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

While Generative Adversarial Networks (GANs) have seen huge successes in image synthesis tasks, they are notoriously difficult to adapt to different datasets, in part due to instability during training and sensitivity to hyperparameters.…

Neural network-based methods have demonstrated effectiveness in solving high-dimensional Mean-Field Games (MFG) equilibria, yet ensuring mathematically consistent density-coupled evolution remains a major challenge. This paper proposes the…

The intersection of Mean Field Games (MFGs) and Reinforcement Learning (RL) has fostered a growing family of algorithms designed to solve large-scale multi-agent systems. However, the field currently lacks a standardized evaluation…

We present a matrix-free multigrid method for high-order discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing various data and compute layouts. Smoother implementations are…

Many methods have been proposed to quantify the predictive uncertainty associated with the outputs of deep neural networks. Among them, ensemble methods often lead to state-of-the-art results, though they require modifications to the…

In this paper, we present a staggered discontinuous Galerkin (SDG) method for a class of nonlinear elliptic equations in two dimensions. The SDG methods have some distinctive advantages, and have been successfully applied to a wide range of…

We introduce a general framework for approximating parabolic Stochastic Partial Differential Equations (SPDEs) based on fluctuation-dissipation balance. Using this approach we formulate Stochastic Discontinuous Galerkin Methods (SDGM). We…

Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering…

Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…

This paper studies approximate solutions to large-scale linear quadratic stochastic games with homogeneous nodal dynamics parameters and heterogeneous network couplings within the graphon mean field game framework in [2]-[4]. A graphon…

We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions and feature-space expansions in the spirit of kernel…

During a geosteering operation the well path is intentionally adjusted in response to the new data acquired while drilling. To achieve consistent high-quality decisions, especially when drilling in complex environments, decision support…

This work develops a robust and efficient framework of the adjoint gradient-based aerodynamic shape optimization (ASO) using high-order discontinuous Galerkin methods (DGMs) as the CFD solver. The adjoint-enabled gradients based on…

First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…

This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…

Recent advances in deep learning has witnessed many innovative frameworks that solve high dimensional mean-field games (MFG) accurately and efficiently. These methods, however, are restricted to solving single-instance MFG and demands…

Generative adversarial networks (GANs) are successful deep generative models. GANs are based on a two-player minimax game. However, the objective function derived in the original motivation is changed to obtain stronger gradients when…

We propose and investigate a general class of discrete time and finite state space mean field game (MFG) problems with potential structure. Our model incorporates interactions through a congestion term and a price variable. It also allows…

The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many…

A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary…