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Towards chemical accuracy using a multi-mesh adaptive finite element method in all-electron density functional theory

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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

Engineered poly(A)-surrogates for translational regulation and therapeutic biocomputation in mammalian cells

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细胞研究（英文版） 2024年第1期34卷 31-46页

作者： Jiawei Shao Shichao Li Xinyuan Qiu Jian Jiang Lihang Zhang Pengli Wang Yaqing Si Yuhang Wu Minghui He Qiqi Xiong Liuqi Zhao Yilin Li Yuxuan Fan Mirta Viviani Yu Fu Chaohua Wu Ting Gao Lingyun Zhu Martin Fussenegger Hui Wang Mingqi Xie International Institutes of Medicine The Fourth Affiliated HospitalZhejiang University School of MedicineYiwuZhejiangChina Key Laboratory of Growth Regulation and Translational Research of Zhejiang Province School of Life SciencesWestlake UniversityHangzhouZhejiangChina Westlake Laboratory of Life Sciences and Biomedicine HangzhouZhejiangChina Institute of Basic Medical Sciences Westlake Institute for Advanced StudyHangzhouZhejiangChina College of Life Sciences Zhejiang UniversityHangzhouZhejiangChina Department of Biology and Chemistry College of ScienceNational University of Defense TechnologyChangshaHunanChina Key Laboratory of Growth Regulation and Translational Research of Zhejiang Province School of Life SciencesWestlake UniversityHangzhouZhejiangChina Westlake Laboratory of Life Sciences and Biomedicine HangzhouZhejiangChina Institute of Basic Medical Sciences Westlake Institute for Advanced StudyHangzhouZhejiangChina School of Life Sciences Fudan UniversityShanghaiChina Key Laboratory of Growth Regulation and Translational Research of Zhejiang Province School of Life SciencesWestlake UniversityHangzhouZhejiangChina Westlake Laboratory of Life Sciences and Biomedicine HangzhouZhejiangChina Institute of Basic Medical Sciences Westlake Institute for Advanced StudyHangzhouZhejiangChina Research Center of Biological Computation Zhejiang LaboratoryHangzhouZhejiangChina Key Laboratory of Growth Regulation and Translational Research of Zhejiang Province School of Life SciencesWestlake UniversityHangzhouZhejiangChina Westlake Laboratory of Life Sciences and Biomedicine HangzhouZhejiangChina Institute of Basic Medical Sciences Westlake Institute for Advanced StudyHangzhouZhejiangChina Key Laboratory of Growth Regulation and Translational Research of Zhejiang Province School of Life SciencesWestlake UniversityHangzhouZhejiangChina Westlake Laboratory of Life Sciences and Biomedicine HangzhouZhejiangChina Institute of Basic Medical Sciences Westlake Institute

Here,we present a gene regulation strategy enabling programmable control over eukaryotic translational *** excising the natural poly-adenylation(poly-A)signal of target genes and replacing it with a synthetic control region harboring RNA-binding protein(RBP)-specific aptamers,cap-dependent translation is rendered exclusively dependent on synthetic translation initiation factors(STIFs)containing different RBPs engineered to conditionally associate with different elF4F-binding proteins(eIFBPs).This modular design framework facilitates the engineering of various gene switches and intracellular sensors responding to many user-defined trigger signals of interest,demonstrating tightly controlled,rapid and reversible regulation of transgene expression in mammalian cells as well as compatibility with various clinically applicable delivery routes of in vivo gene *** efficacy was demonstrated in two animal *** exemplify disease treatments that require on-demand drug secretion,we show that a custom-designed gene switch triggered by the FDA-approved drug grazoprevir can effectively control insulin expression and restore glucose homeostasis in diabetic *** diseases that require instantaneous sense-and-response treatment programs,we create highly specific sensors for various subcellularly(mis)localized protein markers(such as cancer-related fusion proteins)and show that translation-based protein sensors can be used either alone or in combination with other cell-state classification strategies to create therapeutic biocomputers driving self-sufficient elimination of tumor cells in *** design strategy demonstrates unprecedented flexibility for translational regulation and could form the basis for a novel class of programmable gene therapies in vivo.

关键词： Riboswitches Targeted therapies

FAS-UNet: A Novel FAS-driven Unet to Learn Variational Image Segmentation

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arXiv 2022年

作者： Zhu, Hui Shu, Shi Zhang, Jianping The School of Mathematics and Computational Science Xiangtan University Key Laboratory of Intelligent Computing & Information Processing Ministry of Education China The School of Mathematics and Computational Science Xiangtan University Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan411105 China The School of Mathematics and Computational Science Xiangtan University Hunan National Applied Mathematics Center China

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires a lot of parameters and training data, not always available for practical problems. In this paper, inspired by traditional multi-phase convexity Mumford-Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a novel variational-model-informed network (denoted as FAS-Unet) that exploits the model and algorithm priors to extract the multi-scale features. The proposed model-informed network integrates image data and mathematical models, and implements them through learning a few convolution kernels. Based on the variational theory and FAS algorithm, we first design a feature extraction sub-network (FAS-Solution module) to solve the model-driven nonlinear systems, where a skip-connection is employed to fuse the multi-scale features. Secondly, we further design a convolution block to fuse the extracted features from the previous stage, resulting in the final segmentation possibility. Experimental results on three different medical image segmentation tasks show that the proposed FAS-Unet is very competitive with other state-of-the-art methods in qualitative, quantitative and model complexity evaluations. Moreover, it may also be possible to train specialized network architectures that automatically satisfy some of the mathematical and physical laws in other image problems for better accuracy, faster training and improved generalization. The code is available at https://***/zhuhui100/FASUNet. Copyright © 2022, The Authors. All rights reserved.

关键词： Image segmentation

A NEURAL MULTIGRID SOLVER FOR HELMHOLTZ EQUATIONS WITH HIGH WAVENUMBER AND HETEROGENEOUS MEDIA

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SIAM Journal on Scientific Computing 2025年第3期47卷 C655-C679页

作者： Cui, Chen Jiang, Kai Shu, Shi Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this paper, we propose a deep learning-enhanced multigrid solver for high-frequency and heterogeneous Helmholtz equations. By applying spectral analysis, we categorize the iteration error into characteristic and noncharacteristic components. We eliminate the noncharacteristic components by a multigrid wave cycle, which employs carefully selected smoothers on each grid. We diminish the characteristic components by a learned phase function and the approximate solution of an advection-diffusion-reaction (ADR) equation, which is solved using another multigrid V-cycle on a coarser scale, referred to as the ADR cycle. The resulting solver, termed Wave-ADR-NS, enables the handling of error components with varying frequencies and overcomes constraints on the number of grid points per wavelength on coarse grids. Furthermore, we provide an efficient implementation using differentiable programming, making Wave-ADR-NS an end-to-end Helmholtz solver that incorporates parameters learned through semisupervised training. Wave-ADR-NS demonstrates robust generalization capabilities for both in-distribution and out-of-distribution velocity fields of varying difficulty. Comparative experiments with other multigrid methods validate its superior performance in solving heterogeneous 2D Helmholtz equations with wavenumbers exceeding 2000. © 2025 Society for Industrial and Applied Mathematics Publications. All rights reserved.

关键词： Helmholtz equation

Switching between topological edge states using phase-change materials

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

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

The Mean Time to Absorption on Horizontal Partitioned Sierpinski Gasket Networks

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arXiv 2022年

作者： Zhang, Zhizhuo Wu, Bo Yu, Zuguo School of Mathematics Southeast University Nanjing210023 China School of Applied Mathematics Nanjing University of Finance and Economics Nanjing210023 China Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China

The random walk is one of the most basic dynamic properties of complex networks, which has gradually become a research hotspot in recent years due to its many applications in actual networks. An important characteristic of the random walk is the mean time to absorption, which plays an extremely important role in the study of topology, dynamics and practical application of complex networks. Analyzing the mean time to absorption on the regular iterative self-similar network models is an important way to explore the influence of self-similarity on the properties of random walks on the network. The existing literatures have proved that even local self-similar structures can greatly affect the properties of random walks on the global network, but they have failed to prove whether these effects are related to the scale of these self-similar structures. In this article, we construct and study a class of Horizontal Partitioned Sierpinski Gasket network model based on the classic Sierpinski gasket network, which is composed of local self-similar structures, and the scale of these structures will be controlled by the partition coefficient k. Then, the analytical expressions and approximate expressions of the mean time to absorption on the network model are obtained, which prove that the size of the self-similar structure in the network will directly restrict the influence of the self-similar structure on the properties of random walks on the network. Finally, we also analyzed the mean time to absorption of different absorption nodes on the network to find the location of the node with the highest absorption efficiency. Copyright © 2022, The Authors. All rights reserved.

关键词： Complex networks

NUMERICAL METHODS AND ANALYSIS OF COMPUTING QUASIPERIODIC SYSTEMS

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arXiv 2022年

作者： Jiang, Kai Li, Shifeng Zhang, Pingwen Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China

Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method (PM) [J. Comput. Phys., 256: 428, 2014], has been proposed to compute quasiperiodic systems. Various studies have demonstrated that the PM is an accurate and efficient method to solve quasiperiodic systems. However, there is a lack of theoretical analysis of PM. In this paper, we present a rigorous convergence analysis of the PM by establishing a mathematical framework of quasiperiodic functions and their high-dimensional periodic functions. We also give a theoretical analysis of quasiperiodic spectral method (QSM) based on this framework. Results demonstrate that PM and QSM both have exponential decay, and the QSM (PM) is a generalization of the periodic Fourier spectral (pseudo-spectral) method. Then we analyze the computational complexity of PM and QSM in calculating quasiperiodic systems. The PM can use fast Fourier transform, while the QSM cannot. Moreover, we investigate the accuracy and efficiency of PM, QSM and periodic approximation method in solving the linear time-dependent quasiperiodic Schrödinger equation. Copyright © 2022, The Authors. All rights reserved.

关键词： Fast Fourier transforms

A GENERAL ALTERNATING-DIRECTION IMPLICIT FRAMEWORK WITH GAUSSIAN PROCESS REGRESSION PARAMETER PREDICTION FOR LARGE SPARSE LINEAR SYSTEMS

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arXiv 2021年

作者： Jiang, Kai Su, Xuehong Zhang, Juan Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of existing ADI methods can be unified in the developed framework. Meanwhile the GADI framework can derive new ADI methods. Moreover, as the algorithm efficiency is sensitive to the splitting parameters, we offer a data-driven approach, the Gaussian process regression (GPR) method based on the Bayesian inference, to predict the GADI framework’s relatively optimal parameters. The GPR method only requires a small training data set to learn the regression prediction mapping, can predict accurate splitting parameters, and has high generalization capability. It allows us to efficiently solve linear systems with a one-shot computation, and does not require any repeated computations. Finally, we use the three-dimensional convection-diffusion equation, two-dimensional parabolic equation, and continuous Sylvester matrix equation to examine the performance of our proposed methods. Numerical results demonstrate that the proposed framework is faster tens to thousands of times than the existing ADI methods, such as (inexact) Hermitian and skew-Hermitian splitting type methods in which the consumption of obtaining relatively optimal splitting parameters is ignored. As a result, our proposed methods can solve much larger linear systems which these existing ADI methods have not reached. Copyright © 2021, The Authors. All rights reserved.

关键词： Linear systems

Nucleation and phase transition of decagonal quasicrystals

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arXiv 2024年

作者： Zhou, Tiejun Zhang, Lei Zhang, Pingwen Shi, An-Chang Jiang, Kai Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Beijing International Center for Mathematical Research Peking University Beijing100871 China School of Mathematics and Statistics Wuhan University Wuhan430072 China School of Mathematical Sciences Peking University Beijing100871 China Department of Physics and Astronomy McMaster University HamiltonL8S 4M1 Canada

In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely the nullspace-preserving saddle search method. Specifically, we focus on nucleation and phase transitions of the decagonal quasicrystal (DQC) based on the Lifshitz-Petrich model. We present the nucleation path of DQC from the liquid and demonstrate one- and two-stage transition paths between DQC and periodic crystals. We provide a perspective of the group-subgroup phase transition and nucleation rates to understand the nucleation and phase transition mechanisms involving DQC. These results reveal the one-step and stepwise modes of symmetry breaking or recovery in the phase transition from DQC, where the stepwise modes are more probable. Copyright © 2024, The Authors. All rights reserved.

关键词： Quasicrystals