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Automatically discovering ordinary differential equations from data with sparse regression

Egan, Kevin; Li, Weizhen; Carvalho, Rui

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Authors

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Kevin Egan kevin.egan@durham.ac.uk
PGR Student Doctor of Philosophy

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Weizhen Li weizhen.li@durham.ac.uk
PGR Student Doctor of Philosophy



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
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

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