Deep Dynamical Modeling and Control of Unsteady Fluid Flows

By Jeremy Morton, Freddie D. Witherden, Antony Jameson, Mykel J. Kochenderfer. 2018

189 citations recorded by the source corpus.

The design of flow control systems remains a challenge due to the nonlinear nature of the equations that govern fluid flow. However, recent advances in computational fluid dynamics (CFD) have enabled the simulation of complex fluid flows with high accuracy, opening the possibility of using learning-based approaches to facilitate controller design. We present a method for learning the forced and unforced dynamics of airflow over a cylinder directly from CFD data. The proposed approach, grounded in Koopman theory, is shown to produce stable dynamical models that can predict the time evolution of the cylinder system over extended time horizons. Finally, by performing model predictive control with the learned dynamical models, we are able to find a straightforward, interpretable control law for suppressing vortex shedding in the wake of the cylinder.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

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Citations in the corpus

Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow (2018, background): “In addition, learned Koopman operators [MWJK18] were proposed for representing temporal changes, whereas Lusch et al. are searching for representations of Koopman eigenfunctions to globally linearize dynamical systems using deep learning [LKB18].”
Learning to Control PDEs with Differentiable Physics (2020, methodology): “Temporal updates in reduced spaces were learned via the Koopman operator (Morton et al., 2018).”
Lagrangian Fluid Simulation with Continuous Convolutions (2020, background): “Neural networks have emerged as a particularly promising approach to capture the complexity of natural phenomena from data (Ling et al., 2016; Tompson et al., 2017; Morton et al., 2018).”
Transformer for Partial Differential Equations' Operator Learning (2022, methodology): “…done, the system can evolve in time using Recurrent Neural Networks (RNNs) such as LSTM (Wiewel et al., 2019) or even linear propagators based on the assumptions of learning Koopman operator (Morton et al., 2018; Li et al., 2020a; Lusch et al., 2018; Takeishi et al., 2017; Pan & Duraisamy, 2020).”
Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “For example, both steady [19] and unsteady [40], as well as multi-phase flows [16] have been investigated with deep learning based approaches.”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, unknown): “[69, 56, 47, 53], which apply autoencoders to learn approximate invariant subspaces of the Koopman operator; and Ref.”
Data-driven prediction of unsteady flow over a circular cylinder using deep learning (2018, methodology): “…been widely investigated by reduced-order models (ROMs) using mathematical decomposition techniques such as the proper orthogonal decomposition (POD) method (Sirovich 1987), the dynamic mode decomposition (DMD) method (Schmid 2010) and the Koopman operator method (Mezić 2013; Morton et al. 2018).”