle motility or molecular activity, disrupt nematic order by driving flows. In this presentation, I will demonstrate how complex variables enable analytical solutions to a broad range of problems, offering key insights into the roles of body geometry, anchoring conditions, interaction dynamics, activity-induced flows, and body deformations in many biological settings.


<div id="Fraser">
====Adrian Fraser (Colorado)====
Title: Destabilization of transverse waves by periodic shear flows


'''[https://math.yale.edu/people/john-schotland John Schotland] (Yale University)'''
Periodic shear flows have the peculiar property that they are unstable to large-scale, transverse perturbations, and that this instability proceeds via a negative-eddy-viscosity mechanism (Dubrulle & Frisch, 1991). In this talk, I will show an example where this property causes transverse waves to become linearly unstable: a sinusoidal shear flow in the presence of a uniform, streamwise magnetic field in the framework of incompressible MHD. This flow is unstable to a KH-like instability for sufficiently weak magnetic fields, and uniform magnetic fields permit transverse waves known as Alfvén waves. Under the right conditions, these Alfvén waves become unstable, presenting a separate branch of instability that persists for arbitrarily strong magnetic fields which otherwise suppress the KH-like instability. After characterizing these waves with the help of a simple asymptotic expansion, I will show that they drive soliton-like waves in nonlinear simulations. With time permitting, I will discuss other fluid systems where similar dynamics are or may be found, including stratified flows and plasma drift waves.


''Nonlocal PDEs and Quantum Optics''
<div id="Luedtke">
====Jim Luedtke (UW)====
Title: Using integer programming for verification of binarized neural networks


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.
Binarized neural networks (BNNs) are neural networks in which the weights are binary and the activation functions are the sign function. Verification of BNNs against input perturbation is one way to measure robustness of BNNs. BNN verification can be formulated as an integer linear optimization problem and hence can in theory be solved by state-of-the art methods for integer programming such as the branch-and-cut algorithm implemented in solvers like Gurobi. Unfortunately, the natural formulation is often difficult to solve in practice, even by the best such solvers, due to large integrality gap induced by its so-called "big-M" constraints. We present simple but effective techniques for improving the ability of the integer programming approach to solve the verification problem for BNNs. Along the way, we hope to illustrate more generally some of the strategies integer programmers use to attack difficult problems like this. We find that our techniques enable verifying BNNs against a higher range of input perturbation than using the natural formulation directly.


This is joint work with Woojin Kim, Mathematics PhD student at UW-Madison.


'''[https://sites.google.com/view/balazsboros Balazs Boros] (U Vienna)'''
<div id="Zhdankin">
====Vladimir Zhdankin (UW)====
Title: Exploring astrophysical plasma turbulence with particle-in-cell methods


''Oscillatory mass-action systems''
Plasmas throughout the universe (as well as in the laboratory) tend to exist in turbulent, nonequilibrium states due to their "collisionless" nature. Described by the Vlasov-Maxwell equations in a six-dimensional phase space (of position and momentum), the basic physics of such plasmas is difficult to model from first principles. There remain open questions about entropy production, nonthermal particle acceleration, energy partition amongst different particle species, and more. Particle-in-cell simulations are a numerical tool that allow us to explore in depth the rich dynamics and statistical mechanics of collisionless plasmas, validating analytical speculation. I will describe some of the results from my group's work on this topic.


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.
<div id="Boffi">
====Nick Boffi (CMU)====
Title: Generative modeling with stochastic interpolants


We introduce a class of generative models that unifies flows and diffusions. These models are built using a continuous-time stochastic process called a stochastic interpolant, which exactly connects two arbitrary probability densities in finite time. We show that the time-dependent density of the stochastic interpolant satisfies both a first-order transport equation and an infinite family of forward and backward Fokker-Planck equations with tunable diffusion coefficients. This viewpoint yields deterministic and stochastic generative models built dynamically from an ordinary or stochastic differential equation with an adjustable noise level. To formulate a practical algorithm, we discuss how the resulting drift functions can be characterized variationally and learned efficiently over flexible parametric classes such as neural networks. Empirically, we highlight the advantages of our formalism -- and the tradeoffs between deterministic and stochastic sampling -- through numerical examples in image generation, inverse imaging, probabilistic forecasting, and accelerated sampling.


'''[https://shukaidu.github.io/ Shukai Du] (UW)'''
<div id="Shankar">
====Suraj Shankar (Michigan)====
Title: Designer active matter


''Element learning: a systematic approach of accelerating finite element-type methods via machine learning, with applications to radiative transfer''
Active matter, i.e., internally driven matter fueled by a sustained dissipation of free energy, is ubiquitous in the natural world. Examples range from bird flocks and human crowds to migrating cells and biopolymer gels, including synthetic systems like phoretic colloids and robots. While much is known about the emergent collective phenomena and complex dynamics that active matter exhibits, little is known about the inverse problem on how they can be controlled. I will discuss a few different vignettes on our recent efforts in controlling flows, forces and physical features of active materials, highlighting implications for the design of novel metamaterials and biomimetic constructs.


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.
<div id="Loevbak">
==== Emil Loevbak (KIT) ====
Title: Discrete adjoint Monte Carlo for kinetic equations with reversible pseudorandom generators


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]
Abstract: Kinetic equations, PDEs modeling particles in a position-velocity phase space, have many high-impact application areas, including nuclear fusion research and radiation therapy. In these applications, one often uses particle-based Monte Carlo methods to simulate the kinetic models. These methods solve the PDE by tracing sample particle trajectories through physical space in such a way that their ensemble distribution in phase-space corresponds with the solution of the PDE. One then uses these trajectories as samples to compute quantities such as the particles' mass-density, momentum, and energy as a function of space and time. These methods have the advantage of not constructing grids in the high-dimensional phase space but the drawback of producing computational results subject to a stochastic sampling error.


== Future semesters ==
In this talk I consider PDE-constrained optimization, where a PDE is simulated with a Monte Carlo solver. Here, we compute gradients through a discrete adjoint approach. To ensure optimization convergence, it is imperative to ensure that the same particle trajectories are used when solving the original PDE when evaluating the objective functional and the adjoint PDE when computing gradients. I present an approach of using reversible random number generators to ensure path consistency, despite the adjoint PDE running backward in time. I first present this strategy using a didactic example using a 1D diffusion equation and then present some results from a fusion plasma-edge simulation case.
 
 
<div id="Lu">
==== Yue M. Lu (Harvard) ====
Title: Nonlinear Random Matrices in Estimation and Learning: Equivalence Principles and Applications
 
Abstract: In recent years, new classes of structured random matrices have emerged in statistical estimation and machine learning. Understanding their spectral properties has become increasingly important, as these matrices are closely linked to key quantities such as the training and generalization performance of large neural networks and the fundamental limits of high-dimensional signal recovery. Unlike classical random matrix ensembles, these new matrices often involve nonlinear transformations, introducing additional structural dependencies that pose challenges for traditional analysis techniques.
 
In this talk, I will present a set of equivalence principles that establish asymptotic connections between various nonlinear random matrix ensembles and simpler linear models that are more tractable for analysis. I will then demonstrate how these principles can be applied to characterize the performance of kernel methods and random feature models across different scaling regimes and to provide insights into the in-context learning capabilities of attention-based Transformer networks.
 
Bio: Yue M. Lu is a Harvard College Professor and Gordon McKay Professor of Electrical Engineering and Applied Mathematics at Harvard University. He has also held visiting appointments at Duke University (2016) and the École Normale Supérieure (ENS) in Paris (2019). His research focuses on the mathematical foundations of high-dimensional statistical estimation and learning. His contributions have been recognized with several best paper awards (IEEE ICIP, ICASSP, and GlobalSIP), the ECE Illinois Young Alumni Achievement Award (2015), and the IEEE Signal Processing Society Distinguished Lecturership (2022). He is a Fellow of the IEEE (Class of 2024).


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


<div id="Cockburn">
====Bernardo Cockburn (Minnesota)====
Title: Transforming stabilization into spaces


----
In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.


== Archived semesters ==
== Archived semesters ==


*[[Applied/ACMS/Fall2024|Fall 2024]]
*[[Applied/ACMS/Spring2024|Spring 2024]]
*[[Applied/ACMS/Fall2023|Fall 2023]]
*[[Applied/ACMS/Spring2023|Spring 2023]]
*[[Applied/ACMS/Spring2023|Spring 2023]]
*[[Applied/ACMS/Fall2022|Fall 2022]]
*[[Applied/ACMS/Fall2022|Fall 2022]]

Latest revision as of 22:28, 7 March 2025


Applied and Computational Mathematics Seminar


Spring 2025

Date Speaker Title Host(s)
Jan 31 Thomas Chandler (UW) Fluid–structure interactions in active complex fluids Spagnolie
Feb 7 Adrian Fraser (Colorado) Destabilization of transverse waves by periodic shear flows Spagnolie
Feb 14 Jim Luedtke (UW) Using integer programming for verification of binarized neural networks Spagnolie
Feb 21 Vladimir Zhdankin (UW) Exploring astrophysical plasma turbulence with particle-in-cell methods Spagnolie
Feb 28 Nick Boffi (CMU) Generative modeling with stochastic interpolants Li, Rycroft
Mar 7 Suraj Shankar (Michigan) Designer active matter Spagnolie
Mar 10 Emil Loevbak (KIT) Discrete adjoint Monte Carlo for kinetic equations with reversible pseudorandom generators Li
Mar 14 Yue Lu (Harvard) [Colloquium] Nonlinear Random Matrices in Estimation and Learning: Equivalence Principles and Applications Li
Mar 21 Genia Vogman (LLNL) TBA Li
Mar 28 Spring Break
Apr 4 Donghwan Kim (KAIST) TBA Lyu
Apr 11 Pierre Lermusiaux (MIT) TBA Chen
Apr 18 Jack Xin (UC Irvine) [Colloquium] TBA
Apr 25 Bernardo Cockburn (Minnesota) Transforming stabilization into spaces Stechmann, Fabien
May 2 Sylvia Herbert (UCSD) TBA Chen

Abstracts

Thomas G. J. Chandler (UW)

Title: Fluid-structure interactions in active complex fluids

Fluid anisotropy is central to many biological systems, from rod-like bacteria that self-assemble into dense swarms that function as fluids, to the cell cytoskeleton where the active alignment of stiff biofilaments is crucial to cell division. Nematic liquid crystals provide a powerful model for studying these complex environments. However, large immersed bodies elastically frustrate these fluids, leading to intricate interactions. This frustration can be alleviated through body deformations, at the cost of introducing internal stresses. Additionally, active stresses, arising from particle motility or molecular activity, disrupt nematic order by driving flows. In this presentation, I will demonstrate how complex variables enable analytical solutions to a broad range of problems, offering key insights into the roles of body geometry, anchoring conditions, interaction dynamics, activity-induced flows, and body deformations in many biological settings.

Adrian Fraser (Colorado)

Title: Destabilization of transverse waves by periodic shear flows

Periodic shear flows have the peculiar property that they are unstable to large-scale, transverse perturbations, and that this instability proceeds via a negative-eddy-viscosity mechanism (Dubrulle & Frisch, 1991). In this talk, I will show an example where this property causes transverse waves to become linearly unstable: a sinusoidal shear flow in the presence of a uniform, streamwise magnetic field in the framework of incompressible MHD. This flow is unstable to a KH-like instability for sufficiently weak magnetic fields, and uniform magnetic fields permit transverse waves known as Alfvén waves. Under the right conditions, these Alfvén waves become unstable, presenting a separate branch of instability that persists for arbitrarily strong magnetic fields which otherwise suppress the KH-like instability. After characterizing these waves with the help of a simple asymptotic expansion, I will show that they drive soliton-like waves in nonlinear simulations. With time permitting, I will discuss other fluid systems where similar dynamics are or may be found, including stratified flows and plasma drift waves.

Jim Luedtke (UW)

Title: Using integer programming for verification of binarized neural networks

Binarized neural networks (BNNs) are neural networks in which the weights are binary and the activation functions are the sign function. Verification of BNNs against input perturbation is one way to measure robustness of BNNs. BNN verification can be formulated as an integer linear optimization problem and hence can in theory be solved by state-of-the art methods for integer programming such as the branch-and-cut algorithm implemented in solvers like Gurobi. Unfortunately, the natural formulation is often difficult to solve in practice, even by the best such solvers, due to large integrality gap induced by its so-called "big-M" constraints. We present simple but effective techniques for improving the ability of the integer programming approach to solve the verification problem for BNNs. Along the way, we hope to illustrate more generally some of the strategies integer programmers use to attack difficult problems like this. We find that our techniques enable verifying BNNs against a higher range of input perturbation than using the natural formulation directly.

This is joint work with Woojin Kim, Mathematics PhD student at UW-Madison.

Vladimir Zhdankin (UW)

Title: Exploring astrophysical plasma turbulence with particle-in-cell methods

Plasmas throughout the universe (as well as in the laboratory) tend to exist in turbulent, nonequilibrium states due to their "collisionless" nature. Described by the Vlasov-Maxwell equations in a six-dimensional phase space (of position and momentum), the basic physics of such plasmas is difficult to model from first principles. There remain open questions about entropy production, nonthermal particle acceleration, energy partition amongst different particle species, and more. Particle-in-cell simulations are a numerical tool that allow us to explore in depth the rich dynamics and statistical mechanics of collisionless plasmas, validating analytical speculation. I will describe some of the results from my group's work on this topic.

Nick Boffi (CMU)

Title: Generative modeling with stochastic interpolants

We introduce a class of generative models that unifies flows and diffusions. These models are built using a continuous-time stochastic process called a stochastic interpolant, which exactly connects two arbitrary probability densities in finite time. We show that the time-dependent density of the stochastic interpolant satisfies both a first-order transport equation and an infinite family of forward and backward Fokker-Planck equations with tunable diffusion coefficients. This viewpoint yields deterministic and stochastic generative models built dynamically from an ordinary or stochastic differential equation with an adjustable noise level. To formulate a practical algorithm, we discuss how the resulting drift functions can be characterized variationally and learned efficiently over flexible parametric classes such as neural networks. Empirically, we highlight the advantages of our formalism -- and the tradeoffs between deterministic and stochastic sampling -- through numerical examples in image generation, inverse imaging, probabilistic forecasting, and accelerated sampling.

Suraj Shankar (Michigan)

Title: Designer active matter

Active matter, i.e., internally driven matter fueled by a sustained dissipation of free energy, is ubiquitous in the natural world. Examples range from bird flocks and human crowds to migrating cells and biopolymer gels, including synthetic systems like phoretic colloids and robots. While much is known about the emergent collective phenomena and complex dynamics that active matter exhibits, little is known about the inverse problem on how they can be controlled. I will discuss a few different vignettes on our recent efforts in controlling flows, forces and physical features of active materials, highlighting implications for the design of novel metamaterials and biomimetic constructs.

Emil Loevbak (KIT)

Title: Discrete adjoint Monte Carlo for kinetic equations with reversible pseudorandom generators

Abstract: Kinetic equations, PDEs modeling particles in a position-velocity phase space, have many high-impact application areas, including nuclear fusion research and radiation therapy. In these applications, one often uses particle-based Monte Carlo methods to simulate the kinetic models. These methods solve the PDE by tracing sample particle trajectories through physical space in such a way that their ensemble distribution in phase-space corresponds with the solution of the PDE. One then uses these trajectories as samples to compute quantities such as the particles' mass-density, momentum, and energy as a function of space and time. These methods have the advantage of not constructing grids in the high-dimensional phase space but the drawback of producing computational results subject to a stochastic sampling error.

In this talk I consider PDE-constrained optimization, where a PDE is simulated with a Monte Carlo solver. Here, we compute gradients through a discrete adjoint approach. To ensure optimization convergence, it is imperative to ensure that the same particle trajectories are used when solving the original PDE when evaluating the objective functional and the adjoint PDE when computing gradients. I present an approach of using reversible random number generators to ensure path consistency, despite the adjoint PDE running backward in time. I first present this strategy using a didactic example using a 1D diffusion equation and then present some results from a fusion plasma-edge simulation case.


Yue M. Lu (Harvard)

Title: Nonlinear Random Matrices in Estimation and Learning: Equivalence Principles and Applications

Abstract: In recent years, new classes of structured random matrices have emerged in statistical estimation and machine learning. Understanding their spectral properties has become increasingly important, as these matrices are closely linked to key quantities such as the training and generalization performance of large neural networks and the fundamental limits of high-dimensional signal recovery. Unlike classical random matrix ensembles, these new matrices often involve nonlinear transformations, introducing additional structural dependencies that pose challenges for traditional analysis techniques.

In this talk, I will present a set of equivalence principles that establish asymptotic connections between various nonlinear random matrix ensembles and simpler linear models that are more tractable for analysis. I will then demonstrate how these principles can be applied to characterize the performance of kernel methods and random feature models across different scaling regimes and to provide insights into the in-context learning capabilities of attention-based Transformer networks.

Bio: Yue M. Lu is a Harvard College Professor and Gordon McKay Professor of Electrical Engineering and Applied Mathematics at Harvard University. He has also held visiting appointments at Duke University (2016) and the École Normale Supérieure (ENS) in Paris (2019). His research focuses on the mathematical foundations of high-dimensional statistical estimation and learning. His contributions have been recognized with several best paper awards (IEEE ICIP, ICASSP, and GlobalSIP), the ECE Illinois Young Alumni Achievement Award (2015), and the IEEE Signal Processing Society Distinguished Lecturership (2022). He is a Fellow of the IEEE (Class of 2024).


Bernardo Cockburn (Minnesota)

Title: Transforming stabilization into spaces

In the framework of finite element methods for ordinary differential equations, we consider the continuous Galerkin method (introduced in 72) and the discontinuous Galerkin method (introduced in 73/74). We uncover the fact that both methods discretize the time derivative in exactly the same form, and discuss a few of its consequences. We end by briefly describing our ongoing work on the extension of this result to some Galerkin methods for partial differential equations.

Archived semesters


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