Fourier Feature Networks: A Novel Approach for Solving PDEs
A recent publication on arXiv (2608.14733) presents Fourier Feature Networks (FENs), an innovative neural network design aimed at addressing partial differential equations (PDEs). FENs build upon single-hidden-layer neural networks by integrating Fourier features through cosine, sine, or a mix of both. Similar to Extreme Learning Machines (ELMs), they utilize a single-hidden-layer framework to create basis functions, with the target function represented as a linear combination of these basis functions, where coefficients are calculated using least squares. Unlike ELMs, which frequently depend on affine transformations for enhanced representational capacity, FENs deliver precise solutions without such adjustments. The research assesses representational ability by identifying an optimal scaling factor within a specified range for both randomly initialized and fixed weights and biases, facilitating a fair evaluation against other techniques. This paper is classified as a cross announcement and is accessible on arXiv.
Key facts
- The paper is titled 'A Novel Fourier Feature Network for Solving Partial Differential Equations'.
- The arXiv ID is 2608.14733.
- Fourier Feature Networks (FENs) are proposed, incorporating Fourier features using cos, sin, or both.
- FENs use a single-hidden-layer architecture similar to Extreme Learning Machines (ELMs).
- The target function is approximated as a linear combination of basis functions with coefficients determined by least squares.
- Unlike ELMs, FENs do not require affine transformations on input variables.
- An optimal scaling factor is searched within a predefined range for randomly initialized and fixed weights and biases.
- The paper is a cross announcement on arXiv.
Entities
Institutions
- arXiv