FastLSQ: Solving PDEs in One Shot via Fourier Features with Exact Analytical Derivatives
Abstract
We present FastLSQ, a framework for PDE solving and inverse problems built on trigonometric random Fourier features with exact analytical derivatives. Trigonometric features admit closed-form derivatives of any order in $\mathcal{O}(1)$, enabling graph-free operator assembly without autodiff. Linear PDEs: one least-squares call; nonlinear: Newton--Raphson reusing analytical assembly. On 17 PDEs (1--6D), FastLSQ achieves $10^{-7}$ in 0.07s (linear) and $10^{-8}$--$10^{-9}$ in $
Fields of Study & Subjects
Model Reduction and Neural Networks
Neural Networks and Applications
Gaussian Processes and Bayesian Inference
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 11 February 2026
- Language
- EN
- Document type
- Preprint