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A diffuse-interface lattice Boltzmann method for the dendritic growth with thermosolutal convection

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arXiv 2022年

作者： Zhan, Chengjie Chai, Zhenhua Shi, Baochang Jiang, Ping Geng, Shaoning Sun, Dongke School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and Engineering Huazhong University of Science and Technology Wuhan430074 China School of Mechanical Engineering Southeast University Nanjing211189 China

In this work, we proposed a diffuse interface model for the dendritic growth with thermosolutal convection. In this model, the sharp boundary between the fluid and solid dendrite is replaced by a thin but nonzero thickness diffuse interface, which is described by the order parameter governed by the phase-field equation for the dendritic growth. The governing equations for solute and heat transfer are modified such that the previous special treatments for source term can be avoided. To solve the model for the dendritic growth with thermosolutal convection, we also developed a diffuse-interface multi-relaxation-time lattice Boltzmann (LB) method. In this method, the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction, and the treatment on the complex fluid-solid interface can be avoided. In addition, four LB models are developed for the phase-field equation, concentration equation, temperature equation and the Navier-Stokes equations in a unified framework. Finally, to test the present diffuse-interface LB method, we performed some simulations of the dendritic growth, and found that the numerical results are in good agreements with some previous works. © 2022, CC BY-NC-ND.

关键词： Navier Stokes equations

Audio-Driven Talking Face Video Generation with Dynamic Convolution Kernels

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arXiv 2022年

作者： Ye, Zipeng Xia, Mengfei Yi, Ran Zhang, Juyong Lai, Yu-Kun Huang, Xuwei Zhang, Guoxin Liu, Yong-Jin MOE-Key Laboratory of Pervasive Computing The Department of Computer Science and Technology Tsinghua University Beijing China The Department of Computer Science and Engineering Shanghai Jiao Tong University China The School of Mathematical Sciences University of Science and Technology China School of Computer Science and Informatics Cardiff University United Kingdom Kwai Inc.

In this paper, we present a dynamic convolution kernel (DCK) strategy for convolutional neural networks. Using a fully convolutional network with the proposed DCKs, high-quality talking-face video can be generated from multi-modal sources (i.e., unmatched audio and video) in real time, and our trained model is robust to different identities, head postures, and input audios. Our proposed DCKs are specially designed for audio-driven talking face video generation, leading to a simple yet effective end-to-end system. We also provide a theoretical analysis to interpret why DCKs work. Experimental results show that our method can generate high-quality talking-face video with background at 60 fps. Comparison and evaluation between our method and the state-of-the-art methods demonstrate the superiority of our method. Copyright © 2022, The Authors. All rights reserved.

关键词： Convolutional neural networks

GAUSSIAN QUADRATURE RULES FOR COMPOSITE HIGHLY OSCILLATORY INTEGRALS

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arXiv 2021年

作者： Wu, Menghan Wang, Haiyong School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan430074 China Hubei Key Laboratory od Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China

Highly oscillatory integrals of composite type arise in electronic engineering and their calculations are a challenging problem. In this paper, we propose two Gaussian quadrature rules for computing such integrals. The first one is constructed based on the classical theory of orthogonal polynomials and its nodes and weights can be computed efficiently by using tools of numerical linear algebra. An interesting connection between the quadrature nodes and the Legendre points is proved and it is shown that the rate of convergence of this rule depends solely on the regularity of the non-oscillatory part of the integrand. The second one is constructed with respect to a sign-changing function and the classical theory of Gaussian quadrature can not be used anymore. We explore theoretical properties of this Gaussian quadrature, including the trajectories of the quadrature nodes and the convergence rate of these nodes to the endpoints of the integration interval, and prove its asymptotic error estimate under suitable hypotheses. Numerical experiments are presented to demonstrate the performance of the proposed *** Codes 65D30 Copyright © 2021, The Authors. All rights reserved.

关键词： Computation theory

Dissolving Constraints for Riemannian Optimization

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arXiv 2022年

作者： Xiao, Nachuan Liu, Xin Toh, Kim-Chuan The Institute of Operations Research and Analytics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China Department of Mathematics Institute of Operations Research and Analytics National University of Singapore Singapore119076 Singapore

In this paper, we consider optimization problems over closed embedded submanifolds of Rn, which are defined by the constraints c(x) = 0. We propose a class of constraint dissolving approaches for these Riemannian optimization problems. In these proposed approaches, solving a Riemannian optimization problem is transferred into the unconstrained minimization of a constraint dissolving function named CDF. Different from existing exact penalty functions, the exact gradient and Hessian of CDF are easy to compute. We study the theoretical properties of CDF and prove that the original problem and CDF have the same first-order and second-order stationary points, local minimizers, and Lojasiewicz exponents in a neighborhood of the feasible region. Remarkably, the convergence properties of our proposed constraint dissolving approaches can be directly inherited from the existing rich results in unconstrained optimization. Therefore, the proposed constraint dissolving approaches build up short cuts from unconstrained optimization to Riemannian optimization. Several illustrative examples further demonstrate the potential of our proposed constraint dissolving approaches. Copyright © 2022, The Authors. All rights reserved.

关键词： Optimization

A force-based gradient descent method for ab initio atomic structure relaxation

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arXiv 2022年

作者： Hu, Yukuan Gao, Xingyu Zhao, Yafan Liu, Xin Song, Haifeng State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing100088 China CAEP Software Center for High Performance Numerical Simulation Beijing100088 China

Force-based algorithms for ab initio atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive ab initio calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial stepsize capturing the local curvature of the energy surface. The exit is controlled by an unrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only two parameters are present without tuning. © 2022, CC BY.

关键词： Conjugate gradient method

A global optimization approach for multi-marginal optimal transport problems with Coulomb cost

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arXiv 2021年

作者： Hu, Yukuan Chen, Huajie Liu, Xin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China School of Mathematical Sciences Beijing Normal University China

In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding the strongly correlated quantum systems. With a Monge-like ansatz, the orginal high-dimensional problems are transferred into mathematical programmings with generalized complementarity constraints, and thus the curse of dimensionality is surmounted. However, the latter ones are themselves hard to deal with from both theoretical and practical perspective. Moreover in the presence of nonconvexity, brute-force searching for global solutions becomes prohibitive as the problem size grows large. To this end, we propose a global optimization approach for solving the nonconvex optimization problems, by exploiting an efficient proximal block coordinate descent local solver and an initialization subroutine based on hierarchical grid refinements. We provide numerical simulations on some typical physical systems to show the efficiency of our approach. The results match well with both theoretical predictions and physical intuitions, and give the first visualization of optimal transport maps for some two dimensional *** Codes 81V05 (Primary) 49M37, 65K05, 90C26, 90C30 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： Global optimization

Exploring Question-Specific Rewards for Generating Deep Questions 28

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Exploring Question-Specific Rewards for Generating Deep Ques...

28th International Conference on Computational Linguistics, COLING 2020

作者： Xie, Yuxi Pan, Liangming Wang, Dongzhe Kan, Min-Yen Feng, Yansong Wangxuan Institute of Computer Technology Peking University China NUS Graduate School for Integrative Sciences and Engineering ZhuiYi Technology Singapore School of Computing National University of Singapore Singapore The MOE Key Laboratory of Computational Linguistics Peking University China

ISBN: (纸本)9781952148279

Recent question generation (QG) approaches often utilize the sequence-to-sequence framework (Seq2Seq) to optimize the log-likelihood of ground-truth questions using teacher forcing. However, this training objective is inconsistent with actual question quality, which is often reflected by certain global properties such as whether the question can be answered by the document. As such, we directly optimize for QG-specific objectives via reinforcement learning to improve question quality. We design three different rewards that target to improve the fluency, relevance, and answerability of generated questions. We conduct both automatic and human evaluations in addition to a thorough analysis to explore the effect of each QG-specific reward. We find that optimizing question-specific rewards generally leads to better performance in automatic evaluation metrics. However, only the rewards that correlate well with human judgement (e.g., relevance) lead to real improvement in question quality. Optimizing for the others, especially answerability, introduces incorrect bias to the model, resulting in poor question quality. Our code is publicly available at https://***/YuxiXie/RL-for-Question-Generation. © 2020 COLING 2020 - 28th International Conference on Computational Linguistics, Proceedings of the Conference. All rights reserved.

关键词： Reinforcement learning

HOMOGENIZATION OF THE DISTRIBUTION-DEPENDENT STOCHASTIC ABSTRACT FLUID MODELS

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arXiv 2023年

作者： Chen, Junlong Qiu, Zhaoyang Tang, Yanbin School of Sciences Great Bay University Great Bay Institute for Advanced Study Dongguan523000 China School of Mathematics University of Science and Technology of China Anhui Hefei230026 China School of Applied Mathematics Nanjing University of Finance and Economics Nanjing210046 China School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

In this paper, we study the homogenization of the distribution-dependent stochastic abstract fluid models by combining the two−scale convergence and martingale representative approach. A general framework of the homogenization research is established for stochastic abstract fluid models which are the type of nonlinear partial differential equations including the (distribution-dependent) stochastic Navier-Stokes equations, stochastic magneto-hydrodynamic equations, stochastic Boussinesq equations, stochastic micropolar equations, stochastic Allen-Cahn equations. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

A Constraint Dissolving Approach for Nonsmooth Optimization over the Stiefel Manifold

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arXiv 2022年

作者： Hu, Xiaoyin Xiao, Nachuan Liu, Xin Toh, Kim-Chuan School of Computer and Computing Science Hangzhou City University Hangzhou310015 China The Institute of Operations Research and Analytics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences China Department of Mathematics Institute of Operations Research and Analytics National University of Singapore Singapore119076 Singapore

This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint dissolving function named NCDF and show that it has the same first-order stationary points and local minimizers as the original problem in a neighborhood of the Stiefel manifold. Furthermore, we show that the Clarke subdifferential of NCDF is easy to achieve from the Clarke subdifferential of the objective function. Therefore, various existing approaches for unconstrained nonsmooth optimization can be directly applied to nonsmooth optimization problems over the Stiefel manifold. We propose a framework for developing subgradient-based methods and establish their convergence properties based on prior works. Furthermore, based on our proposed framework, we can develop efficient approaches for optimization over the Stiefel manifold. Preliminary numerical experiments further highlight that the proposed constraint dissolving approach yields efficient and direct implementations of various unconstrained approaches to nonsmooth optimization problems over the Stiefel manifold. Copyright © 2022, The Authors. All rights reserved.

关键词： Optimization