Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

arXiv cs.AI · 17 hours ago

Modified Spectral-Informed Neural Networks (SINNs) combine spectral methods with neural networks to solve high-dimensional partial differential equations by operating in the spectral domain. The approach achieved superior accuracy compared to Physics-Informed Neural Networks on problems with dimension d ≫ 10 while outperforming sparse grid spectral methods on middle-dimensional problems with d between 4 and 10. The method integrates coefficient decay scaling and basis embeddings to reduce memory consumption and improve efficiency for high-dimensional PDE solving.