25 citations · 34 across the 9 of their papers we have counts for
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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…
One-sided reflected Brownian motions and the KPZ fixed point
Mihai Nica, Jeremy Quastel, Daniel Remenik
We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition pro…
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…