Separable Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs and approximate very complex solution functions.The number of training points (collocation points) required on these challenging PDEs grows substantially, and it is severely limited due to the expensive computational costs and heavy memory overhead.To overcome this limit, we propose a network architecture and training algorithm for PINNs.The proposed method, separable PINN (SPINN), operates on a per-axis basis to decrease the number of network propagations in multi-dimensional PDEs instead of point-wise processing in conventional PINNs.We also propose using forward-mode automatic differentiation to reduce the computational cost of computing PDE residuals, enabling a large number of collocation points ($> 10^7$) on a single commodity GPU.