Sparse dynamical system identification with simultaneous structural parameters and initial condition estimation

Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition be exactly known in advance and is sensitive noise. In work we propose an integral SINDy (ISINDy) method simultaneously identify model structure parameters nonlinear ordinary differential (ODEs) noisy time-series observations. First, states are estimated via penalized spline smoothing then substituted into integral-form numerical discretization solver, leading a sparse pseudo linear regression. Then, sequential threshold least squares performed extract fewest active terms overdetermined set candidate features, thereby estimating structural meanwhile, making identified dynamics parsimonious interpretable. Simulations detail method’s recovery accuracy robustness Examples include logistic equation, Lotka–Volterra system, Lorenz system.