A data-driven approach to model calibration for nonlinear dynamical systems

Abstract

A data-driven approach to model calibration is developed to accurately obtain the input parameters for nonlinear dynamical systems. The paper focuses on the convergence properties of the proposed method, which play a significant role in understanding the validity and usefulness of any data-driven model. The input parameters of nonlinear dynamical systems are optimized to a reference solution, which can be experimental data or results from a high-fidelity computer simulation, using the Wasserstein metric and a phase-space representation of a set of time-dependent signals. Test cases shown in this paper include the Lorenz system and the discharge plasma of a Hall effect thruster to characterize the numerical uncertainties of the proposed data-driven approach, given a constructed reference solution. Distinct wells in the cost function, the Wasserstein metric, are obtained relative to the reference solution, illustrating the applicability of the proposed method to dynamical problems. The numerical uncertainties associated with the phase-space portrait and sampling time are discussed.