Boundary-Adapted PINNs for Elliptic Dirichlet Problems: $H^2(\Omega )$ A Priori Error Bounds with Application to Mean Escape Time Computation

Nathanael Tepakbong, Jun Fan, Xiang Zhou +1

Motivated by the numerical computation of the Mean Escape Time (MET) $\tau :\Omega \to \mathbb{R}$ of a stochastic process from a bounded domain $\Omega \subseteq {\mathbb{R}}^d$, we study elliptic Di…