Deep neural networks for nonlinear model order reduction of unsteady flows

Abstract

Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena in both time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows into a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for ROM of the unsteady fluid flows is introduced. An autoencoder network is used for nonlinear dimension reduction and feature extraction as an alternative for singular value decomposition (SVD). Then, the extracted features are used as an input for a long short-term memory (LSTM) network to predict the velocity field at future time instances. The proposed autoencoder-LSTM method is compared with non-intrusive reduced order models based on dynamic mode decomposition (DMD) and proper orthogonal decomposition. Moreover, an autoencoder-DMD algorithm is introduced for ROM, which uses the autoencoder network for dimensionality reduction rather than SVD rank truncation. The results show that the autoencoder-LSTM method is considerably capable of predicting fluid flow evolution, where higher values for the coefficient of determination R2 are obtained using autoencoder-LSTM compared to other models.

Predicting Physics in Mesh-reduced Space with Temporal Attention

“…However, applying sequence models to predict high-dimensional systems remains a challenge due to their high memory overhead. Dimensionality reduction techniques, such as CNN autoencoders [33,32,26,22,29,16,11,27], POD [44,48,5,31,18,8,47,10], or Koopman operators [24,9,14] can be used to construct a lowdimensional latent space. The auto-regressive sequence model then operates on these linear (POD modes) or nonlinear (CNNs) latents.…”

Deep learning for surrogate modeling of two-dimensional mantle convection

“…Hence, we turn our attention to recurrent neural networks that have been shown to be successful for a variety of Natural Language Processing tasks. Recurrent architectures such as LSTM [60] provide a back-propagation mechanism acting through a sequence of inputs (such as time steps of a simulation), thereby allowing the network to learn temporal dynamics [34,61].…”

Data-Driven Reduced Order Modeling of Environmental Hydrodynamics Using Deep Autoencoders and Neural Odes

“…Alternatively, nonlinear dimension reduction techniques such as kernel POD [14] or deep learning-based approaches like autoencoders [15,16] have also been used for extracting a reduced basis. Combining autoencoder-generated bases with various specialized machine learning algorithms for time series modeling result in fully non-intrusive reduced order models [17,18,19]. Hybrid methods [20,21] can also be obtained by combining a nonlinear manifold learning technique like autoencoder for discovering the latent space with an intrusive method for the temporal dynamics.…”