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Existing recurrent optical flow estimation networks are computationally expensive since they use a fixed large number of iterations to update the flow field for each sample. An efficient network should skip iterations when the flow improvement is limited. In this paper, we develop a Context-Aware Iteration Policy Network for efficient optical flow estimation, which determines the optimal number of iterations per sample. The policy network achieves this by learning contextual information to realize whether flow improvement is bottlenecked or minimal. On the one hand, we use iteration embedding and historical hidden cell, which include previous iterations information, to convey how flow has changed from previous iterations. On the other hand, we use the incremental loss to make the policy network implicitly perceive the magnitude of optical flow improvement in the subsequent iteration. Furthermore, the computational complexity in our dynamic network is controllable, allowing us to satisfy various resource preferences with a single trained model. Our policy network can be easily integrated into state-of-the-art optical flow networks. Extensive experiments show that our method maintains performance while reducing FLOPs by about 40%/20% for the Sintel/KITTI datasets.

In the present paper, we introduce a new method for the automated generation of residential distribution grid models based on novel building load estimation methods and a two-stage optimization for the generation of the 20 kV and 400 V grid topologies. Using the introduced load estimation methods, various open or proprietary data sources can be utilized to estimate the load of residential buildings. These data sources include available building footprints from OpenStreetMap, 3D building data from OSM Buildings, and the number of electricity meters per address provided by the respective distribution system operator (DSO). For the evaluation of the introduced methods, we compare the resulting grid models by utilizing different available data sources for a specific suburban residential area and the real grid topology provided by the DSO. This evaluation yields two key findings: First, the automated 20 kV network generation methodology works well when compared to the real network. Second, the utilization of public 3D building data for load estimation significantly increases the resulting model accuracy compared to 2D data and enables results similar to models based on DSO-supplied meter data. This substantially reduces the dependence on such normally proprietary data.

Visualization of extremely large datasets in static or dynamic form is a huge challenge because most traditional methods cannot deal with big data problems. A new visualization method for big data is proposed based on Projection Pursuit, Guided Tour and Data Nuggets methods, that will help display interesting hidden structures such as clusters, outliers, and other nonlinear structures in big data. The Guided Tour is a dynamic graphical tool for high-dimensional data combining Projection Pursuit and Grand Tour methods. It displays a dynamic sequence of low-dimensional projections obtained by using Projection Pursuit (PP) index functions to navigate the data space. Different PP indices have been developed to detect interesting structures of multivariate data but there are computational problems for big data using the original guided tour with these indices. A new PP index is developed to be computable for big data, with the help of a data compression method called Data Nuggets that reduces large datasets while maintaining the original data structure. Simulation studies are conducted and a real large dataset is used to illustrate the proposed methodology. Static and dynamic graphical tools for big data can be developed based on the proposed PP index to detect nonlinear structures.

This paper introduces a new numerical approach that integrates local randomized neural networks (LRNNs) and the hybridized discontinuous Petrov-Galerkin (HDPG) method for solving coupled fluid flow problems. The proposed method partitions the domain of interest into several subdomains and constructs an LRNN on each subdomain. Then, the HDPG scheme is used to couple the LRNNs to approximate the unknown functions. We develop LRNN-HDPG methods based on velocity-stress formulation to solve two types of problems: Stokes-Darcy problems and Brinkman equations, which model the flow in porous media and free flow. We devise a simple and effective way to deal with the interface conditions in the Stokes-Darcy problems without adding extra terms to the numerical scheme. We conduct extensive numerical experiments to demonstrate the stability, efficiency, and robustness of the proposed method. The numerical results show that the LRNN-HDPG method can achieve high accuracy with a small number of degrees of freedom.

With the strong robusticity on illumination variations, near-infrared (NIR) can be an effective and essential complement to visible (VIS) facial expression recognition in low lighting or complete darkness conditions. However, facial expression recognition (FER) from NIR images presents more challenging problem than traditional FER due to the limitations imposed by the data scale and the difficulty of extracting discriminative features from incomplete visible lighting contents. In this paper, we give the first attempt to deep NIR facial expression recognition and proposed a novel method called near-infrared facial expression transformer (NFER-Former). Specifically, to make full use of the abundant label information in the field of VIS, we introduce a Self-Attention Orthogonal Decomposition mechanism that disentangles the expression information and spectrum information from the input image, so that the expression features can be extracted without the interference of spectrum variation. We also propose a Hypergraph-Guided Feature Embedding method that models some key facial behaviors and learns the structure of the complex correlations between them, thereby alleviating the interference of inter-class similarity. Additionally, we have constructed a large NIR-VIS Facial Expression dataset that includes 360 subjects to better validate the efficiency of NFER-Former. Extensive experiments and ablation studies show that NFER-Former significantly improves the performance of NIR FER and achieves state-of-the-art results on the only two available NIR FER datasets, Oulu-CASIA and Large-HFE.

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Ampere equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems.

In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with (normalized) gradients, focusing on their role in margin maximization. Inspired by this analysis, we propose a novel algorithm called Progressive Rescaling Gradient Descent (PRGD) and show that PRGD can maximize the margin at an {\em exponential rate}. This stands in stark contrast to all existing algorithms, which maximize the margin at a slow {\em polynomial rate}. Specifically, we identify mild conditions on data distribution under which existing algorithms such as gradient descent (GD) and normalized gradient descent (NGD) {\em provably fail} in maximizing the margin efficiently. To validate our theoretical findings, we present both synthetic and real-world experiments. Notably, PRGD also shows promise in enhancing the generalization performance when applied to linearly non-separable datasets and deep neural networks.

In this paper, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like. Our constitutive model is based on a Generalized Maxwell model, which incorporates viscosity, elasticity and plasticity in one non-linear framework by a unified way. On the one hand, taking advantage of the viscous term, we construct a series of strain-rate dependent models for classical non-Newtonian behaviors such as shear-thickening, shear-thinning, Bingham plastic, etc. On the other hand, benefiting from the elasto-plastic model, we empower our framework with the ability to simulate solid-like non-Newtonian behaviors, i.e., visco-elasticity/plasticity. In addition, we enrich our method with a heat diffusion model to make our method flexible in simulating phase change. Through sufficient experiments, we demonstrate a wide range of non-Newtonian behaviors ranging from viscous fluid to deformable objects. We believe this non-Newtonian model will enhance the realism of physically-based animation, which has great potential for computer graphics.

Approaches based on deep neural networks have achieved striking performance when testing data and training data share similar distribution, but can significantly fail otherwise. Therefore, eliminating the impact of distribution shifts between training and testing data is crucial for building performance-promising deep models. Conventional methods assume either the known heterogeneity of training data (e.g. domain labels) or the approximately equal capacities of different domains. In this paper, we consider a more challenging case where neither of the above assumptions holds. We propose to address this problem by removing the dependencies between features via learning weights for training samples, which helps deep models get rid of spurious correlations and, in turn, concentrate more on the true connection between discriminative features and labels. Extensive experiments clearly demonstrate the effectiveness of our method on multiple distribution generalization benchmarks compared with state-of-the-art counterparts. Through extensive experiments on distribution generalization benchmarks including PACS, VLCS, MNIST-M, and NICO, we show the effectiveness of our method compared with state-of-the-art counterparts.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.