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math.NA2026
Solving Hamilton-Jacobi equations by residual minimization of monotone finite-difference discretizations
Olivier Bokanowski, Carlos Esteve-Yagüe, Richard Tsai
We introduce a method for solving Hamilton--Jacobi equations, both inviscid and viscous, by minimizing the squared residuals of monotone finite-difference discretizations on grids…
math.NA2024
Finite-difference least square methods for solving Hamilton-Jacobi equations using neural networks
Carlos Esteve-Yagüe, Richard Tsai, Alex Massucco
We present a simple algorithm to approximate the viscosity solution of Hamilton-Jacobi (HJ) equations by means of an artificial deep neural network. The algorithm uses a stochastic…
math.NA2024
A Volumetric Approach to Monge's Optimal Transport on Surfaces
Richard Tsai, Axel G. R. Turnquist
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in , found in disciplines like optics, computer graphics, and comp…