Multi-Scale Separable Fourier Neural Networks for Solving High-Frequency PDEs
Solving high-frequency partial differential equations (PDEs) with neural networks is notoriously difficult due to the spectral bias of conventional architectures. We propose the Multi-Scale Separable Fourier Neural Network (MS-SFNN), a framework designed to overcome this limitation by explicitly encoding multi-scale Fourier features within a separable representation. The network factorizes the solution into $d$ single-coordinate subnetworks with fixed, randomly initialized weights; these subnetworks are combined via element-wise products to form a rich set of basis functions. This separable construction scales linearly with the problem dimension, thus inherently alleviating the curse of d...
| Authors | Qihong Yang, Qiaolin He |
|---|---|
| Primary category | cs.LG |
| Published | 29 May 2026 |
| Last updated at source | 11 July 2026 |
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