Machine Learning for Fluid Mechanics

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202

Φ\Phi-DVAE: Learning Physically Interpretable Representations with Nonlinear Filtering

Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be known. This prevents these methods from achieving a consistent model-data synthesis in configurations where the mapping from data-space to model-space is unknown. To address these shortcomings, in this paper we develop a physics-informed dynamical variational autoencoder ($\Phi$-DVAE) for embedding diverse data streams into time-evolving physical systems described by differential equations. Our approach combines a standard (possibly nonlinear) filter for the latent state-space model and a VAE, to embed the unstructured data stream into the latent dynamical system. A variational Bayesian framework is used for the joint estimation of the embedding, latent states, and unknown system parameters. To demonstrate the method, we look at three examples: video datasets generated by the advection and Korteweg-de Vries partial differential equations, and a velocity field generated by the Lorenz-63 system. Comparisons with relevant baselines show that the $\Phi$-DVAE provides a data efficient dynamics encoding methodology that is competitive with standard approaches, with the added benefit of incorporating a physically interpretable latent space.Comment: 10 pages, 6 figure

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award Number DE-SC0019290. O.S. gratefully acknowledges the Early Career Research Program (ECRP) support of the U.S. Department of Energy. O.S. also gratefully acknowledges the financial support of the National Science Foundation under Award No. DMS-2012255. T.I. acknowledges support through National Science Foundation Grant No. DMS-2012253.acceptedVersio