On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations

We propose novel connections between several neural network architectures and viscosity solutions of some Hamilton--Jacobi (HJ) partial differential equations (PDEs) whose Hamiltonian is convex only depends on the spatial gradient solution. To be specific, we prove that under certain assumptions, two proposed represent to sets HJ PDEs with zero error. also implement our using Tensorflow provide examples illustrations. Note these representations can avoid curve dimensionality for PDEs, since they do not involve neither grids nor discretization. Our results suggest efficient dedicated hardware implementation networks leveraged evaluate PDEs.