61 citations · 78 across the 9 of their papers we have counts for
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math.NA2020★ 6 cited
Solving Elliptic Equations with Brownian Motion: Bias Reduction and Temporal Difference Learning
Cameron Martin, Hongyuan Zhang, Julia Costacurta +2
The Feynman-Kac formula provides a way to understand solutions to elliptic partial differential equations in terms of expectations of continuous time Markov processes. This connect…
cs.LG2020★ 61 cited
A Derivative-Free Method for Solving Elliptic Partial Differential Equations with Deep Neural Networks
Jihun Han, Mihai Nica, Adam R Stinchcombe
We introduce a deep neural network based method for solving a class of elliptic partial differential equations. We approximate the solution of the PDE with a deep neural network wh…