Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
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. In this paper, we present a minimal interpretable framework for noise-robust derivative-free equation learning that combines recent advances in sparse system identification with classical signal proce
Zhiheng Chen Email: zc548@cornell.edu Affiliation: Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA, 14850 and Department of Aeronautics, Imperial College London, London, United Kingdom and Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA, 14850 Anastasia Bizyaeva Email: anastasiab@cornell.edu Affiliation: 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…
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