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arXiv 2023年

作者： Kuang, Yang Shen, Yedan Hu, Guanghui Guangdong University of Technology China School of Mathematics and Information Science Guangzhou University China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University China Department of Mathematics Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications University of Macau China Zhuhai UM Science and Technology Research Institute Zhuhai China

Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn-Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn-Sham wavefunctions but also the Hartree potential, should be approximated accurately. Under the adaptive finite element framework, this can be implemented by constructing the a posteriori error indicator based on approximations of the aforementioned two quantities. However, this way results in a large amount of computational cost. To reduce the computational cost, we propose a novel multi-mesh adaptive method, in which the Kohn-Sham equation and the Poisson equation are solved in two different meshes on the same computational domain, respectively. With the proposed method, chemical accuracy can be achieved with less computational consumption compared with the adaptive method on a single mesh, as demonstrated in a number of numerical experiments. © 2023, CC BY.

关键词： Poisson equation

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Quantum Circuits for the Heat Equation with Physical Boundary Conditions Via Schrödingerisation

SSRN

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SSRN 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel's principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, The Authors. All rights reserved.

关键词： Boundary conditions

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Quantum Circuits for the heat equation with physical boundary conditions via Schrödingerisation

arXiv

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arXiv 2024年

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel’s principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, CC BY-NC-ND.

关键词： Ordinary differential equations

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A unifying framework for n-dimensional quasi-conformal mappings

arXiv

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arXiv 2021年

作者： Zhang, Daoping Choi, Gary P.T. Zhang, Jianping Lui, Lok Ming School of Mathematical Sciences Nankai University Tianjin300071 China Department of Mathematics Massachusetts Institute of Technology CambridgeMA02139 United States School of Mathematics and Computational Science Hunan National Center for Applied Mathematics Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China Department of Mathematics The Chinese University of Hong Kong Hong Kong

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal theory can be utilized for ensuring the bijectivity of the mappings. In addition, it is often desirable for the mappings to satisfy certain prescribed geometric constraints and possess low distortion in conformality or volume. In this work, we develop a unifying framework for computing n-dimensional quasi-conformal mappings. More specifically, we propose a variational model that integrates quasi-conformal distortion, volumetric distortion, landmark correspondence, intensity mismatch and volume prior information to handle a large variety of deformation problems. We further prove the existence of a minimizer for the proposed model and devise efficient numerical methods to solve the optimization problem. We demonstrate the effectiveness of the proposed framework using various experiments in two- and three-dimensions, with applications to medical image registration, adaptive remeshing and shape modeling. Copyright © 2021, The Authors. All rights reserved.

关键词： Numerical methods

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Whole genome/proteome based phylogeny reconstruction for prokaryotes using higher order Markov model and chaos game representation

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Molecular phylogenetics and evolution 2016年 96卷 102-111页

作者： Wei-Feng Yang Zu-Guo Yu Vo Anh Hunan Key Laboratory for Computation and Simulation in Science and Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University Hunan 411105 PR China Department of Mathematics and Physics Hunan Institute of Engineering Hunan 411104 PR China. Electronic address: yangweifeng09@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: yuzuguo@***. School of Mathematical Sciences Queensland University of Technology GPO Box 2434 Brisbane QLD 4001 Australia. Electronic address: v.anh@qut.edu.au.

UNLABELLED:Traditional methods for sequence comparison and phylogeny reconstruction rely on pair wise and multiple sequence alignments. But alignment could not be directly applied to whole genome/proteome comparison and phylogenomic studies due to their high computational complexity. Hence alignment-free methods became popular in recent years. Here we propose a fast alignment-free method for whole genome/proteome comparison and phylogeny reconstruction using higher order Markov model and chaos game representation. In the present method, we use the transition matrices of higher order Markov models to characterize amino acid or DNA sequences for their comparison. The order of the Markov model is uniquely identified by maximizing the average Shannon entropy of conditional probability distributions. Using one-dimensional chaos game representation and linked list, this method can reduce large memory and time consumption which is due to the large-scale conditional probability distributions. To illustrate the effectiveness of our method, we employ it for fast phylogeny reconstruction based on genome/proteome sequences of two species data sets used in previous published papers. Our results demonstrate that the present method is useful and efficient. AVAILABILITY AND IMPLEMENTATION:The source codes for our algorithm to get the distance matrix and genome/proteome sequences can be downloaded from ftp://121.199.20.25/. The software Phylip and EvolView we used to construct phylogenetic trees can be referred from their websites.

关键词： Alignment-free whole proteome comparison Chaos game representation Higher order Markov model Phylogenetic tree Shannon entropy

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Switching between singular points and exceptional-point-enhanced sensing in non-Hermitian photonic structures 13

Switching between singular points and exceptional-point-enha...

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Active Photonic Platforms XIII 2021

作者： Veronis, Georgios Huang, Yin Wang, Lanyan Shen, Yuecheng School of Electrical Engineering and Computer Science Louisiana State University Baton RougeLA70803 United States Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States Department of Optoelectrics Information Science and Engineering School of Physics and Electronics Central South University Hunan Changsha410012 China State Key Laboratory of Optoelectronic Materials and Technologies School of Electronics and Information Technology Sun Yat-Sen University Guangdong Guangzhou510275 China

ISBN: (纸本)9781510644304

We investigate the exceptional points in a two-layer cylindrical waveguide structure consisting of absorbing and nonabsorbing dielectrics. We show that by tuning the parameters of the structure the complex effective indices of two waveguide modes can coalesce so that an exceptional point is formed. We show that the sensitivity of the effective index of the waveguide mode is enhanced at the exceptional point. We also investigate using phase-change materials in multilayer structures to switch between singular points. We show that in multilayer structures consisting of phasechange, lossless dielectric, lossy, and gain materials, absorbing or spectral singularities can be switched to exceptional points, and self-dual spectral singularities can be switched to unidirectional spectral singularities by switching the phasechange material from its crystalline to its amorphous phase. Our results could be important for developing new compact reconfigurable singularity-enhanced optical devices. © 2021 SPIE.

关键词： Physical optics

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Constrained Probabilistic Pareto Dominance for Expensive Constrained Multiobjective Optimization Problems

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IEEE Transactions on Evolutionary computation 2024年 1-1页

作者： Zhang, Zhiyao Wang, Yong Sun, Guangyong Pang, Tong Tang, Ke School of Automation Central South University Changsha China State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle Hunan University Changsha China Guangdong Key Laboratory of Brain-Inspired Intelligent Computation Department of Computer Science and Engineering and the Research Institute of Trustworthy Autonomous Systems Southern University of Science and Technology Shenzhen China

This paper proposes a new parameterless constraint-handling technique, named constrained probabilistic Pareto dominance (CPPD), for expensive constrained multiobjective optimization problems (CMOPs). In CPPD, when comparing two solutions, in terms of each original objective, we design a new objective for each solution, which is the negative product of two probabilities calculated based on the predicted fitness mean values and the uncertainty information provided by Kriging models: 1) the probability that this solution satisfies all constraints, denoted as PoF, and 2) the probability that this solution is better than the other on the original objective, denoted as PoB. It is evident that for each solution, PoF and PoB indicate its feasibility and its optimality on the corresponding original objective, respectively. Then, Pareto dominance based on new objectives is executed. As a result, both competitive feasible solutions and promising infeasible solutions with good diversity can be preserved by CPPD. These two kinds of solutions can help the population to exploit the located feasible parts and to explore new feasible parts, respectively. Further, based on CPPD, we develop a Pareto-based Kriging-assisted constrained multiobjective evolutionary algorithm (called PEA) to deal with expensive CMOPs with two or three objectives. Finally, PEA is generalized to solve expensive constrained many-objective optimization problems, named PEA+. The effectiveness of CPPD, PEA, and PEA+ is verified by comprehensive experiments. IEEE

关键词： Evolutionary algorithms

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Topological Edge States at Singular Points in Non-Hermitian Plasmonic Waveguide-Cavity Systems

Topological Edge States at Singular Points in Non-Hermitian ...

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CLEO: science and Innovations, S and I 2022

作者： Huang, Yin Shen, Yuecheng Veronis, Georgios Department of Optoelectrics Information Science and Engineering School of Physics and Electronics Central South University Hunan Changsha410012 China State Key Laboratory of Optoelectronic Materials and Technologies School of Electronics and Information Technology Sun Yat-Sen University Guangdong Guangzhou510275 China School of Electrical Engineering and Computer Science Louisiana State University Baton RougeLA70803 United States Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States

We show that non-Hermitian plasmonic waveguide-cavity systems can simultaneously exhibit both topological edge states and singular points. We also show that the sensitivity of the reflected light intensity is greatly ... 详细信息

ISBN: (纸本)9781557528209

关键词： Topology

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Switching between topological edge states using phase-change materials

Switching between topological edge states using phase-change...

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2023 Active Photonic Platforms, APP 2023

作者： Veronis, Georgios Huang, Yin Shen, Yuecheng School of Electrical Engineering and Computer Science Louisiana State University Baton RougeLA70803 United States Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States Department of Optoelectrics Information Science and Engineering School of Physics and Electronics Central South University Hunan Changsha410012 China State Key Laboratory of Optoelectronic Materials and Technologies School of Electronics and Information Technology Sun Yat-Sen University Guangdong Guangzhou510275 China

ISBN: (纸本)9781510665088

We introduce non-Hermitian plasmonic waveguide-cavity structures based on the Aubry-Andre-Harper model to realize switching between right and left topological edge states using the phase-change material germanium-antimony-tellurium (GST). The structure unit cells consist of a metal-dielectric-metal (MDM) waveguide side-coupled to MDM stub resonators with modulated distances between adjacent stubs. In such structures the modulated distances introduce an effective gauge magnetic field. We show that switching between the crystalline and amorphous phases of GST leads to a shift of the dispersion relation of the optimized structure so that a right topological edge state for the crystalline phase, and a left topological edge state for the amorphous phase occur at the same frequency. Thus, we realize switching between right and left topological edge states at that frequency by switching between the crystalline and amorphous phases of GST. Our results could be potentially important for developing compact reconfigurable topological photonic devices. © 2023 SPIE.

关键词： Gages

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A Progressive Image Restoration Network for High-order Degradation Imaging in Remote Sensing

arXiv

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arXiv 2024年

作者： Feng, Yujie Yang, Yin Fan, Xiaohong Zhang, Zhengpeng Bu, Lijing Zhang, Jianping School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory for Intelligent Computing and Information Processing of the Ministry of Education Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University National Center for Applied Mathematics in Hunan Hunan International Scientific and Technological Innovation Cooperation Base of Computational Science Xiangtan411105 China College of Mathematical Medicine Zhejiang Normal University Jinhua321004 China School of Automation and Electronic Information Xiangtan University Xiangtan411105 China

Recently, deep learning methods have gained remarkable achievements in the field of image restoration for remote sensing (RS). However, most existing RS image restoration methods focus mainly on conventional first-order degradation models, which may not effectively capture the imaging mechanisms of remote sensing images. Furthermore, many RS image restoration approaches that use deep learning are often criticized for their lacks of architecture transparency and model interpretability. To address these problems, we propose a novel progressive restoration network for high-order degradation imaging (HDI-PRNet), to progressively restore different image degradation. HDI-PRNet is developed based on the theoretical framework of degradation imaging, offering the benefit of mathematical interpretability within the unfolding network. The framework is composed of three main components: a module for image denoising that relies on proximal mapping prior learning, a module for image deblurring that integrates Neumann series expansion with dual-domain degradation learning, and a module for super-resolution. Extensive experiments demonstrate that our method achieves superior performance on both synthetic and real remote sensing images. Copyright © 2024, The Authors. All rights reserved.

关键词： Image reconstruction

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