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

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Real-time people tracking in a camera network

Visual tracking is a fundamental key to the recognition and analysis of human behaviour. In this thesis we present an approach to track several subjects using multiple cameras in real time. The tracking framework employs a numerical Bayesian estimator, also known as a particle lter, which has been developed for parallel implementation on a Graphics Processing Unit (GPU). In order to integrate multiple cameras into a single tracking unit we represent the human body by a parametric ellipsoid in a 3D world. The elliptical boundary can be projected rapidly, several hundred times per subject per frame, onto any image for comparison with the image data within a likelihood model. Adding variables to encode visibility and persistence into the state vector, we tackle the problems of distraction and short-period occlusion. However, subjects may also disappear for longer periods due to blind spots between cameras elds of view. To recognise a desired subject after such a long-period, we add coloured texture to the ellipsoid surface, which is learnt and retained during the tracking process. This texture signature improves the recall rate from 60% to 70-80% when compared to state only data association. Compared to a standard Central Processing Unit (CPU) implementation, there is a signi cant speed-up ratio

An efficient polynomial chaos-based proxy model for history matching and uncertainty quantification of complex geological structures

A novel polynomial chaos proxy-based history matching and uncertainty quantification method is presented that can be employed for complex geological structures in inverse problems. For complex geological structures, when there are many unknown geological parameters with highly nonlinear correlations, typically more than 106 full reservoir simulation runs might be required to accurately probe the posterior probability space given the production history of reservoir. This is not practical for high-resolution geological models. One solution is to use a "proxy model" that replicates the simulation model for selected input parameters. The main advantage of the polynomial chaos proxy compared to other proxy models and response surfaces is that it is generally applicable and converges systematically as the order of the expansion increases. The Cameron and Martin theorem 2.24 states that the convergence rate of the standard polynomial chaos expansions is exponential for Gaussian random variables. To improve the convergence rate for non-Gaussian random variables, the generalized polynomial chaos is implemented that uses an Askey-scheme to choose the optimal basis for polynomial chaos expansions [199]. Additionally, for the non-Gaussian distributions that can be effectively approximated by a mixture of Gaussian distributions, we use the mixture-modeling based clustering approach where under each cluster the polynomial chaos proxy converges exponentially fast and the overall posterior distribution can be estimated more efficiently using different polynomial chaos proxies. The main disadvantage of the polynomial chaos proxy is that for high-dimensional problems, the number of the polynomial chaos terms increases drastically as the order of the polynomial chaos expansions increases. Although different non-intrusive methods have been developed in the literature to address this issue, still a large number of simulation runs is required to compute high-order terms of the polynomial chaos expansions. This work resolves this issue by proposing the reduced-terms polynomial chaos expansion which preserves only the relevant terms in the polynomial chaos representation. We demonstrated that the sparsity pattern in the polynomial chaos expansion, when used with the Karhunen-Loéve decomposition method or kernel PCA, can be systematically captured. A probabilistic framework based on the polynomial chaos proxy is also suggested in the context of the Bayesian model selection to study the plausibility of different geological interpretations of the sedimentary environments. The proposed surrogate-accelerated Bayesian inverse analysis can be coherently used in practical reservoir optimization workflows and uncertainty assessments