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

Zhiheng Chen, Urban Fasel, Anastasia Bizyaeva
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:557-573, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-chen26b, title = {Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification}, author = {Chen, Zhiheng and Fasel, Urban and Bizyaeva, Anastasia}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {557--573}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/chen26b/chen26b.pdf}, url = {https://proceedings.mlr.press/v331/chen26b.html}, 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.} }
Endnote
%0 Conference Paper %T Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification %A Zhiheng Chen %A Urban Fasel %A Anastasia Bizyaeva %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-chen26b %I PMLR %P 557--573 %U https://proceedings.mlr.press/v331/chen26b.html %V 331 %X 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.
APA
Chen, Z., Fasel, U. & Bizyaeva, A.. (2026). Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:557-573 Available from https://proceedings.mlr.press/v331/chen26b.html.

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