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math.NA2020
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.NA2020
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…