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== '''Fall 2024''' ==
== '''Spring 2025''' ==
{| class="wikitable"
{| cellpadding="8"
|+
! align="left" |Date
!Date
! align="left" |Speaker
!Speaker
! align="left" |Title
!Title
! align="left" |Host(s)
!Host(s)
|-
|-
|Sep 13*
|Jan 31
|[https://people.math.wisc.edu/~nchen29/ Nan Chen] (UW)
|[https://people.math.wisc.edu/~tgchandler/ Thomas Chandler] (UW)
|Intro. to Uncertainty Quantification (UQ) (tutorial)
|[[#Chandler|''Fluid–structure interactions in active complex fluids'']]
|Spagnolie
|Spagnolie
|-
|-
|Sep 20
|Feb 7
|[https://knewhall.web.unc.edu Katie Newhall] (UNC Chapel Hill)
|[https://afraser3.github.io/ Adrian Fraser] (Colorado)
|Energy landscapes, metastability, and transition paths
|[[#Fraser|''Destabilization of transverse waves by periodic shear flows'']]
|Rycroft
|Spagnolie
|-
|-
|Sep 27
|Feb 14
|[https://ptg.ukzn.ac.za Indresan Govender] (Mintek / Univ. of KwaZulu-Natal, South Africa)
|[https://jrluedtke.github.io/ Jim Luedtke] (UW)
|Granular flow modeling and visualization using nuclear imaging
|[[#Luedtke|Using integer programming for verification of binarized neural networks]]
|Rycroft
|Spagnolie
|-
|-
|Oct 4*
|Feb 21
|[https://sse.tulane.edu/math/people/hongfei-chen Hongfei Chen] (Tulane)
|[https://zhdankin.physics.wisc.edu/ Vladimir Zhdankin] (UW)
|Investigating Hydrodynamics of Choanoflagellate Colonies: A Reduced Model Approach
|[[#Zhdankin|Exploring astrophysical plasma turbulence with particle-in-cell methods]]
|Jean-Luc
|Spagnolie
|-
|-
|Oct 11 '''Colloquium in B239 at 4:00pm'''
|Feb 28
|[https://people.math.ethz.ch/~imikaela/ Mikaela Iacobelli] (ETH/IAS)
|[https://nmboffi.github.io/ Nick Boffi] (CMU)
|[[# TBA| TBA  ]]
|[[#Boffi|Generative modeling with stochastic interpolants]]
|Li
|Li, Rycroft
|-
|-
|Oct 18 '''Colloquium in B239 at 4:00pm'''
|Mar 7
|[https://galton.uchicago.edu/~guillaumebal/ Guillaume Bal] (U Chicago)
|[https://sites.lsa.umich.edu/shankar-lab/ Suraj Shankar] (Michigan)
|[[#Bal| Speckle formation of laser light in random media: The Gaussian conjecture  ]]
|[[#Shankar|Designer active matter]]
| Li, Stechmann
|Spagnolie
|-
|-
|Oct 23 ('''Wednesday''')
|Mar 10
|[https://www.sandia.gov/ccr/staff/teresa-portone/ Teresa Portone] (Sandia)
|[https://www.math.kit.edu/csmm/~loevbak/en Emil Loevbak] (KIT)
|[[#Portone | Beyond parametric uncertainty: quantifying model-form uncertainty in model predictions ]]
|[[#Loevbak|Discrete adjoint Monte Carlo for kinetic equations with reversible pseudorandom generators]]
|Stechmann
|Li
|-
|-
|Oct 25
|Mar 14
|[https://www.cs.cornell.edu/~damle/ Anil Damle] (Cornell)
|[https://lu.seas.harvard.edu/ Yue Lu] (Harvard) '''[Colloquium]'''
|[[#Damle | Fine-grained Theory and Hybrid Algorithms for Randomized Numerical Linear Algebra ]]
|[[#Lu|Nonlinear Random Matrices in Estimation and Learning: Equivalence Principles and Applications]]
|Li
|Li
|-
|-
| Nov 1
|Mar 21
|[https://research-hub.nrel.gov/en/persons/michael-sprague Michael Sprague] (NREL)
|[https://people.llnl.gov/vogman1 Genia Vogman] (LLNL)
|[[#Sprague| Exascale supercomputing and predictive wind energy simulations  ]]
|[[#Vogman|TBA]]
|Spagnolie
|Li
|-
|-
| Nov 8
|Mar 28
|[https://personal.math.ubc.ca/~holmescerfon/ Miranda Holmes-Cerfon] (UBC)
|''Spring Break''
|[[#Holmes-Cerfon | The dynamics of particles with ligand-receptor contacts ]]
|
|Stechmann
|
|-
|-
| Nov 15*
|Apr 4
| [http://sun-yue.com Yue Sun] (UW–Madison)
|[https://mathsci.kaist.ac.kr/~donghwankim/ Donghwan Kim] (KAIST)
|[[#Holmes-Cerfon | Simulating fluid–structure interaction: A tale of two methods ]]
|TBA
| Rycroft
|Lyu
|-
|-
| Nov 22
|Apr 11
|[https://ibd.uchicago.edu/joinus/yenfellowship/ Ondrej Maxian] (U Chicago)
|[https://meche.mit.edu/people/faculty/pierrel@mit.edu Pierre Lermusiaux] (MIT)
|[[#Maxian | From slender body numerics to patterning the cell cortex: two stories of actin filament dynamics ]]  
|[[#Lermusiaux|TBA]]
|Ohm & Spagnolie
|Chen
|-
|-
| Nov 29*
|Apr 18
|''Thanksgiving''
|[https://www.math.uci.edu/~jxin/ Jack Xin] (UC Irvine) '''[Colloquium]'''
|
|[[#Xin|TBA]]
|
|
|-
|-
| Dec 6
|Apr 25
|[https://www.simonsfoundation.org/people/ido-lavi/ Ido Lavi] (Flatiron)
|[https://www-users.cse.umn.edu/~bcockbur/ Bernardo Cockburn] (Minnesota)
|[[#Lavi| Emergence of large-scale patterns in active matter: from nematic fluids to multicellular systems ]]
|[[#Cockburn|''Transforming stabilization into spaces'']]
|Spagnolie
| Stechmann, Fabien
|-
|May 2
|[https://sylviaherbert.com/ Sylvia Herbert] (UCSD)
|[[#Herbert|TBA]]
|Chen
|}
|}


Dates marked with an asterisk correspond to [https://uwbadgers.com/sports/football/schedule home football games of the UW–Madison Badgers]. On these dates it can be difficult to get a hotel room close to campus at short notice.
==Abstracts==


== Abstracts ==
<div id="Chandler">
====Thomas G. J. Chandler (UW)====
Title: Fluid-structure interactions in active complex fluids


===Nan Chen (UW–Madison)===
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.


Title: Taming Uncertainty in a Complex World: The Rise of Uncertainty Quantification -- A Tutorial for Beginners
<div id="Fraser">
====Adrian Fraser (Colorado)====
Title: Destabilization of transverse waves by periodic shear flows


I will provide a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more about this area. The talk will exploit many elementary examples, which are understandable to graduate students and senior undergraduates, to present the ideas of UQ. Topics include characterizing uncertainties using information theory, UQ in linear and nonlinear dynamical systems, UQ via data assimilation, the role of uncertainty in diagnostics, and UQ in advancing efficient modeling. The surprisingly simple examples in each topic explain why and how UQ is essential. Both Matlab and Python codes have been made available for these simple examples.
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.


===Katie Newhall (UNC Chapel Hill)===
<div id="Luedtke">
====Jim Luedtke (UW)====
Title: Using integer programming for verification of binarized neural networks


Title: Energy landscapes, metastability, and transition paths
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.


The concept of an energy landscape emerged in the 1930’s as a way to calculate chemical reaction rate constants via Henry Eyring’s transition state theory. Its use has expanded since then, remaining central to quantifying metastability (infrequent jumps between deterministically-stable, energy minimizing, states) that arises in noisy systems when the thermal energy is small relative to the energy barrier separating two states. In this talk, I will present extensions of this theory that I have developed and applied to physical and biological systems. The first is an infinite dimensional system for which I prove metastability is present in the absence of an energy barrier; I extend transition state theory to compute mean transition times. In the second, I derive a model for a spatially-extended magnetic system with spatially-correlated noise designed to sample the Gibbs distribution relative to a defined energy functional. In the third, I show a quasi-potential can be found and used to describe metastable transitions between stable clusters in a bead-spring polymer model of chromosome dynamics with additional stochastic binding pushing the system out of equilibrium.
This is joint work with Woojin Kim, Mathematics PhD student at UW-Madison.


===Indresan Govender (Mintek / Univ. of KwaZulu Natal, South Africa)===
<div id="Zhdankin">
====Vladimir Zhdankin (UW)====
Title: Exploring astrophysical plasma turbulence with particle-in-cell methods


Title: Granular flow modeling and visualization using nuclear imaging
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.


Despite its ubiquity, a complete theory to describe the underlying rheology of granular flows remains elusive. Central to this problem is the lack of detailed, in-situ measurements of the granular flow field. To this end, we present two non-invasive imaging techniques currently employed to measure the flow of individual grains within granular flow systems that span simple mono-sized flows of plastic beads to complex industrial mixture flows of rocks and slurry. The first technique employs diagnostic X-rays operated in biplanar mode to triangulate the motion of low-density granules in simplified flow systems to within a 3D spatial accuracy of 0.15 mm at tracking frequencies up to 100 Hz. The second—arguably the workhorse of our research operation—is the nuclear imaging technique of Positron Emission Particle Tracking (PEPT) which triangulates the back-to-back gamma rays emanating from radiolabeled particles to within a millimeter in 3D space at a millisecond timing resolution. PEPT can track the motion of any particle with a diameter greater than ∼20 microns. Both techniques are well suited to studying the flow of granular materials after the data is cast into volume and time averages consistent with the continuum framework. In this talk I will explore the many interesting analysis techniques employed to mapping out the complex flow regimes found in typical granular systems, and the insights they offer towards better understanding their rheological character. Examples explored will include rotating drum flows (wet and dry), shear cells and their industrial counterpart the IsaMill<sup>TM</sup>, hydrocyclone separator flows, and the motivation for tracking of multiple particles. The validation offered to numerical schemes like the Discrete Element Method will also be explored wherein we highlight the complimentary role that measurement and simulation play in unravelling the secrets of granular flows. Finally, and deviating somewhat from the imaging world, I will present our efforts towards utilizing granular flow modeling in real-time control of complex industrial flows encountered in mineral processing.
<div id="Boffi">
====Nick Boffi (CMU)====
Title: Generative modeling with stochastic interpolants


===Hongfei Chen (Tulane)===
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.


Title: Investigating Hydrodynamics of Choanoflagellate Colonies: A Reduced Model Approach
<div id="Shankar">
====Suraj Shankar (Michigan)====
Title: Designer active matter


Abstract: Choanoflagellates, eukaryotes with a distinctive cellular structure consisting of a cell body, a flagellum, and a collar of microvilli, exhibit fascinating biological behavior. While many species exist as single cells, some form colonies, with the species ''C. Flexa'' standing out for its ability to dynamically transition its flagella between positions inside and outside the colony.
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.


Modeling the hydrodynamics of these colonies ideally requires detailed representations of each cell’s flagellum, microvilli, and body. However, the computational cost of simulating colonies with hundreds of cells makes this approach very expensive. To address this, we propose a reduced modeling framework that simplifies each cell to a force dipole while retaining key hydrodynamic features.
<div id="Loevbak">
==== Emil Loevbak (KIT) ====
Title: Discrete adjoint Monte Carlo for kinetic equations with reversible pseudorandom generators


Our force dipole model is calibrated against detailed computational simulations that account for the complete cellular structure. We show that this reduced model closely matches experimental data for non-deforming, free-swimming colonies. We further investigate how colony swimming and feeding performance depend on the flagellar position relative the colony, cell density, and overall colony shape. Finally, we explore the impact of the wall for flagella-in colonies, which are frequently observed in laboratory settings.
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.


<div id="Bal">
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.
===Guillaume Bal (Chicago)===
Title: Speckle formation of laser light in random media: The Gaussian conjecture


A widely accepted conjecture in the physical literature states that classical wave-fields propagating in random media over large distances eventually follow a complex circular Gaussian distribution. In this limit, the wave intensity becomes exponentially distributed, which corroborates the speckle patterns of, e.g., laser light observed in experiments. This talk reports on recent results settling the conjecture in the weak-coupling, paraxial regime of wave propagation. The limiting macroscopic Gaussian wave-field is fully characterized by a correlation function that satisfies an unusual diffusion equation.


The paraxial model of wave propagation is an approximation of the Helmholtz model where backscattering has been neglected. It is mathematically simpler to analyze but quite accurate practically for wave-fields that maintain a beam-like structure as in the application of laser light propagating in turbulent atmospheres.
<div id="Lu">
==== Yue M. Lu (Harvard) ====
Title: Nonlinear Random Matrices in Estimation and Learning: Equivalence Principles and Applications


The derivation of the limiting model is first obtained in the Itô-Schrödinger regime, where the random medium is replaced by its white noise limit. The resulting stochastic PDE has the main advantage that finite dimensional statistical moments of the wave-field satisfy closed form equations. The proof of the derivation of the macroscopic model is based on showing that these moment solutions are asymptotically those of the Gaussian limit, on obtaining a stochastic continuity (and tightness) result, and on establishing that moments in the paraxial and the Itô-Schrödinger regimes are asymptotically close.
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.


This is joint work with Anjali Nair.
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.


<div id="Portone">
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).
===Teresa Portone (Sandia)===
Title: Beyond parametric uncertainty: quantifying model-form uncertainty in model predictions


Uncertainty quantification (UQ) is the science of characterizing, quantifying, and reducing
uncertainties in mathematical models. It is critical for informing decisions, because it provides a measure
of confidence in model predictions, given the uncertainties present in the model. While approaches to
characterize uncertainties in model parameters, boundary and initial conditions are well established, it is
less clear how to address uncertainties arising when the equations of a mathematical model are
themselves uncertain—that is, when there is model-form uncertainty. Model-form uncertainty often
arises in models of complex physical phenomena where (1) simplifications for computational tractability
or (2) lack of knowledge lead to unknowns in the governing equations for which appropriate
mathematical forms are unknown or may not exist. In this talk, I briefly introduce major concepts in UQ,
then I discuss approaches to characterize model-form uncertainty and its impact on model predictions.


<div id="Damle">
<div id="Cockburn">
=== Anil Damle (Cornell) ===
====Bernardo Cockburn (Minnesota)====
Title: Fine-grained Theory and Hybrid Algorithms for Randomized Numerical Linear Algebra
Title: Transforming stabilization into spaces


Randomized algorithms have gained increased prominence within numerical linear algebra and they play a key role in an ever-expanding range of problems driven by a breadth of scientific applications. In this talk we will explore two aspects of randomized algorithms by (1) providing experiments and accompanying theoretical analysis that demonstrate how their performance depends on matrix structures beyond singular values (such as coherence of singular subspaces), and (2) showing how to leverage those insights to build hybrid algorithms that blend favorable aspects of deterministic and randomized methods. A focus of this talk will be on methods that approximate matrices using subsets of columns. Relevant motivating applications will be discussed and numerical experiments will illuminate directions for further research.
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.


<div id="Sprague">
== Archived semesters ==
=== Michael Sprague (NREL) ===
Title: Exascale supercomputing and predictive wind energy simulations
 
The predictive simulation modern wind turbines and wind farms is a high-performance-computing (HPC) grand challenge.   Wind turbines are the largest rotating machines in the world, with rotor diameters exceeding 200 meters, and with heights reaching well into the atmospheric boundary layer.  To address this grand challenge, the U.S. Department of Energy (DOE) Wind Energy Technologies Office and the DOE Exascale Computing Project have been supporting the creation of the ExaWind modeling and simulation environment since 2016.   ExaWind is composed of the incompressible-flow computational-fluid-dynamics (CFD) solvers AMR-Wind and Nalu-Wind and the wind-turbine-dynamics solver OpenFAST.  ExaWind codes have been developed with performance portability as a priority, with the first U.S. exascale computer, Frontier, being our target platform. Frontier relies on graphical processing units (GPUs) for acceleration, which presents a major challenge to codes designed for CPUs. In this talk I will give a historical overview of the Exascale Computing Project, an eight-year $1.7 billion project.  I will show results from our ExaWind challenge problem on Frontier and describe the strong-scaling challenges, and I will describe the challenges of modeling and simulating floating offshore wind turbines.  I will also give my perspectives on life as a Research Scientist in Applied Mathematics at a DOE national laboratory.
 
<div id="Holmes-Cerfon">
=== Miranda Holmes-Cerfon (UBC) ===
Title: The dynamics of particles with ligand-receptor contacts
 
One way to glue objects together at the nanoscale or microscale is by ligand-receptor interactions, where short sticky hair-like ligands stick to receptors on another surface, much like velcro on the nanoscale. Such interactions are common in biological systems, such as white blood cells, virus particles, cargo in the nuclear pore complex, etc, and they are also useful in materials science, where coating colloids with single-stranded DNA creates particles with programmable interactions. In these systems, the ligand-receptor interactions not only hold particles together, but also influence their dynamics. How do such particles move? Do they “roll” on each others’ surfaces, as is commonly thought? Or could they slide? And does it matter? In this talk I will introduce our modelling and experimental efforts aimed at understanding the coarse-grained dynamics of particles with ligand-receptor interactions. Our models predict these interactions can change the particles' effective diffusion by orders of magnitude. Our experiments, using DNA-coated colloids, verify this dramatic dynamical slowdown, but also show other dynamical features not yet captured by our models, which suggest new avenues for exploration.
 
<div id="Sun">
=== Yue Sun (UW–Madison) ===
Title: Simulating fluid–structure interaction: A tale of two methods
 
Computational approaches have become essential for complementing experimental and theoretical methods in the study of fluid–structure interaction (FSI)—from matching specific experimental conditions to creating digital twins for exploring otherwise unattainable data, to developing adaptable domain-specific methods. In this talk, I will discuss our collaborative work on developing two FSI methods for experimental digital twin applications and general method development.
 
The first part will highlight our collaboration with the Prigozhin Group at Harvard to create a 3D digital twin of the cryo-plunging process. Using ''cryoflo'', a massively parallelized code with adaptive mesh refinement (AMR) built on AMReX, we model fluid–structure interactions and heat transfer between biological samples and cryogen. This simulation captures critical cooling dynamics, providing insights that inform experimental protocols for cryo-electron microscopy (cryo-EM).
 
The second part will focus on general method development. Over the past decade, Rycroft ''et al.'' introduced the reference map technique (RMT), a fully Eulerian method for modeling finite-strain deformation in FSI. Here, we integrate the RMT with the lattice Boltzmann (LB) method, introducing a new approach (LBRMT) to simulate finite-strain solids on the LB’s fixed Eulerian grid. We demonstrate LBRMT’s capabilities by modeling interactions among multiple solid structures in fluids, showcasing its adaptability for various FSI scenarios such as collective behavior in active and soft matter.
 
<div id="Maxian">
=== Ondrej Maxian (U Chicago) ===
 
Title: From slender body numerics to patterning the cell cortex: two stories of actin filament dynamics
 
Actin filaments are the main ingredient in the cell cytoskeleton, which controls cell division, motility, and structure. In this talk, I will present two projects whose shared goal is to determine how microscopic dynamics of actin shape larger-scale behaviors of the cell cortex. In the first part, I will detail a new general purpose simulation package for fiber dynamics which accounts for filament inextensibility, Brownian motion, and nonlocal hydrodynamics. I will focus in particular on how to formulate a mobility matrix (force-velocity relationship) which is positive definite (necessary for Brownian motion) and has cost independent of the fiber slenderness (necessary for efficient simulation), then demonstrate how the package can be used to simulate cross-linked actin networks and sedimenting fiber arrays. In the second part, I will present a model for how actin filaments shape their own homeostasis through biochemical coupling with the protein RhoA. I will introduce an activator-inhibitor model for RhoA/actin coupling, then use a Bayesian inverse framework to infer the distribution of actin dynamics parameters associated with experimental data in ''C. elegans'' and starfish embryos. The inferred parameter values demonstrate how varying actin kinetics can explain changing patterns of RhoA excitability observed across multiple experimental systems.
 
<div id='Lavi'>
=== Ido Lavi (Flatiron) ===
 
Title: Emergence of large-scale patterns in active matter: from nematic fluids to multicellular systems
 
Active systems exhibit a fascinating interplay of chaos, order, and collective dynamics. If time permits, I will explore two stories of emergent behavior: the dynamical arrest in defect-free active nematics and the role of intercellular adhesions in coordinating multicellular systems.
 
In the realm of active nematics, our large-scale simulations reveal that defect-free active turbulence can transition into a dynamically arrested state. We find that the flow alignment coupling, which determines how nematics reorient under shear, acts as a control parameter that tunes the contrast between contractile and extensile systems. In contractile systems, it amplifies chaotic jets, while in extensile systems, it promotes a tree-like network of persistent streams, aligned with a maze of nematic domain walls. These findings highlight a novel role for topological defects and invite experimental investigation of defect-free systems. They also suggest an intriguing mechanism by which chaos is harnessed to generate patterns.
 
Turning to multicellular systems, adhesion molecules like E-cadherins play a key role in tissue mechanics by dynamically linking the cytoskeletons of neighboring cells. Far from being passive glue, these molecules couple actin filaments across cells, enabling coordinated collective behavior. To explore these dynamics, we developed a theoretical model describing cytoskeletons as contractile gels, with boundary conditions controlled by E-cadherin linkers attached to actin on both sides. Our finite element simulations reveal emergent patterns such as global polarization, anti-polarization, ring-like arrangements, and transient supracellular networks of actin cables. Beyond specific predictions, this study provides a mathematical framework for understanding how intracellular activity and intercellular adhesion feedback drive emergent multicellular dynamics.
 
== Future semesters ==


*[[Applied/ACMS/Fall2024|Fall 2024]]
*[[Applied/ACMS/Fall2024|Fall 2024]]
*[[Applied/ACMS/Spring2025|Spring 2025]]
== Archived semesters ==
*[[Applied/ACMS/Spring2024|Spring 2024]]
*[[Applied/ACMS/Spring2024|Spring 2024]]
*[[Applied/ACMS/Fall2023|Fall 2023]]
*[[Applied/ACMS/Fall2023|Fall 2023]]

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.

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