Control-oriented cluster-based reduced-order modelling

TL;DR

This paper introduces CNMc, a novel control-oriented reduced-order modeling framework that generalizes to unseen conditions by learning from cluster-based models and applying a Procrustes transformation.

Contribution

The work presents CNMc, enabling parameter-aware ROMs that generalize across unobserved regimes without requiring simulation data at those conditions.

Findings

CNMc accurately predicts statistics at unseen conditions.

CNMc outperforms existing interpolation-based methods.

The approach is validated on fluid dynamics benchmarks.

Abstract

This work addresses the challenge of learning reduced-order models (ROMs) capable of generalizing to unobserved dynamical regimes across unseen control parameters. We introduce the Control-oriented Cluster-based Network Model (CNMc), a framework for synthesizing reduced-order dynamics at held-out operating conditions without requiring simulation data at those conditions. While the traditional Cluster Network Model (CNM) is limited to observed regimes, CNMc enables generalization by fitting supervised regression models to the transition probabilities and transition times of the CNM as functions of the control parameter. A key enabler is a Procrustes transformation that maps each operating condition's state space to a common coordinate system in which trajectories across all conditions are standardised and shape-aligned, permitting a shared cluster partition to be learned. We evaluate CNMc on two fluid dynamics benchmarks, the Lorenz-63 system and a controlled turbulent boundary layer, demonstrating that the predicted statistics at the withheld condition closely match those of a CNM trained directly on test data. CNMc also outperforms the competing interpolation-based CNM approaches under identical conditions. These results represent a step toward parameter-aware ROMs suitable for real-time flow control and the acceleration of parametric design studies.