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.

The energy transfer from granular landslides to water bodies explained by a data-driven, physics-based numerical model

“…It consists in a data-driven, physics-based model (e.g. : Greve et al 2019) which is calibrated with our experimental data. The model evaluates energy losses and energy transfer between landslide and water body during the landslide motion along a fixed bed.…”

Numerical and Experimental Investigation of Longitudinal Oscillations in Hall Thrusters

“…Among the two modeling approaches, fully-fluid models are easier to tune against reference data, as they are entirely formulated in terms of deterministic spatiotemporal plasma characteristics. In hybrid approaches, in any case, tuning can be carried out on the fluid part of the model, as proposed, for instance, in [33]. Moreover, fully-fluid models are particularly suitable to be used for stability analyses, as they can be linearized in a rather straightforward way.…”

Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures

“…This work aims to reintroduce non-random causal state-space flow information inherent to emergent physical phenomena to the parameter identification problem as applied to chaotic systems that elude asymptotic trajectory convergence. Though methods such as sparse identification of nonlinear dynamics (SINDy) [59,14,58] can be used to estimate parameters for chaotic systems composed from a library of assumed functional forms, the longer-term goal of this effort is to make rigorous the empirically motivated black-box calibration methodology proposed in [31] for general state-space dynamics. While the techniques developed here are applied to simple dynamical systems to demonstrate the approach, these are intended only as illustrative examples to describe the proposed process and necessary inputs required to extend this theoretic framework to the general case in subsequent efforts.…”

“…Following [31], we use the Wasserstein metric from optimal transport to compare the observed DNS-generated invariant measure and the synthetic FPE steady state. The Wasserstein metric has been actively studied since the late 20th century [65].…”

“…A Different Forward Model. While matching shadow state-space density in [31] provided a potential route to resolve the issue of chaotic divergence of statespace trajectories, the direct estimation of state-space density from trajectory data still retained two major challenges. The most significant issue with using this approach to parameter inference revolved around the inability to calculate a gradient of the Wasserstein metric with respect to the system parameters forcing the reliance on evolutionary or other gradient-free optimization methods.…”