Learning low-dimensional feature dynamics using convolutional recurrent autoencoders

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing equations onto a subspace spanned by basis functions obtained from the compression of a dataset of solution snapshots. However, this method is intrusive since the projection requires access to the system operators. Further, some systems may require special treatment of nonlinearities to ensure computational efficiency or additional modeling to preserve stability. In this work we propose a deep learning-based strategy for nonlinear model reduction that is inspired by projection-based model reduction where the idea is to identify some optimal low-dimensional representation and evolve it in time. Our approach constructs a modular model consisting of a deep convolutional autoencoder and a modified LSTM network. The deep convolutional autoencoder returns a low-dimensional representation in terms of coordinates on some expressive nonlinear data-supporting manifold. The dynamics on this manifold are then modeled by the modified LSTM network in a computationally efficient manner. An offline training strategy that exploits the model modularity is also developed. We demonstrate our model on three illustrative examples each highlighting the model's performance in prediction tasks for systems with large parameter-variations and its stability in long-term prediction.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Gonzalez, Francisco Javier

Contributors dc:contributor

• Balajewicz, Maciej

• Nonlinear model reduction
• deep learning
• dynamical systems
• data-driven modeling
• convolutional neural networks
• recurrent neural networks

Statement dc:rights

• Copyright 2018 Francisco J. Gonzalez

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101628

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101628