Related papers: Deep Learning for Mean Field Games with non-separa…

We propose a MFG model with quadratic Hamiltonian involving $N$ populations. This results in a system of $N$ Hamilton-Jacobi-Bellman and $N$ Fokker-Planck equations with non-local interactions. As in the classical case we introduce an…

A graph neural network (GCN) is employed in the deep energy method (DEM) model to solve the momentum balance equation in 3D for the deformation of linear elastic and hyperelastic materials due to its ability to handle irregular domains over…

Mean field games models describing the limit of a large class of stochastic differential games, as the number of players goes to $+\infty$, have been introduced by J.-M. Lasry and P.-L. Lions. We use a change of variables to transform the…

Generative adversarial networks (GANs) are among the most successful models for learning high-complexity, real-world distributions. However, in theory, due to the highly non-convex, non-concave landscape of the minmax training objective,…

We study convergence rates of the generalized conditional gradient (GCG) method applied to fully discretized Mean Field Games (MFG) systems. While explicit convergence rates of the GCG method have been established at the continuous PDE…

We propose a policy iteration method to solve an inverse problem for a mean-field game (MFG) model, specifically to reconstruct the obstacle function in the game from the partial observation data of value functions, which represent the…

The recent increase in computational resources and data availability has led to a significant rise in the use of Machine Learning (ML) techniques for data analysis in physics. However, the application of ML methods to solve differential…

In this work, we consider a first order mean field games system with non-local couplings. A Lagrange-Galerkin scheme for the continuity equation, coupled with a semi-Lagrangian scheme for the Hamilton-Jacobi-Bellman equation, is proposed to…

In this paper, we present a Fast Motion Deblurring-Conditional Generative Adversarial Network (FMD-cGAN) that helps in blind motion deblurring of a single image. FMD-cGAN delivers impressive structural similarity and visual appearance after…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…

We propose an efficient semi-Lagrangian method for solving the two-dimensional incompressible Euler equations with high precision on a coarse grid. The new approach evolves the flow map using the gradient-augmented level set method (GALSM).…

This paper develops and analyzes a class of semi-discrete and fully discrete weak Galerkin finite element methods for unsteady incompressible convective Brinkman-Forchheimer equations. For the spatial discretization, the methods adopt the…

Mixed optimal stopping and stochastic control problems define variational inequalities with non-linear Hamilton-Jacobi-Bellman (HJB) operators, whose numerical solution is notoriously difficult and lack of reliable benchmarks. We first use…

The use of distributions and high-level features from deep architecture has become commonplace in modern computer vision. Both of these methodologies have separately achieved a great deal of success in many computer vision tasks. However,…

We present a neural network-based method for solving linear and nonlinear partial differential equations, by combining the ideas of extreme learning machines (ELM), domain decomposition and local neural networks. The field solution on each…

We present the development and analysis of a reinforcement learning (RL) algorithm designed to solve continuous-space mean field game (MFG) and mean field control (MFC) problems in a unified manner. The proposed approach pairs the…

This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover…

Fine-grained image search is still a challenging problem due to the difficulty in capturing subtle differences regardless of pose variations of objects from fine-grained categories. In practice, a dynamic inventory with new fine-grained…

We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master…

Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…