Numerical Differentiation and Its Impact on Uncertainty in Learned Dynamical Systems
Keywords: differential equation discovery, uncertainty, differentiation methods
TL;DR: Differentiation method choice is crucial for different equaiton discovery applications
Abstract: This work examines how different differentiation techniques impact the discovery of differential equations from data. Since real-world measurements are often noisy, accurately computing derivatives is crucial for reliable algorithm performance. We explore alternatives to finite difference methods, which are prone to instability and amplify data errors. Our study considers four approaches: Savitzky-Golay filtering, spectral differentiation using neural networks, and derivative regularization strategies. By assessing their suitability for realistic scenarios and their influence on equation discovery convergence, we provide insights into enhancing the robustness of data-driven modeling.
Submission Number: 30
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