Data-driven modeling of the chaotic thermal convection in an annular thermosyphon

TL;DR

This paper demonstrates how combining dimensionality reduction and sparse system identification can produce accurate, interpretable low-order models of chaotic thermal convection in an annular thermosyphon, closely resembling the Lorenz system.

Contribution

The work introduces a data-driven approach using dynamic mode decomposition and SINDy to derive low-order models of chaotic convection, extending the Lorenz system framework.

Findings

The identified model closely resembles the Lorenz system.

The approach accurately captures the physical properties of the flow.

Extensions to other configurations are discussed.

Abstract

dentifying accurate and yet interpretable low-order models from data has gained a renewed interest over the past decade. In the present work, we illustrate how the combined use of dimensionality reduction and sparse system identification techniques allows us to obtain an accurate model of the chaotic thermal convection in a two-dimensional annular thermosyphon. Taking as guidelines the derivation of the Lorenz system, the chaotic thermal convection dynamics simulated using a high-fidelity computational fluid dynamics solver are first embedded into a low-dimensional space using dynamic mode decomposition. After having reviewed the physical properties the reduced-order model should exhibit, the latter is identified using SINDy, an increasingly popular and flexible framework for the identification of nonlinear continuous-time dynamical systems from data. The identified model closely resembles the canonical Lorenz system, having a similar structure and exhibiting the same physical properties. Finally, extensions to other flow configurations with or without control are discussed.