Overview

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.

Video (Click to YouTube)

Paper

Check out our paper linked here.

Codebase

Check out our codebase at https://github.com/generalroboticslab/AutomatedGlobalAnalysis

Citation

@misc{moore2024automatedglobalanalysisexperimental,
      title={Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings}, 
      author={Samuel A. Moore and Brian P. Mann and Boyuan Chen},
      year={2024},
      eprint={2411.00989},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2411.00989}, 
}    

Acknowledgment

This work was supported by the National Science Foundation Graduate Research Fellowship, the ARL STRONG program under awards W911NF2320182 and W911NF2220113, by ARO W911NF2410405, by DARPA FoundSci program under award HR00112490372, and DARPA TIAMAT program under award HR00112490419.

Contact

If you have any questions, please feel free to contact Sam Moore.