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math.NA2025
WoSNN: Stochastic Solver for PDEs with Machine Learning
Silei Song, Arash Fahim, Michael Mascagni
Solving elliptic partial differential equations (PDEs) is a fundamental step in various scientific and engineering studies. As a classic stochastic solver, the Walk-on-Spheres (WoS…
math.NA2011
A Stochastic Approximation for Fully Nonlinear Free Boundary Parabolic Problems
Erhan Bayraktar, Arash Fahim
We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the…