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 unsupervised 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.

本研究提出一种基于深度学习的非线性模型降维策略，通过深度卷积自编码器和LSTM网络构建模块化模型，实现繁重计算任务中的模型降维，同时保持计算效率和系统稳定性。

用深度卷积循环自编码器学习流体系统低维特征动态