Spectral Informed Neural Network: An Efficient and Low-Memory PINN

Abstract

With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of current PINNs is computing the high-order derivatives via automatic differentiation which often necessitates substantial computing resources. In this paper, we focus on removing the automatic differentiation of the spatial derivatives and propose a spectral-based neural network that substitutes the differential operator with a multiplication. Compared to the PINNs, our approach requires lower memory and shorter training time. Thanks to the exponential convergence of the spectral basis, our approach is more accurate. Moreover, to handle the different situations between physics domain and spectral domain, we provide two strategies to train networks by their spectral information. Through a series of comprehensive experiments, We validate the aforementioned merits of our proposed network.

References in corpus (9)

• Solving high-dimensional partial differential equations using deep learning
• NSFnets (Navier-Stokes Flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
• B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
• Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems
• A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
• PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs
• Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
• Hutchinson Trace Estimation for High-Dimensional and High-Order Physics-Informed Neural Networks
• Preconditioned FEM-based Neural Networks for Solving Incompressible Fluid Flows and Related Inverse Problems