Organizing Committee
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 cross-fertilization and collaborations.

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Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

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Monday, May 6, 2024
  • 8:50 - 9:00 am EDT
    Welcome
    11th Floor Lecture Hall
  • 9:00 - 9:40 am EDT
    Interacting particle systems: a journey to kinetic theory and back
    Tutorial - 11th Floor Lecture Hall
    • Li Wang, University of Minnesota
  • 9:50 - 10:30 am EDT
    Optimal Control for Mean Field Games and Transition Paths
    Tutorial - 11th Floor Lecture Hall
    • Jian-Guo Liu, Duke 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. Gamma-convergence 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 - 11:40 am EDT
    A duality method for mean-field limits with singular interactions
    11th Floor Lecture Hall
    • Virtual Speaker
    • Pierre-Emmanuel Jabin, Pennyslvania State University
    Abstract
    We introduce a new approach to justify mean-field limits for first-and second-order 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 square-integrable interaction forces at possibly vanishing temperature. In case of first-order systems, it allows to recover in particular the mean-field limit to the 2d Euler and Navier-Stokes 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 EDT
    Wasserstein gradient flow in an inhomogeneous media: convergence and the effective Wasserstein metric
    11th Floor Lecture Hall
    • Yuan Gao, Purdue University
    Abstract
    The Fokker-Planck 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 Gromov-Hausdorff limiting Wasserstein distance will also be discussed.
  • 12:40 - 2:00 pm EDT
    Networking Lunch
    Working Lunch
  • 2:00 - 2:40 pm EDT
    Quantitative Propagation of Chaos for 2D Viscous Vortex Model on the Whole Space
    11th Floor Lecture Hall
    • Zhenfu Wang, Peking University
    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 Navier-Stokes equation in the vorticity formulation on the whole space. We obtain as key tools the Li-Yau-type estimates and Hamilton-type heat kernel estimates for 2D Navier-Stokes on the whole space. This is based on a joint work with Xuanrui Feng from Peking University.
  • 2:50 - 3:10 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:10 - 3:50 pm EDT
    TBA
    11th Floor Lecture Hall
    • Oliver Tse, Eindhoven University of Technology
  • 4:00 - 4:40 pm EDT
    Opinion formation in social network
    11th Floor Lecture Hall
    • Marie-Therese Wolfram, Emory University
    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 EDT
    Reception
    11th Floor Collaborative Space
Tuesday, May 7, 2024
  • 9:00 - 9:40 am EDT
    TBA
    Tutorial - 11th Floor Lecture Hall
    • Kavita Ramanan, Brown University
  • 9:50 - 10:30 am EDT
    TBA
    Tutorial - 11th Floor Lecture Hall
    • Mauro Maggioni, Johns Hopkins University
  • 10:40 - 11:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 - 11:40 am EDT
    Wasserstein proximal coordinate gradient algorithms
    11th Floor Lecture Hall
    • Xiaohui Chen, University of Illinois at Urbana-Champaign
    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 self-interaction 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 mean-field variational approximation, and the computation of equilibrium in multi-species systems with cross-interaction. Numerical results for both examples are consistent with our theoretical findings.
  • 11:50 am - 12:30 pm EDT
    Learning Interaction Kernels in Particle and Agent-based Systems
    11th Floor Lecture Hall
    • Sui Tang, University of California 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 near-optimal convergence rate, independent of the system's state space dimension. In addition, we analyze errors result from discrete-time observations and demonstrate our approach through numerical experiments on models like stochastic opinion dynamics and Lennard-Jones. Finally, we extend our analysis to identify nonlocal interaction potentials in aggregation-diffusion equations from noisy data using sparsity-promoting approaches. This is based on join work with Fei Lu, Mauro Maggioni, Jose A. Carrillo, Gissell Estrada-Rodriguez, Laszlo Mikolas.
  • 12:40 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:40 pm EDT
    Recent Advances in Weak From-Based Learning of Interacting Particle Systems
    11th Floor Lecture Hall
    • David Bortz, University of Colorado Boulder
    Abstract
    Recent advances in data-driven 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:20 - 4:00 pm EDT
    TBA
    11th Floor Lecture Hall
    • Eric Vanden-Eijnden, New York University
  • 4:10 - 5:00 pm EDT
    Lightning Talks
    11th Floor Lecture Hall
Wednesday, May 8, 2024
  • 9:00 - 9:40 am EDT
    Stabilizing particles across scales
    11th Floor Lecture Hall
    • Dante Kalise, Imperial College London
    Abstract
    This talk explores the control of interacting particle systems to desired stationary configurations across scales, connecting microscopic particle dynamics with macroscopic mean-field descriptions. We discuss two approaches: stabilizing the McKean-Vlasov PDE around unstable steady states and optimally controlling consensus-based optimization (CBO) dynamics. For interacting particle systems and their mean-field limit governed by the McKean-Vlasov 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 gradient-based 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 Hamilton-Jacobi-Bellman equation. This control guides particles towards the global minimizer of the objective function. We establish the well-posedness of the controlled CBO system and demonstrate its improved performance over standard CBO methods.
  • 9:50 - 10:30 am EDT
    Nonlocal approximation of linear and nonlinear diffusion
    11th Floor Lecture Hall
    • Olga Turanova, Michigan State 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 EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 - 11:40 am EDT
    TBA
    11th Floor Lecture Hall
    • Jianfeng Lu, Duke University
  • 11:50 am - 12:30 pm EDT
    Dynamics of Strategic Agents and Algorithms as PDEs
    11th Floor Lecture Hall
    • Franca Hoffmann, California Institute of Technology
    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 opposing-goal objective dynamics. We illustrate how our framework can accurately model real-world data and show via synthetic examples how it captures sophisticated distribution changes which cannot be modeled with simpler methods.
  • 12:40 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:40 pm EDT
    TBA
    11th Floor Lecture Hall
    • Yannis Kevrekidis, Johns Hopkins University
  • 2:50 - 5:00 pm EDT
    Poster Session/Coffee Break
    Poster Session - 11th Floor Collaborative Space
Thursday, May 9, 2024
  • 9:00 - 9:40 am EDT
    TBA
    11th Floor Lecture Hall
    • Adil Salim, Microsoft Research
  • 9:50 - 10:30 am EDT
    FedCBO: Reaching Group Consensus in Clustered Federated Learning and Robustness to Backdoor Adversarial Attacks.
    11th Floor Lecture Hall
    • Nicolas Garcia Trillos, University of Wisconsin Madison
    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 consensus-based optimization (CBO). Our new CBO-type 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 bi-level 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.
  • 10:40 - 11:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 - 11:40 am EDT
    Adjoint Monte Carlo Methods for Optimization Problems of Kinetic Equation
    11th Floor Lecture Hall
    • Yunan Yang, Cornell University
    Abstract
    We explore adjoint Monte Carlo methods for solving optimization problems governed by kinetic equations, a common challenge in areas such as plasma control and device design. These optimization problems are particularly demanding due to the high dimensionality of the phase space and the randomness in evaluating the objective functional, a consequence of using a forward Monte Carlo solver. To overcome these difficulties, we design a range of "adjoint Monte Carlo methods'', which involve interactive adjoint particles, mimicking the interactive nature of the forward propagation for these kinetic equations. They skillfully combine Monte Carlo gradient estimators with PDE-constrained optimization, introducing innovative solutions tailored for kinetic applications. The general approach leads to the formulation of effective adjoint Monte Carlo methods, enabling efficient gradient estimation in complex, high-dimensional optimization problems.
  • 11:50 am - 12:30 pm EDT
    Sampling through optimization of divergences
    11th Floor Lecture Hall
    • Anna Korba, ENSAE/CREST
    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 well-chosen discrepancy (e.g. a divergence or distance). In this talk, we'll discuss several properties of sampling algorithms for some choices of discrepancies (well-known ones, or novel proxies), both regarding their optimization and quantization aspects.
  • 12:40 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 2:40 pm EDT
    Sharp quantitative propagation of chaos for mean field and non-exchangeable diffusions
    11th Floor Lecture Hall
    • Daniel Lacker, Columbia University
    Abstract
    This talk discusses recent and ongoing work on a new "local" perspective on quantitative propagation of chaos, both for exchangeable and non-exchangeable 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 non-exchangeable 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 non-exchangeable setting, indexed by sets rather than numbers of particles, and we analyze it by means of an unexpected connection with first-passage percolation.
  • 2:50 - 3:10 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:10 - 3:50 pm EDT
    Weakly interacting jump processes with graphon interactions
    11th Floor Lecture Hall
    • Ruoyu Wu, Iowa State University
    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. Individual-based epidemic models, as an application, and Join-the-shortest-queue(d) systems, as a relevant queueing model, will be briefly discussed.
  • 4:00 - 4:40 pm EDT
    Opinion dynamics on complex networks
    11th Floor Lecture Hall
    • Mariana Cravioto, University of North Carolina Chapel Hill
    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 Friedkin-Johnsen model, with the added complexity of vertex-dependent 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 real-world 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 EDT
    Particle-Based Stochastic Reaction-Diffusion Models: Mean field limits and fluctuation corrections.
    11th Floor Lecture Hall
    • Konstantinos Spiliopoulos, Boston University
    Abstract
    Particle-based stochastic reaction-diffusion (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 coarse-grained deterministic partial integro-differential 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 measure-valued 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 large-population (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 EDT
    Interacting Particle Systems for Optimization: from Particle Swarm Optimization to Consensus-based Optimization
    11th Floor Lecture Hall
    • Hui Huang, Karl-Franzens-University Graz
    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 Consensus-based Optimization (CBO) through the limit of zero inertia.
  • 10:40 - 11:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 - 11:40 am EDT
    TBA
    11th Floor Lecture Hall
    • Lorenzo Pareschi, Heriot Watt University
  • 11:50 am - 12:30 pm EDT
    An interacting particle consensus method for constrained global optimization
    11th Floor Lecture Hall
    • Yuhua Zhu, University of California, San Diego
    Abstract
    This talk addresses the global minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system has been derived, the convergence of the mean-field 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 EDT
    Lunch/Free Time
  • 2:00 - 2:40 pm EDT
    Opinion-dynamics models with random-time interactions
    11th Floor Lecture Hall
    • Weiqi Chu, University of Massachusetts Amherst
    Abstract
    Opinion-dynamics 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, real-world social interactions and opinion updates often exhibit randomness in time. In this talk, we propose a novel approach to incorporate random-time interactions by modeling them as renewal processes on networks. Through this framework, we derive corresponding opinion-dynamics models that capture the stochastic nature of social interactions. Notably, when renewal processes exhibit non-Poisson interevent statistics, the resulting opinion models naturally yield non-Markovian dynamics. These memory-dependent effects offer insights into various phenomena (such as stereotypes) observed in social and information sciences.
  • 2:50 - 3:30 pm EDT
    Lagrangian flows for PME and particle implications
    11th Floor Lecture Hall
    • Matt Jacobs, Purdue 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 EDT
    Coffee Break
    11th Floor Collaborative Space

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