Spectral Informed Neural Network: An Efficient and Low-Memory PINN
This work addresses efficiency and memory issues in PINNs for scientific computing, offering incremental improvements over existing methods.
The paper tackles the computational bottleneck of high-order derivative calculations in physics-informed neural networks (PINNs) by proposing a spectral-based neural network that replaces differential operators with multiplications, resulting in lower memory usage, shorter training time, and improved accuracy due to exponential convergence of spectral bases.
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.