Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917427692961792 |
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| author | Chen, Zhiheng Fasel, Urban Bizyaeva, Anastasia |
| author_facet | Chen, Zhiheng Fasel, Urban Bizyaeva, Anastasia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20141 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification Chen, Zhiheng Fasel, Urban Bizyaeva, Anastasia Machine Learning Dynamical Systems 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. |
| title | Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification |
| topic | Machine Learning Dynamical Systems |
| url | https://arxiv.org/abs/2604.20141 |