Separable Physics-Informed Neural Networks

Understand

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 highly complex solution functions.
• The number of training points (collocation points) required on these challenging PDEs grows substantially, but it is severely limited due to the expensive computational costs and heavy memory overhead.
• To overcome this issue, we propose a network architecture and training algorithm for PINNs.