# Data-driven identification of nonlinear dynamical systems with LSTM autoencoders and Normalizing Flows

arXiv: https://arxiv.org/abs/2503.03977 · HTML: https://mlsanity.com/paper/2503.03977/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 36 references that are in the map.
- First posted on arXiv 5 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows](https://mlsanity.com/paper/2010.13129/) (2020)
- [Deep State Space Models for Nonlinear System Identification](https://mlsanity.com/paper/2003.14162/) (2020)
- [Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks](https://mlsanity.com/paper/2109.11213/) (2021)
- [Nonlinear Systems Identification Using Deep Dynamic Neural Networks](https://mlsanity.com/paper/1610.01439/) (2016)
- [Dendrite Net: A White-Box Module for Classification, Regression, and System Identification](https://mlsanity.com/paper/2004.03955/) (2020)
- [Learning Stable Normalizing-Flow Control for Robotic Manipulation](https://mlsanity.com/paper/2011.00072/) (2020)

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

- [Comparison of neural network training strategies for the simulation of dynamical systems](https://mlsanity.com/paper/2512.03851/) (2025)

## Abstract (arXiv)

While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the design and control of these systems. However, identifying a nonlinear system is more complicated than identifying a linear one. Therefore, modeling and identifying nonlinear systems are crucial for the design, manufacturing, and testing of complex systems. This study presents using advanced nonlinear methods based on deep learning for system identification. Two deep neural network models, LSTM autoencoder and Normalizing Flows, are explored for their potential to extract temporal features from time series data and relate them to system parameters, respectively. The presented framework offers a nonlinear approach to system identification, enabling it to handle complex systems. As case studies, we consider Duffing and Lorenz systems, as well as fluid flows such as flows over a cylinder and the 2-D lid-driven cavity problem. The results indicate that the presented framework is capable of capturing features and effectively relating them to system parameters, satisfying the identification requirements of nonlinear systems.