arxivmath.NAmath.OCstat.ML2026-07-18
A Deep Second-Order Stochastic Residual Method for Fully Nonlinear Parabolic PDEs
We introduce the Deep Second-Order Stochastic Residual Method (D2SRM) for high-dimensional, Hessian-dependent fully nonlinear parabolic PDEs. A single scalar space--time network generates derivative-consistent approximations of the solution, gradient, and Hessian, which are train…