Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks

Understand

Physics-informed neural networks (PINNs) have emerged as new data-driven PDE solvers for both forward and inverse problems.

• While promising, the expensive computational costs to obtain solutions often restrict their broader applicability.
• We demonstrate that the computations in automatic differentiation (AD) can be significantly reduced by leveraging forward-mode AD when training PINN.
• However, a naive application of forward-mode AD to conventional PINNs results in higher computation, losing its practical benefit.