Coupling Physics Informed Neural Networks with External Solvers

Abstract: The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN's major difficulties in coupling with external forward solvers arise from the inability to access the discretized form (Finite difference, finite volume, finite element, etc.) of the governing equation directly through the network and to include them in its computational graph. This poses a significant challenge to conventional automatic-differentiation-based derivative computation of physics-based loss terms concerning the neural network hyperparameters if gradient-based optimization techniques are adopted. Therefore, we propose modifying the physics-based loss term to account for the residual arising from the external solver and to compute the derivative required for the optimization machinery. The proposed methodologies are demonstrated on benchmark full-order and reduced-order systems.