3 papers
math.OC2026
Operator Learning for Families of Finite-State Mean-Field Games
William Hofgard, Asaf Cohen, Mathieu Laurière
Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consi…
math.OC2024
Convergence Guarantees for Neural Network-Based Hamilton-Jacobi Reachability
William Hofgard
We provide a novel uniform convergence guarantee for DeepReach, a deep learning-based method for solving Hamilton-Jacobi-Isaacs (HJI) equations associated with reachability analysi…
math.OC2024
Convergence of the Deep Galerkin Method for Finite State Mean Field Control Problems
William Hofgard, Jingruo Sun, Asaf Cohen
We establish the convergence of the deep Galerkin method (DGM), a deep learning-based scheme for solving high-dimensional nonlinear PDEs, for Hamilton-Jacobi-Bellman (HJB) equation…