Boundary value problems (BVPs) and partial differential equations (PDEs) are critical components of modern applied mathematics, underpinning the theoretical and practical analyses of complex systems.

Physics-informed neural networks (PINNs) represent a burgeoning paradigm in computational science, whereby deep learning frameworks are augmented with explicit physical laws to solve both forward and ...

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic ...