Automatically discovering ordinary differential equations from data with sparse regression

Egan, Kevin; Li, Weizhen; Carvalho, Rui

Abstract

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. While current methods can identify such equations, they often require extensive manual hyperparameter tuning, limiting their applicability. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques to smooth the signal, sparse regression to identify the relevant parameters, and bootstrap confidence intervals to quantify the uncertainty of the estimates. We evaluate our method on well-known ordinary differential equations with an ensemble of random initial conditions, time series of increasing length, and varying signal-to-noise ratios. Our algorithm consistently identifies three-dimensional systems, given moderately-sized time series and high levels of signal quality relative to background noise. By accurately discovering dynamical systems automatically, our methodology has the potential to impact the understanding of complex systems, especially in fields where data are abundant, but developing mathematical models demands considerable effort.

Citation

Egan, K., Li, W., & Carvalho, R. (2024). Automatically discovering ordinary differential equations from data with sparse regression. Communications Physics, 7(1), Article 20. https://doi.org/10.1038/s42005-023-01516-2

• Journal Article Type: Article
• Acceptance Date: Dec 25, 2023
• Online Publication Date: Jan 9, 2024
• Publication Date: 2024-01
• Deposit Date: Jan 16, 2024
• Publicly Available Date: Feb 2, 2024
• Journal: Communications Physics
• Electronic ISSN: 2399-3650
• Publisher: Nature Research
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Issue: 1
• Article Number: 20
• DOI: https://doi.org/10.1038/s42005-023-01516-2
• Public URL: https://durham-repository.worktribe.com/output/2120230