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 system identification for large populations separating "what" and "where"

Neuroscientists classify neurons into different types that perform similar computations at different locations in the visual field. Traditional methods for neural system identification do not capitalize on this separation of 'what' and 'where'. Learning deep convolutional feature spaces that are shared among many neurons provides an exciting path forward, but the architectural design needs to account for data limitations: While new experimental techniques enable recordings from thousands of neurons, experimental time is limited so that one can sample only a small fraction of each neuron's response space. Here, we show that a major bottleneck for fitting convolutional neural networks (CNNs) to neural data is the estimation of the individual receptive field locations, a problem that has been scratched only at the surface thus far. We propose a CNN architecture with a sparse readout layer factorizing the spatial (where) and feature (what) dimensions. Our network scales well to thousands of neurons and short recordings and can be trained end-to-end. We evaluate this architecture on ground-truth data to explore the challenges and limitations of CNN-based system identification. Moreover, we show that our network model outperforms current state-of-the art system identification models of mouse primary visual cortex.Comment: NIPS 201

A new class of multiscale lattice cell (MLC) models for spatio-temporal evolutionary image representation

Spatio-temporal evolutionary (STE) images are a class of complex dynamical systems that evolve over both space and time. With increased interest in the investigation of nonlinear complex phenomena, especially spatio-temporal behaviour governed by evolutionary laws that are dependent on both spatial and temporal dimensions, there has been an increased need to investigate model identification methods for this class of complex systems. Compared with pure temporal processes, the identification of spatio-temporal models from observed images is much more difficult and quite challenging. Starting with an assumption that there is no apriori information about the true model but only observed data are available, this study introduces a new class of multiscale lattice cell (MLC) models to represent the rules of the associated spatio-temporal evolutionary system. An application to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, is investigated to demonstrate the new modelling framework

Estimation of the mixing kernel and the disturbance covariance in IDE-based spatiotemporal systems

The integro-difference equation (IDE) is an increasingly popular mathematical model of spatiotemporal processes, such as brain dynamics, weather systems, and disease spread. We present an efficient approach for system identification based on correlation techniques for linear temporal systems that extended to spatiotemporal IDE-based models. The method is derived from the average (over time) spatial correlations of observations to calculate closed-form estimates of the spatial mixing kernel and the disturbance covariance function. Synthetic data are used to demonstrate the performance of the estimation algorithm

Lattice dynamical wavelet neural networks implemented using particle swarm optimisation for spatio-temporal system identification

Starting from the basic concept of coupled map lattices, a new family of adaptive wavelet neural networks, called lattice dynamical wavelet neural networks (LDWNN), is introduced for spatiotemporal system identification, by combining an efficient wavelet representation with a coupled map lattice model. A new orthogonal projection pursuit (OPP) method, coupled with a particle swarm optimisation (PSO) algorithm, is proposed for augmenting the proposed network. A novel two-stage hybrid training scheme is developed for constructing a parsimonious network model. In the first stage, by applying the orthogonal projection pursuit algorithm, significant wavelet-neurons are adaptively and successively recruited into the network, where adjustable parameters of the associated waveletneurons are optimised using a particle swarm optimiser. The resultant network model, obtained in the first stage, may however be redundant. In the second stage, an orthogonal least squares (OLS) algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet-neurons from the network. The proposed two-stage hybrid training procedure can generally produce a parsimonious network model, where a ranked list of wavelet-neurons, according to the capability of each neuron to represent the total variance in the system output signal is produced. Two spatio-temporal system identification examples are presented to demonstrate the performance of the proposed new modelling framework