Nonlinear dynamical models from time series

TL;DR

This paper introduces a variational optimization method for estimating parameters in nonlinear dynamical models from chaotic time series, effectively handling noise and reducing model complexity.

Contribution

It presents a novel variational approach for parameter estimation in ODE systems from chaotic data, emphasizing robustness and model simplification.

Findings

Method is robust to noise in time series.

Effective in reducing model complexity by discarding insignificant parameters.

Demonstrated success on numerical studies with chaotic data.

Abstract

We present an optimization process to estimate parameters in systems of ordinary differential equations from chaotic time series. The optimization technique is based on a variational approach, and numerical studies on noisy time series demonstrate that it is very robust and appropriate to reduce the complexity of the model. The proposed process also allows to discard the parameters with scanty influence on the dynamic.