Solving Problems of Mathematical Physics on Radial Basis Function Networks

Abstract

The solution of boundary value problems described by partial differential equations on physics-informed neural networks is considered. Radial basis function networks are proposed as physics-informed neural networks. Such are easier to train compared to the fully connected networks usually used as physics-informed neural networks. An algorithm for solving the system of partial differential equations for the hydrodynamics problem is developed. On the example of the model problem of Kovasznay flow, programs for solving two-dimensional stationary Navier–Stokes equations using physics-informed radial basis function networks trained by the Nesterov method are developed.