Automatically identifying ordinary differential equations from data
This addresses the fundamental challenge of discovering dynamical laws from data in fields like complex systems where data are abundant but model development is effort-intensive.
The researchers tackled the problem of automatically discovering nonlinear differential equations from empirical data by developing a method that integrates denoising, sparse regression, and bootstrap confidence intervals. Their algorithm consistently identified three-dimensional systems given moderately-sized time series and high signal-to-noise ratios.
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.