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

Kernel-based Inference of Functions over Graphs

The study of networks has witnessed an explosive growth over the past decades with several ground-breaking methods introduced. A particularly interesting -- and prevalent in several fields of study -- problem is that of inferring a function defined over the nodes of a network. This work presents a versatile kernel-based framework for tackling this inference problem that naturally subsumes and generalizes the reconstruction approaches put forth recently by the signal processing on graphs community. Both the static and the dynamic settings are considered along with effective modeling approaches for addressing real-world problems. The herein analytical discussion is complemented by a set of numerical examples, which showcase the effectiveness of the presented techniques, as well as their merits related to state-of-the-art methods.Comment: To be published as a chapter in `Adaptive Learning Methods for Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C. Principe (2018). This chapter surveys recent work on kernel-based inference of functions over graphs including arXiv:1612.03615 and arXiv:1605.07174 and arXiv:1711.0930

Large-scale and Deep Spatiotemporal Point-Process Models

Many accurate spatiotemporal data sets have recently become available for research. Real-world applications create strong demands for a better multivariate point-process modeling. In this thesis, we develop new multivariate models with generalization ability and scalability. The first two chapters provide a research background, real-world problems and a mathematical introduction to point-process models. In chapter 3, we develop a nonparametric method for multivariate spatiotemporal Hawkes processes with applications on network reconstruction. In contrast to prior work, which has often focused on exclusively temporal information, our approach uses spatiotemporal information and does not assume a specific parametric form. Our results demonstrate that, in comparison to using only temporal data, our approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis---such as examinations of community structure and motifs---of the reconstructed networks. In chapter 4, we present a fast and accurate estimation method for multivariate Hawkes processes. Our method, with guaranteed consistency, combines two estimation approaches. Extensive numerical experiments, with synthetic data and real-world social network data, show that our method improves the accuracy, scalability and computational efficiency of prevailing estimation approaches. Moreover, it greatly boosts the performance of Hawkes process-based models on social network reconstruction and helps to understand the spatiotemporal triggering dynamics over social media.In chapter 5, we focus on multivariate spatial point processes, which can describe heterotopic data over space. However, highly multivariate intensities are computationally challenging due to the curse of dimensionality. To bridge this gap, we introduce a declustering-based hidden-variable model that leads to an efficient inference via a variational autoencoder (VAE). We also prove that this model is a generalization of the VAE-based model for collaborative filtering. This leads to an interesting application of spatial point-process models to recommender systems. Experimental results show the method's utility on both synthetic data and real-world data. Finally, in chapter 6, we show how multivariate point processes can be applied to opioid overdose events and real-time prediction of the hourly crime rate. In chapter 7, we discuss future directions and conclude the thesis

Graph Neural Network for spatiotemporal data: methods and applications

In the era of big data, there has been a surge in the availability of data containing rich spatial and temporal information, offering valuable insights into dynamic systems and processes for applications such as weather forecasting, natural disaster management, intelligent transport systems, and precision agriculture. Graph neural networks (GNNs) have emerged as a powerful tool for modeling and understanding data with dependencies to each other such as spatial and temporal dependencies. There is a large amount of existing work that focuses on addressing the complex spatial and temporal dependencies in spatiotemporal data using GNNs. However, the strong interdisciplinary nature of spatiotemporal data has created numerous GNNs variants specifically designed for distinct application domains. Although the techniques are generally applicable across various domains, cross-referencing these methods remains essential yet challenging due to the absence of a comprehensive literature review on GNNs for spatiotemporal data. This article aims to provide a systematic and comprehensive overview of the technologies and applications of GNNs in the spatiotemporal domain. First, the ways of constructing graphs from spatiotemporal data are summarized to help domain experts understand how to generate graphs from various types of spatiotemporal data. Then, a systematic categorization and summary of existing spatiotemporal GNNs are presented to enable domain experts to identify suitable techniques and to support model developers in advancing their research. Moreover, a comprehensive overview of significant applications in the spatiotemporal domain is offered to introduce a broader range of applications to model developers and domain experts, assisting them in exploring potential research topics and enhancing the impact of their work. Finally, open challenges and future directions are discussed

Learning to represent surroundings, anticipate motion and take informed actions in unstructured environments

Contemporary robots have become exceptionally skilled at achieving specific tasks in structured environments. However, they often fail when faced with the limitless permutations of real-world unstructured environments. This motivates robotics methods which learn from experience, rather than follow a pre-defined set of rules. In this thesis, we present a range of learning-based methods aimed at enabling robots, operating in dynamic and unstructured environments, to better understand their surroundings, anticipate the actions of others, and take informed actions accordingly

MULTIVARIATE MODELING OF COGNITIVE PERFORMANCE AND CATEGORICAL PERCEPTION FROM NEUROIMAGING DATA

State-of-the-art cognitive-neuroscience mainly uses hypothesis-driven statistical testing to characterize and model neural disorders and diseases. While such techniques have proven to be powerful in understanding diseases and disorders, they are inadequate in explaining causal relationships as well as individuality and variations. In this study, we proposed multivariate data-driven approaches for predictive modeling of cognitive events and disorders. We developed network descriptions of both structural and functional connectivities that are critical in multivariate modeling of cognitive performance (i.e., fluency, attention, and working memory) and categorical perceptions (i.e., emotion, speech perception). We also performed dynamic network analysis on brain connectivity measures to determine the role of different functional areas in relation to categorical perceptions and cognitive events. Our empirical studies of structural connectivity were performed using Diffusion Tensor Imaging (DTI). The main objective was to discover the role of structural connectivity in selecting clinically interpretable features that are consistent over a large range of model parameters in classifying cognitive performances in relation to Acute Lymphoblastic Leukemia (ALL). The proposed approach substantially improved accuracy (13% - 26%) over existing models and also selected a relevant, small subset of features that were verified by domain experts. In summary, the proposed approach produced interpretable models with better generalization.Functional connectivity is related to similar patterns of activation in different brain regions regardless of the apparent physical connectedness of the regions. The proposed data-driven approach to the source localized electroencephalogram (EEG) data includes an array of tools such as graph mining, feature selection, and multivariate analysis to determine the functional connectivity in categorical perceptions. We used the network description to correctly classify listeners behavioral responses with an accuracy over 92% on 35 participants. State-of-the-art network description of human brain assumes static connectivities. However, brain networks in relation to perception and cognition are complex and dynamic. Analysis of transient functional networks with spatiotemporal variations to understand cognitive functions remains challenging. One of the critical missing links is the lack of sophisticated methodologies in understanding dynamics neural activity patterns. We proposed a clustering-based complex dynamic network analysis on source localized EEG data to understand the commonality and differences in gender-specific emotion processing. Besides, we also adopted Bayesian nonparametric framework for segmentation neural activity with a finite number of microstates. This approach enabled us to find the default network and transient pattern of the underlying neural mechanism in relation to categorical perception. In summary, multivariate and dynamic network analysis methods developed in this dissertation to analyze structural and functional connectivities will have a far-reaching impact on computational neuroscience to identify meaningful changes in spatiotemporal brain activities