Tianchi Yu

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

Tianchi Yu, Ivan Oseledets

For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems ($4 \leq d \lesssim 10$), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-di…Read more