2023/04/21 by Kevin J. Egan, Weizhen Li, Egan, Kevin +3
Computer Science · Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Computational Physics (physics.comp-ph) #Data Visualization and Analytics #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (cs.LG) #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2304.11182
openalex publication_date 2023/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. 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.