Automatically identifying dynamical systems from data
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Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to automatically identify dynamical laws by integrating denoising techniques, sparse regression, and bootstrap confidence intervals. 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 signal quality levels relative to background noise. By accurately identifying dynamical systems, our methodology has the potential to impact diverse fields, such as the physical and biological sciences, as well as engineering, where understanding complex systems is crucial.
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