Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
This work addresses the challenge of learning equations from noisy data for researchers in dynamical systems, though it appears incremental as it builds on existing weak-form and spectral methods.
The paper tackled the problem of robust model identification in chaotic systems by introducing Fourier Weak SINDy, a derivative-free method that uses spectral test functions for noise robustness, achieving accurate results in numerical experiments on ODE benchmarks.
We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By using orthogonal sinusoidal test functions inspired by their prevalence in Modulating Function-based system identification, the weak-form sparse regression problem reduces to a regression over Fourier coefficients. Dominant frequencies are then selected via multitaper estimation of the frequency spectrum of the data. This formulation unifies weak-form learning and spectral estimation within a compact and flexible framework. We illustrate the effectiveness of this approach in numerical experiments across multiple chaotic and hyperchaotic ODE benchmarks.