Data-driven Discovery of Closure Models
This work addresses closure modeling for dynamical systems, which is important for researchers in computational physics and engineering, but it appears incremental as it builds on existing operator inference methods.
The authors tackled the problem of modeling memory effects in reduced-order representations of dynamical systems by developing a data-driven framework using operator inference, sparse polynomial regression, and neural networks, achieving predictive performance on unseen data across linear to nonlinear systems, including chaotic ones.
Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this work, we present a framework of operator inference to extract the governing dynamics of closure from data in a compact, non-Markovian form. We employ sparse polynomial regression and artificial neural networks to extract the underlying operator. For a special class of non-linear systems, observability of the closure in terms of the resolved dynamics is analyzed and theoretical results are presented on the compactness of the memory. The proposed framework is evaluated on examples consisting of linear to nonlinear systems with and without chaotic dynamics, with an emphasis on predictive performance on unseen data.