INTEGRAL PINNS FOR HYPERBOLIC CONSERVATION LAWS

Traditional physics-informed neural networks (PINNs) are trained based on differential equations and thus have difficulty capturing shock discontinuities in weak solutions of hyperbolic PDEs, since the differential equation doesn’t apply at the discontinuity. We propose Integral PINNs (IPINNs), which are trained based on the integral form of the conservation law, which holds at both continuous and discontinuous points of the solution. We use neural nets to model the integrals of the solution instead of the solution itself. We apply IPINNs to systems of hyperbolic conservation laws and show that they are much better at capturing the correct location and speed of shocks, compared to traditional PINNs. We also present a heuristic approach for detecting shock locations.