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

arXiv: https://arxiv.org/abs/2411.00989 · HTML: https://mlsanity.com/paper/2411.00989/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 74 references that are in the map.
- First posted on arXiv 1 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Deep Learning of Koopman Representation for Control](https://mlsanity.com/paper/2010.07546/) (2020)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [Deep Variational Koopman Models: Inferring Koopman Observations for Uncertainty-Aware Dynamics Modeling and Control](https://mlsanity.com/paper/1902.09742/) (2019)
- [Data-Driven Model Predictive Control using Interpolated Koopman Generators](https://mlsanity.com/paper/2003.07094/) (2020)
- [Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control](https://mlsanity.com/paper/1911.08751/) (2019)
- [Deep Identification of Nonlinear Systems in Koopman Form](https://mlsanity.com/paper/2110.02583/) (2021)
- [Koopman-Based Neural Lyapunov Functions for General Attractors](https://mlsanity.com/paper/2203.12303/) (2022)
- [A Model-Free Sampling Method for Estimating Basins of Attraction Using Hybrid Active Learning (HAL)](https://mlsanity.com/paper/2003.10976/) (2020)
- [Physics-Informed Koopman Network](https://mlsanity.com/paper/2211.09419/) (2022)

## Built on by (most cited first, 1 of 1)

- [Reproducible macroscopic dynamics in a closed-loop human-AI learning system](https://mlsanity.com/paper/2608.30946/) (2026)

## Abstract (arXiv)

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.