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

• URL: http://arxiv.org/abs/2604.20141v1
• Date: Wed, 22 Apr 2026 03:09:56 GMT
• Title: Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
• Abstract summary: We introduce 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.<n>We illustrate the effectiveness of this approach in numerical experiments across multiple chaotic and hyperchaotic ODE benchmarks.
• Score: 1.2535148942290433
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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