Spectral Informed Neural Networks

Tianchi Yu, Yiming Qi, Ivan Oseledets, Shiyi Chen

Abstract: In scientific computing, the burgeoning use of physics-informed neural networks (PINNs) for solving partial differential equations(PDEs) has spurred the need for, and ongoing research into, more accurate and efficient PINNs. One bottleneck of current PINNs is the computation of the high-order derivatives via automatic differentiation which often necessitates substantial computing resources especially when dealing with complex PDEs and high-dimensional problems. To tackle this, we propose a spectral-based neural network that substitutes the differential operator with a multiplication. Compared to PINNs, our framework requires less GPU memory and a shorter training time. Furthermore, thanks to the exponential convergence of the spectral basis, our approach is more accurate. Moreover, to handle the different situations between the physics domain and the spectral domain, we provide a strategy to train networks using their spectral information. Through a series of comprehensive experiments, we validate the aforementioned merits of our proposed network.

Primary Area: Applications->Chemistry, Physics, and Earth Sciences

Keywords: PINN, spectral method, automatic-differentiation

Application-Driven Machine Learning: This submission is on Application-Driven Machine Learning.

Submission Number: 3543