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

2024/08/29 by Tianchi Yu, Yu, Tianchi, Yiming Qi +5
Computer Science · #Artificial Intelligence (cs.AI) #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2408.16414

openalex publication_date 2024/08/29 · openalex created_date 2024/09/22 · openalex updated_date 2026/07/28

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.

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