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

2025-03-05

AI Summary

Nonlinear dynamical system identification suffers from strong reliance on prior structural assumptions and challenges in modeling parameter uncertainty. Method: This paper proposes an end-to-end deep learning framework integrating an LSTM autoencoder with normalizing flows. It jointly learns time-series features and the probabilistic distribution of system parameters: the LSTM autoencoder extracts low-dimensional dynamic representations, while normalizing flows map latent variables to the parameter space, enabling differentiable, invertible inference from observations to the posterior parameter distribution. Contribution/Results: Evaluated on benchmark chaotic systems (Duffing, Lorenz) and CFD datasets (cylinder wake, 2D lid-driven cavity flow), the framework significantly improves parameter inversion accuracy and dynamical behavior reconstruction quality for strongly nonlinear, multiscale systems. It demonstrates robust generalization and enhanced physical interpretability without requiring explicit structural priors.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

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.

Problem

• Identify nonlinear dynamical systems using deep learning.
• Extract temporal features from time series data.
• Relate extracted features to system parameters effectively.

Innovation

• Uses LSTM autoencoders for temporal feature extraction
• Applies Normalizing Flows to relate features to parameters
• Develops a deep learning-based nonlinear system identification framework