277 citations · 461 across the 25 of their papers we have counts for
Showing 2020Show all
3 papers · 1 filter
math.NA2020★ 277 cited
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
Yeonjong Shin, Jerome Darbon, George Em Karniadakis
Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering. Gu…
math.ST2020
On Bayesian posterior mean estimators in imaging sciences and Hamilton-Jacobi Partial Differential Equations
Jerome Darbon, Gabriel P. Langlois
Variational and Bayesian methods are two approaches that have been widely used to solve image reconstruction problems. In this paper, we propose original connections between Hamilt…
math.NA2020★ 71 cited
On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton--Jacobi partial differential equations
Jérôme Darbon, Tingwei Meng
We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamilton…