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

Deep Markov Random Field for Image Modeling

Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic factors to capture local patterns. In this paper, we move beyond such limitations, and propose a novel MRF model that uses fully-connected neurons to express the complex interactions among pixels. Through theoretical analysis, we reveal an inherent connection between this model and recurrent neural networks, and thereon derive an approximated feed-forward network that couples multiple RNNs along opposite directions. This formulation combines the expressive power of deep neural networks and the cyclic dependency structure of MRF in a unified model, bringing the modeling capability to a new level. The feed-forward approximation also allows it to be efficiently learned from data. Experimental results on a variety of low-level vision tasks show notable improvement over state-of-the-arts.Comment: Accepted at ECCV 201

Spatio-Temporal Facial Expression Recognition Using Convolutional Neural Networks and Conditional Random Fields

Automated Facial Expression Recognition (FER) has been a challenging task for decades. Many of the existing works use hand-crafted features such as LBP, HOG, LPQ, and Histogram of Optical Flow (HOF) combined with classifiers such as Support Vector Machines for expression recognition. These methods often require rigorous hyperparameter tuning to achieve good results. Recently Deep Neural Networks (DNN) have shown to outperform traditional methods in visual object recognition. In this paper, we propose a two-part network consisting of a DNN-based architecture followed by a Conditional Random Field (CRF) module for facial expression recognition in videos. The first part captures the spatial relation within facial images using convolutional layers followed by three Inception-ResNet modules and two fully-connected layers. To capture the temporal relation between the image frames, we use linear chain CRF in the second part of our network. We evaluate our proposed network on three publicly available databases, viz. CK+, MMI, and FERA. Experiments are performed in subject-independent and cross-database manners. Our experimental results show that cascading the deep network architecture with the CRF module considerably increases the recognition of facial expressions in videos and in particular it outperforms the state-of-the-art methods in the cross-database experiments and yields comparable results in the subject-independent experiments.Comment: To appear in 12th IEEE Conference on Automatic Face and Gesture Recognition Worksho

Using deterministic tourist walk as a small-world metric on Watts-Strogatz networks

The Watts-Strogatz model (WS) has been demonstrated to effectively describe real-world networks due to its ability to reproduce the small-world properties commonly observed in a variety of systems, including social networks, computer networks, biochemical reactions, and neural networks. As the presence of small-world properties is a prevalent characteristic in many real-world networks, the measurement of "small-worldness" has become a crucial metric in the field of network science, leading to the development of various methods for its assessment over the past two decades. In contrast, the deterministic tourist walk (DTW) method has emerged as a prominent technique for texture analysis and network classification. In this paper, we propose the use of a modified version of the DTW method to classify networks into three categories: regular networks, random networks, and small-world networks. Additionally, we construct a small-world metric, denoted by the coefficient $\chi$, from the DTW method. Results indicate that the proposed method demonstrates excellent performance in the task of network classification, achieving over $90\%$ accuracy. Furthermore, the results obtained using the coefficient $\chi$ on real-world networks provide evidence that the proposed method effectively serves as a satisfactory small-world metric.Comment: 9 pages, 4 figure