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

Sub-grid modelling for two-dimensional turbulence using neural networks

In this investigation, a data-driven turbulence closure framework is introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the sub-grid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a-priori and a-posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability density function based validation of sub-grid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for sub-grid quantity inference. In addition, it is also observed that some measure of a-posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data

Mapping Big Data into Knowledge Space with Cognitive Cyber-Infrastructure

Big data research has attracted great attention in science, technology, industry and society. It is developing with the evolving scientific paradigm, the fourth industrial revolution, and the transformational innovation of technologies. However, its nature and fundamental challenge have not been recognized, and its own methodology has not been formed. This paper explores and answers the following questions: What is big data? What are the basic methods for representing, managing and analyzing big data? What is the relationship between big data and knowledge? Can we find a mapping from big data into knowledge space? What kind of infrastructure is required to support not only big data management and analysis but also knowledge discovery, sharing and management? What is the relationship between big data and science paradigm? What is the nature and fundamental challenge of big data computing? A multi-dimensional perspective is presented toward a methodology of big data computing.Comment: 59 page

Communication Theoretic Data Analytics

Widespread use of the Internet and social networks invokes the generation of big data, which is proving to be useful in a number of applications. To deal with explosively growing amounts of data, data analytics has emerged as a critical technology related to computing, signal processing, and information networking. In this paper, a formalism is considered in which data is modeled as a generalized social network and communication theory and information theory are thereby extended to data analytics. First, the creation of an equalizer to optimize information transfer between two data variables is considered, and financial data is used to demonstrate the advantages. Then, an information coupling approach based on information geometry is applied for dimensionality reduction, with a pattern recognition example to illustrate the effectiveness. These initial trials suggest the potential of communication theoretic data analytics for a wide range of applications.Comment: Published in IEEE Journal on Selected Areas in Communications, Jan. 201