Title: A stochastic approach for solving PDEs: derivative-free loss method

Speaker: 한지훈 박사 (Dartmouth College, Hanover, NH, USA)

Abstract: I will present the derivative-free loss method (DFLM), a stochastic approach for solving PDEs using neural networks. Inspired by the Feynman-Kac formula, DFLM utilizes the stochastic representation of the PDE solution, capturing collective information averaged from the paths of stochastic walkers as they explore the neighborhood of points of interest. Through iterative averaging, the neural network is progressively trained to approximate the PDE solution. I will cover its analysis regarding trainability and demonstrate its effectiveness across a range of applications, including interface problems, multiscale problems with highly oscillatory coefficients, and perforated domains, all addressed in a non-intrusive manner.