Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings

TL;DR

This paper presents a data-driven framework that derives low-dimensional linear models from raw experimental data to analyze complex nonlinear dynamical systems, enabling stability analysis and long-term predictions.

Contribution

It introduces a novel combination of time-delay embedding, physics-informed autoencoders, and annealing regularization to identify interpretable low-dimensional representations of nonlinear systems.

Findings

Successfully applied to simulated and experimental systems

Achieves accurate long-horizon predictions

Provides empirical stability guarantees

Abstract

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical modeling, nonlinearity, and high dimensionality. In this work, we introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems directly from raw experimental data. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our approach employs time-delay embedding, physics-informed deep autoencoders, and annealing-based regularization to identify novel low-dimensional coordinate representations, unlocking insights across a variety of simulated and previously unstudied experimental dynamical systems. These new coordinate representations enable accurate long-horizon predictions and automatic identification of intricate invariant sets while providing empirical stability guarantees. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering, with broad implications for understanding nonlinear systems in the real world.