Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification

TL;DR

Fourier Weak SINDy is a novel, noise-robust method for data-driven model identification that combines spectral density estimation with weak-form sparse regression, enhancing interpretability and robustness.

Contribution

It introduces a spectral test function selection approach within weak-form sparse regression, unifying spectral estimation and model learning for improved robustness.

Findings

Effective in numerical experiments with chaotic and hyperchaotic ODEs.

Reduces regression to Fourier coefficients, simplifying the learning process.

Unifies weak-form learning with spectral density estimation.

Abstract

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.