Related papers: Deep Learning for Mean Field Games with non-separa…
In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with…
We analyze asymptotic convergence properties of Newton's method for a class of evolutive Mean Field Games systems with non-separable Hamiltonian arising in mean field type models with congestion. We prove the well posedness of the Mean…
Graph generation is a crucial task in many fields, including network science and bioinformatics, as it enables the creation of synthetic graphs that mimic the properties of real-world networks for various applications. Graph Generative…
We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for explaining, enhancing, and designing generative models. In generative flows, a Lagrangian formulation is used where each particle (generated sample)…
We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in…
Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques…
Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…
We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…
This paper establishes a data-driven solution for infinite horizon linear quadratic Gaussian Mean Field Games with network-coupled heterogeneous agent populations where the dynamics of the agents are unknown. The solution technique relies…
The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular…
Achievement of solutions in Navier-Stokes equation is one of challenging quests, especially for its closure problem. For achievement of particular solutions, there are variety of numerical simulations including Direct Numerical Simulation…
Deep learning approaches to generic (non-semantic) segmentation have so far been indirect and relied on edge detection. This is in contrast to semantic segmentation, where DNNs are applied directly. We propose an alternative approach called…
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…
This paper aims at studying the difference between Ritz-Galerkin (R-G) method and deep neural network (DNN) method in solving partial differential equations (PDEs) to better understand deep learning. To this end, we consider solving a…
We study multi-agent general-sum Markov games with nonlinear function approximation. We focus on low-rank Markov games whose transition matrix admits a hidden low-rank structure on top of an unknown non-linear representation. The goal is to…
In a variety of geoscientific applications scientists often need to image properties of the Earth's interior in order to understand the heterogeneity and processes taking place within the Earth. Seismic tomography is one such method which…
We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…
We study the long time behavior of an underdamped mean-field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under different conditions. The results on the MFL equation can be…
Reinforcement Learning (RL) algorithms allow artificial agents to improve their action selections so as to increase rewarding experiences in their environments. Deep Reinforcement Learning algorithms require solving a nonconvex and…