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Fourier Weak SINDy is introduced as a derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for test function selection. The method utilizes orthogonal sinusoidal test functions, reducing the weak-form sparse regression to a regression over Fourier coefficients. Multitaper spectral estimation is then used to select dominant frequencies, resulting in a noise-robust and interpretable framework demonstrated on chaotic ODE benchmarks.
Forget finite differences: Fourier Weak SINDy offers a derivative-free approach to system identification that's robust to noise and leverages spectral estimation for interpretable equation learning.
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.
