aiqbench analysis
Fourier Weak SINDy advances equation learning by integrating spectral density estimation into weak-form sparse regression, offering a robust framework for identifying dynamical systems from noisy data without requiring derivatives. This method leverages orthogonal sinusoidal test functions to reduce complex regression problems to Fourier coefficient analysis, demonstrating improved performance on chaotic and hyperchaotic ordinary differential equations. The approach represents a significant step forward in making model identification more interpretable and resilient against noise within the machine learning community.
Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification
arXiv:2604.20141v2 Announce Type: replace 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.
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.
Machine Learning (cs.LG); Dynamical Systems (math.DS)
arXiv:2604.20141 [cs.LG]
(or arXiv:2604.20141v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2604.20141 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 197 words
