# Registered Data

## [00140] Interacting particle systems: modeling, learning and applications

**Session Date & Time**:- 00140 (1/2) : 3C (Aug.23, 13:20-15:00)
- 00140 (2/2) : 3D (Aug.23, 15:30-17:10)

**Type**: Proposal of Minisymposium**Abstract**: Systems of interacting particles or agents are ubiquitous in science and technology, with new theory and applications developing at a rapid pace. This mini-symposium aims at a cross-fertilization of areas in the study of topics in interacting particle systems, including, but not limited to: their analysis, computational techniques, parametric and nonparametric inference problems, control, interacting particles on graphs, use of interacting particle-based methods in optimization and neural networks, modeling and applications.**Organizer(s)**: Fei Lu, Mauro Maggioni**Classification**:__82C22__,__49Q99__,__35R30__,__68T09__,__35Q83__**Speakers Info**:- David Bortz (University of Colorado Boulder)
- Grigorios Pavliotis (Imperial University)
- Pierre-Emmanuel Jabin (Penn State University)
- Xiaohui Chen (University of Illinois at Urbana-Champaign)
- Sui Tang (University of California, Santa Barbara)
- Mauro Bonafini (University of Verona)
- Karthik Elamvazhuthi (University of California, Riverside)
- Lei Li (Shanghai Jiao Tong University)

**Talks in Minisymposium**:**[03149] The mean field limit of random batch interacting particle systems****Author(s)**:**Lei Li**(Shanghai Jiao Tong University)

**Abstract**: The Random Batch Method proposed in our previous work (J Comput Phys, 2020) is not only a numerical method for interacting particle systems and its mean-field limit, but also can be viewed as a new model in which particles interact, at discrete time, with randomly selected mini-batch of particles. We investigate the mean-field limit of this model as the number of particles tends to infinity. The mean field limit now exhibits some new features. We will not only justify this mean-field limit (discrete in time) but will also show that the limit approaches to the solution of a nonlinear Fokker-Planck equation as the discrete time step goes to zero.

**[03624] Weak Form Equation Learning for Interacting Particle System Models of Collective Motion****Author(s)**:**David Bortz**(University of Colorado - Boulder)- Daniel Messenger (University of Colorado - Boulder)

**Abstract**: The Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) methodology efficiently identifies governing equations from noisy data. We develop WSINDy for inference of 1st and 2nd-order IPS models as well as a joint model selection and classification method to both learn governing IPS equations and sort individuals into distinct interaction rule classes. We demonstrate the efficiency and proficiency of these methods on several test scenarios, motivated by common cell migration experiments.

**[03774] Mean-field nonparametric estimation of interacting particle systems****Author(s)**:**Xiaohui Chen**(University of Southern California)- Rentian Yao (University of Illinois at Urbana-Champaign)
- Yun Yang (University of Illinois at Urbana-Champaign)

**Abstract**: This talk concerns the nonparametric estimation problem of the distribution-state dependent drift vector field in an interacting $N$-particle system. Observing single-trajectory data for each particle, we derive the mean-field rate of convergence for the maximum likelihood estimator (MLE), which depends on both Gaussian complexity and Rademacher complexity of the function class. In particular, when the function class contains $\alpha$-smooth Hölder functions, our rate of convergence is minimax optimal on the order of $N^{-\frac{\alpha}{d+2\alpha}}$. Combining with a Fourier analytical deconvolution estimator, we derive the consistency of MLE for the external force and interaction kernel in the McKean-Vlasov equation.

**[03778] The mean-field limit of non-exchangeable integrate and fire systems****Author(s)**:**Pierre-Emmanuel Jabin**(Pennsylvania State University)- Datong Zhou (Pennsylvania State University)

**Abstract**: We investigate the mean-field limit of large networks of interacting biological neurons. The neurons are represented by the so-called integrate and fire models that follow the membrane potential of each neurons and captures individual spikes. However we do not assume any structure on the graph of interactions but consider instead any connection weights between neurons that obey a generic mean-field scaling. We are able to extend the concept of extended graphons, introduced in Jabin-Poyato-Soler, by introducing a novel notion of discrete observables in the system.

**[04464] Data-driven discovery of interacting particle systems with Gaussian Processes****Author(s)**:**Sui Tang**(University of California Santa Barbara)- Charles Kulick (University of California Santa Barabra)
- Jinchao Feng (Johns Hopkins University)

**Abstract**: We present a data-driven approach for discovering interacting particle models with latent interactions. Our approach uses Gaussian processes to model latent interactions, providing an uncertainty-aware approach to modeling interacting particle systems. We demonstrate the effectiveness of our approach through numerical experiments on prototype systems and real data. Moreover, we develop an operator-theoretic framework to provide theoretical guarantees for the proposed approach. We analyze recoverability conditions and establish the statistical optimality of our approach.

**[04754] Game-based learning of interaction rules for rational agents****Author(s)**:**Mauro Bonafini**(University of Verona)- Massimo Fornasier (Technical University of Munich)
- Bernhard Schmitzer (University of Göttingen)

**Abstract**: We introduce novel multi-agent interaction models obtained as fast-reaction limits of evolutionary games. We discuss the well-posedness of these models and the learnability of individual payoff functions from observation data. We formulate the payoff learning as a variational problem, minimizing the discrepancy between the observations and the predictions by the payoff function. The abstract framework is fully constructive and numerically implementable. We illustrate this on computational examples.

**[04827] Neural parameter calibration for large-scale multi-agent systems****Author(s)**:**Thomas Gaskin**(University of Cambridge)

**Abstract**: I present a method to calibrate multi-agent systems to datasets using neural networks, allowing for uncertainty quantification in a manner that reflects both the noise on the data as well as the non-convexity of the parameter estimation problem. I will discuss applications to various different examples, including learning entire network adjacency matrices, and give a comparative analysis of the method’s performance in terms of speed, prediction accuracy, and uncertainty quantification to classical techniques.

**[05244] Non-local regularization of Semilinear PDE for Probability Density Stabilization****Author(s)**:**Karthik Elamvazhuthi**(University of California, Riverside)

**Abstract**: In this talk, I will present some recent work on a particle method for numerically simulating a class of semilinear PDEs that provide strategies for probability density stabilization. These have important applications in problems such as sampling and multi-agent control. We will consider a semilinear diffusion model in which the reaction parameters are to be designed so that the solution of PDE converges to a target probability density. Since the parameters of these PDEs depend on the local density, they are not suitable for implementation on a finite number of particles. We construct a particle method by regularizing the local dependence to construct a non-local PDE. While the nonlocal approximations make numerical implementation easier, their local limits have good analytical properties from the point of view of understanding long-term behavior. Motivated by applications in robotics, the method also easily generalizes to situations where the particle diffusions are degenerate and hence, not elliptic, but only hypoelliptic.