5 papers
When does least-squares residual minimization solve a differential equation?
Carlos Esteve-Yagüe, Richard Tsai, Stanley Osher
Least-squares residual minimization approximates a differential equation through an optimization problem. This paper investigates the conditions required to transition from station…
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…
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…
Error Analysis for the Implicit Boundary Integral Method
Yimin Zhong, Kui Ren, Olof Runborg +1
The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provid…
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…