Finite-difference least square methods for solving Hamilton-Jacobi equations using neural networks

Carlos Esteve Yague, Richard Tzong-Han Tsai, Alex Massucco

Keywords: Hamilton-Jacobi equations, Deep learning, Finite-difference methods, Least squares principle, Optimal control, Differential games

TL;DR: This study proposes a versatile deep learning algorithm to approximate the viscosity solutions for Hamilton-Jacobi equations in high dimensions minimizing a least square principle defined through a finite-difference scheme

Confirmation Of Submission Requirements: I submit a previously published paper. It was published in an archival peer–reviewed venue on or after September 8th 2024, I specify the DOI in the field below, and I submit the camera-ready version of the paper.

DOI: https://doi.org/10.1016/j.jcp.2025.113721

Submission Number: 45