Traffic state estimation (TSE) bifurcates into two main categories, model-driven and data-driven (e.g., machine learning, ML) approaches, while each suffers from either deficient physics or small data. To mitigate these limitations, recent studies introduced hybrid methods, such as physics-informed deep learning (PIDL), which contains both model-driven and data-driven components. This paper contributes an improved paradigm, called physics-informed deep learning with a fundamental diagram learner (PIDL + FDL), which integrates ML terms into the model-driven component to learn a functional form of a fundamental diagram (FD), i.e., a mapping from traffic density to flow or velocity. The proposed PIDL + FDL has the advantages of performing the TSE learning, model parameter identification, and FD estimation simultaneously. This paper focuses on highway TSE with observed data from loop detectors, using traffic density or velocity as traffic variables. We demonstrate the use of PIDL + FDL to solve popular first-order and second-order traffic flow models and reconstruct the FD relation as well as model parameters that are outside the FD term. We then evaluate the PIDL + FDL-based TSE using the Next Generation SIMulation (NGSIM) dataset. The experimental results show the superiority of the PIDL + FDL in terms of improved estimation accuracy and data efficiency over advanced baseline TSE methods, and additionally, the capacity to properly learn the unknown underlying FD relation.

In this paper, we propose a deep learning approach to tackle the automatic summarization tasks by incorporating topic information into the convolutional sequence-to-sequence (ConvS2S) model and using self-critical sequence training (SCST) for optimization. Through jointly attending to topics and word-level alignment, our approach can improve coherence, diversity, and informativeness of generated summaries via a biased probability generation mechanism. On the other hand, reinforcement training, like SCST, directly optimizes the proposed model with respect to the non-differentiable metric ROUGE, which also avoids the exposure bias during inference. We carry out the experimental evaluation with state-of-the-art methods over the Gigaword, DUC-2004, and LCSTS datasets. The empirical results demonstrate the superiority of our proposed method in the abstractive summarization.

Nonlocal neural networks have been proposed and shown to be effective in several computer vision tasks, where the nonlocal operations can directly capture long-range dependencies in the feature space. In this paper, we study the nature of diffusion and damping effect of nonlocal networks by doing spectrum analysis on the weight matrices of the well-trained networks, and then propose a new formulation of the nonlocal block. The new block not only learns the nonlocal interactions but also has stable dynamics, thus allowing deeper nonlocal structures. Moreover, we interpret our formulation from the general nonlocal modeling perspective, where we make connections between the proposed nonlocal network and other nonlocal models, such as nonlocal diffusion process and Markov jump process.

Many important properties of materials such as strength, ductility, hardness and conductivity are determined by the microstructures of the material. During the formation of these microstructures, grain coarsening plays an important role. The Cahn-Hilliard equation has been applied extensively to simulate the coarsening kinetics of a two-phase microstructure. It is well accepted that the limited capabilities in conducting large scale, long time simulations constitute bottlenecks in predicting microstructure evolution based on the phase field approach. We present here a scalable time integration algorithm with large stepsizes and its efficient implementation on the Sunway TaihuLight supercomputer. The highly nonlinear and severely stiff Cahn-Hilliard equations with degenerate mobility for microstructure evolution are solved at extreme scale, demonstrating that the latest advent of high performance computing platform and the new advances in algorithm design are now offering us the possibility to simulate the coarsening dynamics accurately at unprecedented spatial and time scales.

We present a new method for modeling discrete constant mean curvature (CMC) surfaces, which arise frequently in nature and are highly demanded in architecture and other engineering applications. Our method is based on a novel use of the CVT ( centroidal Voronoi tessellation ) optimization framework. We devise a CVT-CMC energy function defined as a combination of an extended CVT energy and a volume functional. We show that minimizing the CVT-CMC energy is asymptotically equivalent to minimizing mesh surface area with a fixed volume, thus defining a discrete CMC surface. The CVT term in the energy function ensures high mesh quality throughout the evolution of a CMC surface in an interactive design process for form finding. Our method is capable of modeling CMC surfaces with fixed or free boundaries and is robust with respect to input mesh quality and topology changes. Experiments show that the new method generates discrete CMC surfaces of improved mesh quality over existing methods.

Clustering and tessellations are basic tools in data mining. The k-means and EM algorithms are two of the most important algorithms in the Mixture Model-based clustering and tessellations. In this paper, we introduce a new clustering strategy which shares common features with both the EM and k-means algorithms. Our methods also lead to more general tessellations of a spatial region with respect to a continuous and possibly anisotropic density distribution. Moreover, we propose some probabilistic methods for the construction of these clusterings and tessellations corresponding to a continuous density distribution. Some numerical examples are presented to demonstrate the effectiveness of our new approach. In addition, we also discuss the parallel implementation and performance of our algorithms on some distributed memory systems.

A new method for the simplification and the visualization of vector fields is presented based on the notion of centroidal Voronoi tessellations (CVT's). A CVT is a special Voronoi tessellation for which the generators of the Voronoi regions in the tessellation are also the centers of mass (or means) with respect to a prescribed density. A distance function in both the spatial and vector spaces is introduced to measure the similarity of the spatially distributed vector fields. Based on such a distance, vector fields are naturally clustered and their simplified representations are obtained. Our method combines simple geometric intuitions with the rigorously established optimality properties of the CVTs. It is simple to describe, easy to understand and implement. Numerical examples are also provided to illustrate the effectiveness and competitiveness of the CVT-based vector simplification and visualization methodology.