Sparsity enabled cluster reduced-order models for control

TL;DR

This paper introduces a sparsity-enabled cluster-based reduced-order modeling approach that uses optimized measurements to efficiently control complex high-dimensional nonlinear systems in real-time.

Contribution

It develops a method to identify critical measurements and sensor locations for efficient CROM, enabling real-time control of high-dimensional systems with limited data.

Findings

Sparsity-enabled CROM accurately captures system dynamics with fewer measurements.

Optimized sensor placement outperforms random measurements in preserving dynamics.

Method demonstrated on three high-dimensional nonlinear systems, including flow control.

Abstract

Characterizing and controlling nonlinear, multi-scale phenomena play important roles in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, and uncertainty can be managed with data assimilation. CROM is typically computed on high-dimensional data, however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.