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

Neural-inspired sensors enable sparse, efficient classification of spatiotemporal data

Sparse sensor placement is a central challenge in the efficient characterization of complex systems when the cost of acquiring and processing data is high. Leading sparse sensing methods typically exploit either spatial or temporal correlations, but rarely both. This work introduces a new sparse sensor optimization that is designed to leverage the rich spatiotemporal coherence exhibited by many systems. Our approach is inspired by the remarkable performance of flying insects, which use a few embedded strain-sensitive neurons to achieve rapid and robust flight control despite large gust disturbances. Specifically, we draw on nature to identify targeted neural-inspired sensors on a flapping wing to detect body rotation. This task is particularly challenging as the rotational twisting mode is three orders-of-magnitude smaller than the flapping modes. We show that nonlinear filtering in time, built to mimic strain-sensitive neurons, is essential to detect rotation, whereas instantaneous measurements fail. Optimized sparse sensor placement results in efficient classification with approximately ten sensors, achieving the same accuracy and noise robustness as full measurements consisting of hundreds of sensors. Sparse sensing with neural inspired encoding establishes a new paradigm in hyper-efficient, embodied sensing of spatiotemporal data and sheds light on principles of biological sensing for agile flight control.Comment: 21 pages, 19 figure

Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves observable functions of the state-space of a dynamical system [Koopman 1931, PNAS]. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems [Williams et al. 2015, JNLS]. Choosing nonlinear observable functions to form an invariant subspace where it is possible to obtain linear models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis using a new algorithm to determine terms in a dynamical system by sparse regression of the data in a nonlinear function space [Brunton et al. 2015, arxiv]; we show how this algorithm is related to DMD. Finally, we demonstrate how to design optimal control laws for nonlinear systems using techniques from linear optimal control on Koopman invariant subspaces.Comment: 20 pages, 5 figures, 2 code