Model Order Reduction from Data with Certification

TL;DR

This paper presents a data-driven method for creating reduced-order models of unknown dynamical systems using simulation functions, enabling effective control and property verification without requiring detailed system knowledge.

Contribution

It introduces a novel data-driven approach leveraging simulation functions to construct certified reduced-order models from minimal data, applicable to unknown systems.

Findings

Constructed ROMs from only two trajectories per system

Provided formal guarantees for model accuracy and control synthesis

Validated approach on various benchmark physical systems

Abstract

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for high-dimensional systems with complex behaviors can be challenging, rendering MOR a practical alternative to achieve results that closely resemble those of the original complex systems. To construct such effective reduced-order models (ROMs), existing literature generally necessitates precise knowledge of original systems, which is often unavailable in real-world scenarios. This paper introduces a data-driven scheme to construct ROMs of dynamical systems with unknown mathematical models. Our methodology leverages data and establishes similarity relations between output trajectories of unknown systems and their data-driven ROMs via the notion of simulation functions (SFs), capable of formally quantifying their closeness. To achieve this, under a rank condition readily fulfillable using data, we collect only two input-state trajectories from unknown systems to construct both ROMs and SFs, while offering correctness guarantees. We demonstrate that the proposed ROMs derived from data can be leveraged for controller synthesis endeavors while effectively ensuring high-level logic properties over unknown dynamical models. We showcase our data-driven findings across a range of benchmark scenarios involving various unknown physical systems, demonstrating the enforcement of diverse complex properties.