Applied/ACMS

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+subscribe@g-groups.wisc.edu.

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

• Fall 2024
• Spring 2024
• Fall 2023
• 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

---

Return to the Applied Mathematics Group Page