Organizing Committee
 Jose Carrillo
University of Oxford  Katy Craig
UC Santa Barbara  Massimo Fornasier
Technical University of Munich  Fei Lu
Johns Hopkins University  Mauro Maggioni
Johns Hopkins University  Kavita Ramanan
Brown University
Abstract
Systems of interacting particles or agents are studied across many scientific disciplines. They are used as effective models in a wide variety of sciences and applications, to represent the dynamics of particles in physics, cells in biology, people in urban mobility studies, but also, more abstractly in the context of mathematics, as sample particles in Monte Carlo simulations or parameters of neural networks in machine learning.
This workshop aims at bringing together researchers in analysis, computation, inference, control and applications, to facilitate crossfertilization and collaborations.
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Pedro Aceves Sanchez
University of Arizona

Manuel Arnese
Columbia University

Yonatan Ashenafi
Worcester Polytechnic Institute

Ayoub Belhadji
Massachusetts Institute of Technology

Sara Bicego
Imperial College London

David Bortz
University of Colorado Boulder

Andrey Bryutkin
Massachusetts Institute of Technology

Fei Cao
University of Massachusetts Amherst

Rossana Capuani
University of Arizona

Jose Carrillo
University of Oxford

Xiaohui Chen
University of Illinois at UrbanaChampaign

ChiAn Chen
Illinois Institute of Technology

Lin Chen
carnegie mellon university

Weiqi Chu
University of Massachusetts Amherst

Lauren Conger
Caltech

Katy Craig
UC Santa Barbara

Michel Davydov
Brown University

Uresha Dias
Clarkson University

Irene Erazo
Tulane University

Antonio Esposito
University of Oxford

Christian Fiedler
Columbia University

Ankan Ganguly
Boston University

Yuan Gao
Purdue University

Nicolas Garcia Trillos
University of Wisconsin Madison

Fuqun Han
University of Califonia, Los Angeles

Baoli Hao
Illinois Institute of Technology

Franca Hoffmann
California Institute of Technology

Alexandra Holzinger
University of Oxford

Michael Hott
University of Minneapolis  Twin Cities

Kevin Hu
Brown University

Hui Huang
KarlFranzensUniversity Graz

Juntao Huang
Texas Tech University

Vasily Ilin
University of Washington

PierreEmmanuel Jabin
Pennyslvania State University

Matt Jacobs
Purdue University

Gustaaf Jacobs
San Diego State University

Dante Kalise
Imperial College London

Yannis Kevrekidis
Johns Hopkins University

Aditya Khanna
Brown University

Anna Korba
ENSAE/CREST

Daniel Lacker
Columbia University

Quanjun Lang
Duke University

Sixu Li
University of WisconsinMadison

Xingjie Li
University of North Carolina at Charlotte

Wuchen Li
University of South Carolina

JianGuo Liu
Duke University

Shanqing LIU
Brown University

Shu Liu
UCLA

Jianfeng Lu
Duke University

Fei Lu
Johns Hopkins University

Xiaohang Ma
University of Connecticut

Mauro Maggioni
Johns Hopkins University

Brendan Mallery
Tufts University

Aimee Maurais
Massachusetts Institute of Technology

Ian Oliver McPherson
Johns Hopkins University

Daniel Messenger
University of Colorado Boulder

Joseph Miller
University of Texas at Austin

Claire Murphy
UC Santa Barbara

Djordje Nikolic
University of California, Santa Barbara

Pierre Nyquist
KTH Royal Institute of Technology

Mariana OlveraCravioto
University of North Carolina Chapel Hill

Melkior Ornik
University of Illinois UrbanaChampaign

Lorenzo Pareschi
Heriot Watt University

Jack Pfaffinger
University of California, Santa Barbara

Kavita Ramanan
Brown University

Nipuni Senani De Silva Rammini
Clarkson University

Ali Akbar Rezaei Lori
University of NebraskaLincoln

Nazia Riasat
North Dakota State University

Konstantin Riedl
Technical University of Munich, Munich Center for Machine Learning

Adil Salim
Microsoft Research

Widodo Samyono
Jarvis Christian University

Jakub Skrzeczkowski
University of Oxford

Chandler Smith
Tufts University

Konstantinos Spiliopoulos
Boston University

Reed Spitzer
Brown University

Sui Tang
University of California Santa Barbara

Carlos Taveras
Rice University

Ilya Timofeyev
University of Houston

Oliver Tse
Eindhoven University of Technology

Olga Turanova
Michigan State University

Cesar Uribe
Rice University

Eric VandenEijnden
New York University

Kyra Veprek
Brown University

Oleksandr Vlasiuk
PTC

Yiwei Wang
University of California, Riverside

Li Wang
University of Minnesota

Xiong Wang
Johns Hopkins University

Zhenfu Wang
Peking University

Jethro Warnett
University of Oxford

Andre Wibisono
Yale University

MarieTherese Wolfram
Emory University

Yantao Wu
Johns Hopkins University

Ruoyu Wu
Iowa State University

Xingchi Yan
Harvard University

Yunan Yang
Cornell University

Edith Zhang
Columbia University

Wenjun Zhao
Brown University

Liming Zhao
Cornell University

Ming Zhong
Illinois Institute of Technology

Mo Zhou
UCLA

Bohan Zhou
University Of California, Santa Barbara

Yuhua Zhu
University of California, San Diego
Workshop Schedule
Monday, May 6, 2024

8:50  9:00 am EDTWelcome11th Floor Lecture Hall

9:00  9:40 am EDTInteracting particle systems: a journey to kinetic theory and backTutorial  11th Floor Lecture Hall
 Speaker
 Li Wang, University of Minnesota
 Session Chair
 Kavita Ramanan, Brown University

9:50  10:30 am EDTOptimal Control for Mean Field Games and Transition PathsTutorial  11th Floor Lecture Hall
 Speaker
 JianGuo Liu, Duke University
 Session Chair
 Kavita Ramanan, Brown University
Abstract
Abstract: In this talk, I will present a stochastic optimal control formulation for (i) transition path problems in an infinite time horizon, specifically for Markov jump processes on Polish spaces, and (ii) mean field games in a finite time horizon. Transition paths connecting metastable states in a stochastic model are rare events that appear in many applications in science and engineering. An unbounded terminal cost at a stopping time, along with a controlled transition rate, regulates the transitions between metastable states. To maintain the original bridges after control, the running cost adopts an entropic form for the control velocity. However, the unbounded terminal cost leads to a singular optimal control and presents difficulties in the Girsanov transform. Gammaconvergence techniques and passing the limit in the corresponding Martingale problem allow us to obtain a singular optimally controlled transition rate. We demonstrate that the committor function, which solves a backward equation with specific boundary conditions, provides an explicit formula for the optimal path measure. The optimally controlled process realizes the transition paths almost surely but without altering the bridges of the original process. This stochastic optimal control formulation is also applicable to mean field games.

10:40  11:00 am EDTCoffee Break11th Floor Collaborative Space

11:00  11:40 am EDTOptimization and sampling by linear kinetic equations11th Floor Lecture Hall
 Virtual Speaker
 Lorenzo Pareschi, Heriot Watt University
 Session Chair
 Kavita Ramanan, Brown University
Abstract
One of the most prominent examples showcasing the close ties between global optimization processes and statistical physics is the simulated annealing method, rooted in the MetropolisHasting sampling approach. In this talk, we emphasize the close connections between the underlying stochastic dynamics and linear Boltzmann equations and how convergence to the global minimum can be related to classical entropy inequalities. This allows us to reinterpret classical results, such as the connections between simulated annealing and meanfield Langevin dynamics, and to derive enhanced algorithms based on different strategies to control the annealing process.

11:50 am  12:30 pm EDTWasserstein gradient flow in an inhomogeneous media: convergence and the effective Wasserstein metric11th Floor Lecture Hall
 Speaker
 Yuan Gao, Purdue University
 Session Chair
 Kavita Ramanan, Brown University
Abstract
The FokkerPlanck equation with fast oscillated coefficients can be regarded as a gradient flow in a Wasserstein space with inhomogeneous dissipation and oscillated free energy. We will use an evolutionary Gamma convergence approach to obtain the homogenized dynamics, which preserves the gradient flow structure in a limiting homogenized Wasserstein space. The comparison between the gradient flow induced limiting Wasserstein distance and the direct GromovHausdorff limiting Wasserstein distance will also be discussed.

12:40  2:00 pm EDTNetworking LunchWorking Lunch

2:00  2:40 pm EDTQuantitative Propagation of Chaos for 2D Viscous Vortex Model on the Whole Space11th Floor Lecture Hall
 Speaker
 Zhenfu Wang, Peking University
 Session Chair
 Jose Carrillo, University of Oxford
Abstract
We derive the quantitative estimates of propagation of chaos for the large interacting particle systems in terms of the relative entropy between the joint law of the particles and the tensorized law of the mean field PDE. We resolve this problem for the first time for the viscous vortex model that approximating 2D NavierStokes equation in the vorticity formulation on the whole space. We obtain as key tools the LiYautype estimates and Hamiltontype heat kernel estimates for 2D NavierStokes on the whole space. This is based on a joint work with Xuanrui Feng from Peking University.

2:50  3:10 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:40 pm EDTOpinion formation in social network11th Floor Lecture Hall
 Speaker
 MarieTherese Wolfram, Emory University
 Session Chair
 Jose Carrillo, University of Oxford
Abstract
In this talk I will discuss an ODE model for opinion formation in evolving networks. As opposed to existing models, in which the network typically evolves by discretely adding or removing edges, we instead propose a model for opinion formation which is coupled to a network evolving through a system of ordinary differential equations for the edge weights. We interpret each edge weight as the strength of the relationship between a pair of individuals, with edges increasing in weight if pairs continually listen to each others' opinions and decreasing if not. We investigate the impact of various edge dynamics at different timescales on the opinion dynamic itself. Time permitting, I will also discuss a very recent work on how to steer opinions towards a target opinion by controlling the strength of network connections.

4:50  6:20 pm EDTReception11th Floor Collaborative Space
Tuesday, May 7, 2024

9:00  9:40 am EDTBeyond MeanField Limits: Rigorous Approximations for Interacting Particle Systems on Sparse GraphsTutorial  11th Floor Lecture Hall
 Speaker
 Kavita Ramanan, Brown University
 Session Chair
 Katy Craig, UC Santa Barbara

9:50  10:30 am EDTLearning Interaction laws in particle and agentbased systemsTutorial  11th Floor Lecture Hall
 Speaker
 Mauro Maggioni, Johns Hopkins University
 Session Chair
 Katy Craig, UC Santa Barbara
Abstract
We consider systems of interacting agents or particles, which are commonly used for modeling across the sciences. While these systems have very highdimensional state spaces, the laws of interaction between the agents may be quite simple, for example they may depend only on pairwise interactions, and only on pairwise distance in each interaction. We consider the following inference problem for a system of interacting particles or agents: given only observed trajectories of the agents in the system, can we learn what the laws of interactions are? We would like to do this without assuming any particular form for the interaction laws, i.e. they might be “any” function of pairwise distances, or other variables, on Euclidean spaces, manifolds, or networks. We consider this problem in the case of a finite number of agents, with observations along an increasing number of paths. We cast this as an inverse problem, discuss when this problem is wellposed, construct estimators for the interaction kernels with provably good statistically and computational properties. We discuss the fundamental role of the geometry of the underlying space, in the cases of Euclidean space, manifolds, and networks, even in the case when the network is unknown. Finally, we consider extensions to secondorder systems, more general interaction kernels, stochastic systems, and to the setting where the variables (e.g. pairwise distance) on which the interaction kernel depends are not known a priori. This is joint work with Q. Lang (Duke), F. Lu (JHU), S. Tang (UCSB), X. Wang (JHU) , M.Zhong (IIT).

10:40  11:00 am EDTCoffee Break11th Floor Collaborative Space

11:00  11:40 am EDTWasserstein proximal coordinate gradient algorithms11th Floor Lecture Hall
 Speaker
 Xiaohui Chen, University of Illinois at UrbanaChampaign
 Session Chair
 Katy Craig, UC Santa Barbara
Abstract
This talk concerns composite (geodesically) convex optimization over multiple distributions. The objective functional under consideration is composed of a convex potential energy, defined on a product of Wasserstein spaces (the space of all distributions with a finite second moment), and a sum of convex selfinteraction and internal energies associated with each distribution. To efficiently solve this problem, we introduce the Wasserstein Proximal Coordinate Gradient (WPCG) algorithm. Under a Quadratic Growth (QG) condition on the objective functional, a condition more relaxed than the typical strongly convex requirement, WPCG is proven to attain exponential convergence to the unique global optimum. Implications regarding the choice of step size and update schemes (parallel, sequential and random) are also discussed. In the absence of the QG condition, WPCG is still demonstrated to converge to the global optimal solution, albeit at a slower polynomial rate. The algorithm and theoretical framework are applied to two representative examples: approximation Bayesian computation using meanfield variational approximation, and the computation of equilibrium in multispecies systems with crossinteraction. Numerical results for both examples are consistent with our theoretical findings.

11:50 am  12:30 pm EDTLearning Interaction Kernels in Particle and Agentbased Systems11th Floor Lecture Hall
 Speaker
 Sui Tang, University of California Santa Barbara
 Session Chair
 Katy Craig, UC Santa Barbara
Abstract
We study inferring interaction kernels from observed behaviors in particle and agent systems, which are crucial in fields ranging from physics to social sciences. We first consider stochastic systems with interaction kernels based on pairwise distances and introduce a nonparametric inference approach utilizing a regularized maximum likelihood estimator to estimate interaction kernels based on pairwise distances. Our estimators can achieve consistency and a nearoptimal convergence rate, independent of the system's state space dimension. In addition, we analyze errors result from discretetime observations and demonstrate our approach through numerical experiments on models like stochastic opinion dynamics and LennardJones. Finally, we extend our analysis to identify nonlocal interaction potentials in aggregationdiffusion equations from noisy data using sparsitypromoting approaches. This is based on join work with Fei Lu, Mauro Maggioni, Jose A. Carrillo, Gissell EstradaRodriguez, Laszlo Mikolas.

12:40  12:45 pm EDTGroup Photo (Immediately After Talk)11th Floor Lecture Hall

12:45  2:00 pm EDTDiscussion on "New Directions and Open Problems in Interacting Particle Systems"Working Lunch

2:00  2:40 pm EDTRecent Advances in Weak FromBased Learning of Interacting Particle Systems11th Floor Lecture Hall
 Virtual Speaker
 David Bortz, University of Colorado Boulder
 Session Chair
 MarieTherese Wolfram, Emory University
Abstract
Recent advances in datadriven modeling approaches have proven highly successful in a wide range of fields in science and engineering. In this talk, I will present our weak form methodology which has proven to have surprising performance and robustness properties. In particular, I will describe our equation learning (WSINDy) method and illustrate application to learning interaction potentials and mean field limits for interacting particle systems. I will also discuss how our approach offers advantages in terms of computational efficiency, noise robustness, and modest data needs.

2:50  3:10 pm EDTCoffee Break11th Floor Collaborative Space

3:20  4:00 pm EDTDeep learning probability flows and entropy production rates in active matter11th Floor Lecture Hall
 Speaker
 Eric VandenEijnden, New York University
 Session Chair
 MarieTherese Wolfram, Emory University
Abstract
Active matter systems, from selfpropelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems of interacting particles generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steadystate probability current provide quantitative ways to do so by measuring the breakdown of timereversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and highdimensional probability density. In this talk, building upon recent advances in generative modeling, I will present a deep learning framework that allows for the estimation of the gradient of the logarithm of this density, a quantity know as the score in the machine learning literature. This score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. I will demonstrate the broad utility and scalability of the method by applying it to several highdimensional systems of interacting active particles undergoing motilityinduced phase separation (MIPS). This is joint work with Nick Boffi <https://arxiv.org/abs/2309.12991>

4:10  4:20 pm EDTSupervised Learning for Kinetic Consensus ControlLightning Talks  11th Floor Lecture Hall
 Speaker
 Sara Bicego, Imperial College London
 Session Chair
 MarieTherese Wolfram, Emory University
Abstract
Modeling and control of agentbased models is twice cursed by the dimensionality of the problem, as both the number of agents and their state space dimension can be large. Even though the computational barrier posed by a large ensemble of agents can be overcome through a mean field formulation of the control problem, the feasibility of its solution is generally guaranteed only for agents operating in lowdimensional spaces. To circumvent the difficulty posed by the high dimensionality of the state space a kinetic model is proposed, requiring the sampling of highdimensional, twoagent subproblems, to evolve the agents' density using a Boltzmann type equation. Such density evolution requires a highfrequency sampling of twoagent optimal control problems, which is efficiently approximated by means of deep neural networks and supervised learning, enabling the fast simulation of highdimensional, largescale ensembles of controlled particles. Numerical experiments demonstrate the effectiveness of the proposed approach in the control of consensus and attractionrepulsion dynamics.

4:20  4:30 pm EDTA dollar exchange model with bank and debtLightning Talks  11th Floor Lecture Hall
 Speaker
 Fei Cao, University of Massachusetts Amherst
 Session Chair
 MarieTherese Wolfram, Emory University
Abstract
We investigate the unbiased model for money exchanges with collective debt limit: agents give at random time a dollar to one another as long as they have at least one dollar or they can borrow a dollar from a central bank if the bank is not empty. Surprisingly, this dynamic eventually leads to an asymmetric Laplace distribution of wealth. In this work, we carry out a formal meanfield limit as the number of agents goes to infinity where we uncover a twophase ODE dynamics. Convergence towards the unique equilibrium (twosided geometric) distribution in the large time limit is also shown and the role played by the bank and debt (in terms of Gini index or wealth inequality) will be explored numerically as well.

4:30  4:40 pm EDTTwo Complementary Analytical Perspectives on ConsensusBased OptimizationLightning Talks  11th Floor Lecture Hall
 Speaker
 Konstantin Riedl, Technical University of Munich, Munich Center for Machine Learning
 Session Chair
 MarieTherese Wolfram, Emory University
Abstract
Consensusbased optimization (CBO) is a multiparticle derivativefree optimization method capable of globally minimizing highdimensional nonconvex and nonsmooth functions. In this lightning talk, we provide insights into the internal mechanisms of CBO, which are responsible for the success of the method. First, based on an experimentally supported intuition that, in the meanfield limit (as the number of particles goes to infinity), CBO always performs a gradient descent of the Wasserstein distance to the global minimizer, we develop a novel technique for proving global convergence in meanfield law for a rich class of objective functions. In particular, we show that CBO performs a convexification of a very large class of optimization problems as the number of optimizing particles tends to infinity. From this result it becomes apparent that the hardness of any global optimization problem is necessarily encoded in the meanfield approximation, i.e., in the way how the empirical measure of the finite particle dynamics is used to approximate the meanfield limit. A combination of these two results allows to obtain a holistic convergence proof of CBO methods. Second, by turning our back on the previous meanfieldfocused analysis point of view and by leveraging a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (logsumexp trick) and the minimizing movement scheme (proximal iteration), we interpret CBO as a stochastic relaxation of gradient descent, thereby providing a novel analytical perspective on the theoretical understanding of gradientbased learning algorithms. We observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the formerly established fact that CBO is provably globally convergent to global minimizers, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent, and, on the other side and contrary to the conventional wisdom for which zeroorder methods ought to be inefficient or not to possess generalization abilities, unveiling an intrinsic gradient descent nature of such heuristics. With this we furnish insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions.

4:40  4:50 pm EDTA stability estimate for the particle system in the Stein gradient descent methodLightning Talks  11th Floor Lecture Hall
 Speaker
 Jakub Skrzeczkowski, University of Oxford
 Session Chair
 MarieTherese Wolfram, Emory University
Abstract
There has been recently a lot of interest in the analysis of the Stein gradient descent method, a deterministic sampling algorithm. It is based on a particle system moving along the gradient flow of the KullbackLeibler divergence towards the asymptotic state corresponding to the desired distribution. Mathematically, the method can be formulated as a joint limit of time t and the number of particles N going to infinity. We first observe that the recent work of Lu, Lu, and Nolen (2019) implies that if time t scales like loglogN, then the joint limit can be rigorously justified in the Wasserstein distance. Not satisfied with this time scale, we explore what happens for larger times by investigating the stability of the method: if the particles are initially close to the asymptotic state (with distance 1/N), how long will they remain close? We prove that this happens in algebraic time scales which is significantly better. The exploited method, developed by Caglioti and Rousset for the Vlasov equation, is based on finding a functional invariant for the linearized equation. This allows us to eliminate linear terms and arrive at an improved Gronwalltype estimate. This is a joint work with Jose A. Carrillo (Oxford).

4:50  5:00 pm EDTMeanField and Graphon Limits of Latent Position Particle Systems with Dynamic Random NetworksLightning Talks  11th Floor Lecture Hall
 Speaker
 Ankan Ganguly, Boston University
 Session Chair
 MarieTherese Wolfram, Emory University
Abstract
Consider an opinion dynamics model in which $n$ agents are each equipped with a latent opinion (represented by a Euclidean vector). As the agents update their positions, they are influenced by their own previous positions as well as the average positions of all neighboring agents in a certain timevarying random network. At any given time, two agents are connected by an edge of the network with a probability that depends on their latent positions as well as the existence or nonexistence of an edge between the agents at the previous time. We are interested in the limiting behavior of this model as $n$ increases to infinity. We show that under suitable conditions, this model has a meanfield limit which can be characterized explicitly. We also describe the joint weak limit of a subpopulation of $k$ agents and the network connecting these agents. This equivalently yields a propagation of chaos result describing the average behavior of agents in the system and a conditional propagation of chaos result describing the average behavior of a particular agent's neighbors and nonneighbors conditioned on the agent's latent position. We finish with a characterization of the graphon limit of the random network and a multigraphon limit of the entire network trajectory. This talk covers ongoing work with Kostas Spiliopoulos and Dan Sussman.
Wednesday, May 8, 2024

9:00  9:40 am EDTStabilizing particles across scales11th Floor Lecture Hall
 Speaker
 Dante Kalise, Imperial College London
 Session Chair
 JianGuo Liu, Duke University
Abstract
This talk explores the control of interacting particle systems to desired stationary configurations across scales, connecting microscopic particle dynamics with macroscopic meanfield descriptions. We discuss two approaches: stabilizing the McKeanVlasov PDE around unstable steady states and optimally controlling consensusbased optimization (CBO) dynamics. For interacting particle systems and their meanfield limit governed by the McKeanVlasov PDE, we propose a numerical method combining spectral Galerkin approximation with deflated Newton's method to identify multiple steady states. The deflation technique systematically eliminates known solutions, enabling the discovery of distinct stationary configurations. To stabilize the particle ensemble around desired unstable steady states, we formulate an optimal control problem, where the control enters as an additional drift term. We derive optimality conditions and propose a gradientbased algorithm, employing model predictive control. We also introduce a controlled CBO framework that incorporates a feedback control term derived from the numerical solution of an auxiliary HamiltonJacobiBellman equation. This control guides particles towards the global minimizer of the objective function. We establish the wellposedness of the controlled CBO system and demonstrate its improved performance over standard CBO methods.

9:50  10:30 am EDTNonlocal approximation of linear and nonlinear diffusion11th Floor Lecture Hall
 Speaker
 Olga Turanova, Michigan State University
 Session Chair
 JianGuo Liu, Duke University
Abstract
This talk concerns recent work on a class of PDEs with linear and nonlinear diffusion, including the heat equation, fast diffusion equations, and height constrained transport. We develop and prove convergence of a nonlocal approximation for such equations. This gives rise to a deterministic particle numerical method for these PDEs, as well as a novel particle method for sampling a wide range of probability measures. In this talk, I will highlight the how our convergence arguments take advantage of both the Wasserstein and the dual Sobolev gradient flow structures of the PDEs under consideration. Based on joint work with Katy Craig and Matt Jacobs.

10:40  11:00 am EDTCoffee Break11th Floor Collaborative Space

11:00  11:40 am EDTTBA11th Floor Lecture Hall
 Speaker
 Jianfeng Lu, Duke University
 Session Chair
 JianGuo Liu, Duke University

11:50 am  12:30 pm EDTDynamics of Strategic Agents and Algorithms as PDEs11th Floor Lecture Hall
 Speaker
 Franca Hoffmann, California Institute of Technology
 Session Chair
 JianGuo Liu, Duke University
Abstract
We propose a partial differential equation framework for modeling distribution shift of a strategic population interacting with a learning algorithm. We consider two particular settings; one, where the objective of the algorithm and population are aligned, and two, where the algorithm and population have opposite goals. We present convergence analysis for both settings, including three timescale settings for the opposinggoal objective dynamics. We illustrate how our framework can accurately model realworld data and show via synthetic examples how it captures sophisticated distribution changes which cannot be modeled with simpler methods.

12:40  2:00 pm EDTLunch/Free Time

2:00  2:40 pm EDTTBA11th Floor Lecture Hall
 Speaker
 Yannis Kevrekidis, Johns Hopkins University
 Session Chair
 Mauro Maggioni, Johns Hopkins University
Abstract
We present a machine learning (ML)assisted framework bridging manifold learning, neural networks, Gaussian processes, and EquationFree multiscale modeling, for (a) detecting tipping points in the emergent behavior of complex systems, and (b) characterizing probabilities of rare events (here, catastrophic shifts) near them. Our illustrative example is an eventdriven, stochastic agentbased model (ABM) describing the mimetic behavior of traders in a simple financial market. Given highdimensional spatiotemporal data  generated by the stochastic ABM  we construct reducedorder models for the emergent dynamics at different scales: (a) mesoscopic IntegroPartial Differential Equations (IPDEs); and (b) meanfieldtype Stochastic Differential Equations (SDEs) embedded in a lowdimensional latent space, targeted to the neighborhood of the tipping point. We contrast the uses of the different models and the effort involved in learning them. If time permits, I will also include examples from evolving epidemiological networks and from the DesaiZwanzig interacting particle model.

2:50  5:00 pm EDT
Thursday, May 9, 2024

9:50  10:30 am EDTOpiniondynamics models with randomtime interactions11th Floor Lecture Hall
 Speaker
 Weiqi Chu, University of Massachusetts Amherst
 Session Chair
 Mauro Maggioni, Johns Hopkins University
Abstract
Opiniondynamics models study how opinions evolve as dynamical processes on networks. Traditionally, these models have treated time as either discrete or continuous, operating under deterministic assumptions. However, realworld social interactions and opinion updates often exhibit randomness in time. In this talk, we propose a novel approach to incorporate randomtime interactions by modeling them as renewal processes on networks. Through this framework, we derive corresponding opiniondynamics models that capture the stochastic nature of social interactions. Notably, when renewal processes exhibit nonPoisson interevent statistics, the resulting opinion models naturally yield nonMarkovian dynamics. These memorydependent effects offer insights into various phenomena (such as stereotypes) observed in social and information sciences.

10:40  11:00 am EDTCoffee Break11th Floor Collaborative Space

11:00  11:40 am EDTMeasureTheoretic Approaches for Stochastic Inverse Problems11th Floor Lecture Hall
 Speaker
 Yunan Yang, Cornell University
 Session Chair
 Mauro Maggioni, Johns Hopkins University
Abstract
Most inverse problems from physical sciences are formulated as PDEconstrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured data. The formulation is powerful and widely used in many sciences and engineering fields. However, one crucial assumption is that the unknown parameter must be deterministic. In reality, however, many problems are stochastic in nature, and the unknown parameter is random. The challenge then becomes recovering the full distribution of this unknown random parameter. It is a much more complex task. In this talk, we examine this problem in a general setting. In particular, we conceptualize the PDE solver as a pushforward map that pushes the parameter distribution to the generated data distribution. This way, the SDEconstrained optimization translates to minimizing the distance between the generated distribution and the measurement distribution. We then formulate a gradientflow equation to seek the groundtruth parameter probability distribution. This opens up a new paradigm for extending many techniques in PDEconstrained optimization to that for systems with stochasticity.

11:50 am  12:30 pm EDTSampling through optimization of divergences11th Floor Lecture Hall
 Speaker
 Anna Korba, ENSAE/CREST
 Session Chair
 Mauro Maggioni, Johns Hopkins University
Abstract
Sampling from a target measure when only partial information is available (e.g. unnormalized density as in Bayesian inference, or true samples as in generative modeling ) is a fundamental problem in computational statistics and machine learning. The sampling problem can be formulated as an optimization over the space of probability distributions of a wellchosen discrepancy (e.g. a divergence or distance). In this talk, we'll discuss several properties of sampling algorithms for some choices of discrepancies (wellknown ones, or novel proxies), both regarding their optimization and quantization aspects.

12:40  2:00 pm EDTLunch/Free Time

2:00  2:40 pm EDTSharp quantitative propagation of chaos for mean field and nonexchangeable diffusions11th Floor Lecture Hall
 Speaker
 Daniel Lacker, Columbia University
 Session Chair
 Nicolas Garcia Trillos, University of Wisconsin Madison
Abstract
This talk discusses recent and ongoing work on a new "local" perspective on quantitative propagation of chaos, both for exchangeable and nonexchangeable systems. For an exchangeable system of $n$ diffusive particles interacting pairwise, the relative entropy between the marginal law of $k$ particles and its limiting product measure is shown to be $O((k/n)^2)$ at each time, as long as the same is true at time zero, and as long as the interaction kernel is sufficiently regular. Gaussian examples show that this is sharp. In contrast, prior "global" methods are based on the analysis of the full collection of $n$ particles and can yield at best $O(k/n)$. For nonexchangeable systems, more nuanced entropy bounds are obtained in terms of the fine structure of the matrix of pairwise interaction strengths. At the heart of the local approach is a hierarchy of differential inequalities, which, in the exchangeable case, bound the $k$particle entropy in terms of the $(k+1)$particle entropy for each $k$. The hierarchy is significantly more complex in the nonexchangeable setting, indexed by sets rather than numbers of particles, and we analyze it by means of an unexpected connection with firstpassage percolation.

2:50  3:10 pm EDTCoffee Break11th Floor Collaborative Space

3:10  3:50 pm EDTWeakly interacting jump processes with graphon interactions11th Floor Lecture Hall
 Speaker
 Ruoyu Wu, Iowa State University
 Session Chair
 Nicolas Garcia Trillos, University of Wisconsin Madison
Abstract
We consider systems of weakly interacting jump processes on heterogeneous random graphs and their large population limit. The interaction is of mean field type weighted by the underlying graphon. A law of large numbers result is established as the system size increases and the underlying graphons converge. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear Markovian processes whose probability distributions are fully coupled. Individualbased epidemic models, as an application, and Jointheshortestqueue(d) systems, as a relevant queueing model, will be briefly discussed.

4:00  4:40 pm EDTOpinion dynamics on complex networks11th Floor Lecture Hall
 Speaker
 Mariana OlveraCravioto, University of North Carolina Chapel Hill
 Session Chair
 Nicolas Garcia Trillos, University of Wisconsin Madison
Abstract
In a world of polarized opinions on many cultural issues, we propose a model for the evolution of opinions on a large complex network. Our model is akin to the popular FriedkinJohnsen model, with the added complexity of vertexdependent media signals and confirmation bias, both of which help explain some of the most important factors leading to polarization. The analysis of the model is done on a directed random graph, capable of replicating highly inhomogeneous realworld networks with various degrees of assortativity and community structure. Our main results give the stationary distribution of opinions on the network, including explicitly computable formulas for the conditional means and variances for the various communities. Our results span the entire range of inhomogeneous random graphs, from the sparse regime, where the expected degrees are bounded, all the way to the dense regime, where a graph having n vertices has order n^2 edges.
Friday, May 10, 2024

9:00  9:40 am EDTParticleBased Stochastic ReactionDiffusion Models: Mean field limits and fluctuation corrections.11th Floor Lecture Hall
 Speaker
 Konstantinos Spiliopoulos, Boston University
 Session Chair
 Mariana OlveraCravioto, University of North Carolina Chapel Hill
Abstract
Particlebased stochastic reactiondiffusion (PBSRD) models are a popular approach for studying biological systems involving both noise in the reaction process and diffusive transport. In this work we derive coarsegrained deterministic partial integrodifferential equation (PIDE) models that provide a mean field approximation to the volume reactivity PBSRD model, a model commonly used for studying cellular processes. We formulate a weak measurevalued stochastic process (MVSP) representation for the volume reactivity PBSRD model, demonstrating for a simplified but representative system that it is consistent with the commonly used Doi Fock Space representation of the corresponding forward equation. We then prove, (a): the convergence of the general volume reactivity model MVSP to the mean field PIDEs in the largepopulation (i.e. thermodynamic) limit, and (b): the next order fluctuation correction to the mean field limit, which satisfies systems of stochastic PIDEs with Gaussian noise. Numerical examples are presented to illustrate how such approximations can enable the accurate estimation of higher order statistics of the underlying PBSRD model. This is joint work with Samuel Isaacson, Max Heldman, Jingwei Ma and Qianhan Liu.

9:50  10:30 am EDTInteracting Particle Systems for Optimization: from Particle Swarm Optimization to Consensusbased Optimization11th Floor Lecture Hall
 Speaker
 Hui Huang, KarlFranzensUniversity Graz
 Session Chair
 Mariana OlveraCravioto, University of North Carolina Chapel Hill
Abstract
In this talk, we explore the application of metaheuristics through large systems of interacting particles to address complex optimization challenges, with a particular focus on the Particle Swarm Optimization (PSO) method. This approach harnesses the power of collective intelligence, where individual particles adjust their movement based on personal success and the influence of their neighbours, guiding the swarm towards the optimal solution. We will investigate the continuous model developed by Grassi and Pareschi, presenting evidence of how it ensures convergence to global minimizers and connects to Consensusbased Optimization (CBO) through the limit of zero inertia.

10:40  11:00 am EDTCoffee Break11th Floor Collaborative Space

11:00  11:40 am EDTA duality method for meanfield limits with singular interactions11th Floor Lecture Hall
 Virtual Speaker
 PierreEmmanuel Jabin, Pennyslvania State University
 Session Chair
 Mariana OlveraCravioto, University of North Carolina Chapel Hill
Abstract
We introduce a new approach to justify meanfield limits for firstand secondorder particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary squareintegrable interaction forces at possibly vanishing temperature. In case of firstorder systems, it allows to recover in particular the meanfield limit to the 2d Euler and NavierStokes equations. We postpone to a forthcoming work the development of quantitative estimates and the extension to more singular interactions. This is a joint work with D. Bresch and M. Duerinckx.

11:50 am  12:30 pm EDTAn interacting particle consensus method for constrained global optimization11th Floor Lecture Hall
 Speaker
 Yuhua Zhu, University of California, San Diego
 Session Chair
 Mariana OlveraCravioto, University of North Carolina Chapel Hill
Abstract
This talk addresses the global minimization problems with equality constraints, particularly in cases where the loss function exhibits nondifferentiability or nonconvexity. The proposed method combines components from consensusbased optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous meanfield limit of the particle system has been derived, the convergence of the meanfield limit to the constrained minimizer has been established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to illustrate the performance of the proposed method.

12:40  2:00 pm EDTLunch/Free Time

2:00  2:40 pm EDTFedCBO: Reaching Group Consensus in Clustered Federated Learning and Robustness to Backdoor Adversarial Attacks.11th Floor Lecture Hall
 Speaker
 Nicolas Garcia Trillos, University of Wisconsin Madison
 Session Chair
 Fei Lu, Johns Hopkins University
Abstract
Federated learning is an important framework in modern machine learning that seeks to integrate the training of learning models from multiple users, each user with their own local data set, in a way that is sensitive to the users’ data privacy and to communication cost constraints. In clustered federated learning, one assumes an additional unknown group structure among users, and the goal is to train models that are useful for each group, rather than training a single global model for all users. In the first part of this talk, I will present a novel solution to the problem of clustered federated learning that is inspired by ideas in consensusbased optimization (CBO). Our new CBOtype method is based on a system of interacting particles that is oblivious to group memberships. Our algorithm is accompanied by theoretical justification that is illustrated by real data experiments. I will then discuss an additional point of concern in federated learning: the vulnerability of federated learning protocols to “backdoor” adversarial attacks. This discussion will motivate the introduction of a modified, improved particle system with enhanced robustness properties that, at an abstract level, can be interpreted as a bilevel optimization algorithm based on interacting particle dynamics. The talk is based on joint works with Jose A. Carrillo, Sixu Li, and Yuhua Zhu; as well as with Sixu Li, Konstantin Riedl, and Yuhua Zhu.

2:50  3:30 pm EDTLagrangian flows for PME and particle implications11th Floor Lecture Hall
 Speaker
 Matt Jacobs, Purdue University
 Session Chair
 Fei Lu, Johns Hopkins University
Abstract
There is a large body of recent work on the approximation of diffusion equations by deterministic interacting particle systems. The analysis of these systems is typically carried out in Eulerian coordinates, despite the fact that the particle viewpoint is inherently Lagrangian. This is largely due to the fact that in the continuous setting, it may be extremely hard to solve diffusion equations in Lagrangian coordinates. In fact, the existence of Lagrangian solutions to the Porous Media Equation (PME) with general initial data was open until 2022. In this talk, I will discuss how to construct Lagrangian solutions to PME. I will then sketch how this analysis can be used to obtain convergence rates for certain deterministic versions of the score matching algorithm (a method for generating new samples from an unknown distribution given some data).

3:40  4:00 pm EDTCoffee Break11th Floor Collaborative Space
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