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Projected gradient descent algorithm for ab initio crystal structure relaxation under a fixed unit cell volume

Physical Review B 2024年第22期109卷 224108-224108页

作者： Yukuan Hu Junlei Yin Xingyu Gao Xin Liu Haifeng Song Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences Innovation Center NPU Chongqing Chongqing 401135 China National Key Laboratory of Computational Physics

This paper is concerned with ab initio crystal structure relaxation under a fixed unit cell volume, which is a step in calculating the static equations of state and forms the basis of thermodynamic property calculations for materials. The task can be formulated as an energy minimization with a determinant constraint. Widely used line minimization-based methods (e.g., conjugate gradient method) lack both efficiency and convergence guarantees due to the nonconvex nature of the determinant constraint as well as the significant differences in the curvatures of the potential energy surface with respect to atomic and lattice components. To this end, we propose a projected gradient descent algorithm named PANBB. It is equipped with (i) search direction projections for lattice vectors, (ii) distinct curvature-aware initial trial step sizes for atomic and lattice updates, and (iii) a nonrestrictive line minimization criterion as the stopping rule for the inner loop. It can be proved that PANBB favors theoretical convergence to equilibrium states. Across a benchmark set containing 223 structures from various categories, PANBB achieves average speedup factors of approximately 1.41 and 1.45 over the conjugate gradient method and direct inversion in the iterative subspace implemented in off-the-shelf simulation software, respectively. Moreover, it normally converges on all the systems, manifesting its robustness. As an application, we calculate the static equations of state for the high-entropy alloy AlCoCrFeNi, which remains elusive owing to 160 atoms representing both chemical and magnetic disorder and the strong local lattice distortion. The results are consistent with the previous calculations and are further validated by experimental thermodynamic data.

关键词： Crystal structure Structural properties Density functional theory

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On the deterioration of convergence rate of spectral differentiations for functions with singularities

arXiv

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arXiv 2025年

作者： Wang, Haiyong School of Mathematics and Statistics 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

Spectral differentiations are basic ingredients of spectral methods. In this work, we analyze the pointwise rate of convergence of spectral differentiations for functions containing singularities and show that the deteriorations of the convergence rate at the endpoints, singularities and other points in the smooth region exhibit different patterns. As the order of differentiation increases by one, we show for functions with an algebraic singularity that the convergence rate of spectral differentiation by Jacobi projection deteriorates two orders at both endpoints and only one order at each point in the smooth region. The situation at the singularity is more complicated and the convergence rate either deteriorates two orders or does not deteriorate, depending on the parity of the order of differentiation, when the singularity locates in the interior of the interval and deteriorates two orders when the singularity locates at the endpoint. Extensions to some related problems, such as the spectral differentiation using Chebyshev interpolation, are also discussed. Our findings justify the error localization property of Jacobi approximation and differentiation and provide some new insight into the convergence behavior of Jacobi spectral *** Codes 65D25, 41A10, 41A25 Copyright © 2025, The Authors. All rights reserved.

关键词： Chebyshev approximation

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RANDOM PERTURBATIONS FOR THE CHEMOTAXIS-FLUID MODEL WITH FRACTIONAL DISSIPATION: GLOBAL PATHWISE WEAK SOLUTIONS

arXiv

引用

arXiv 2023年

作者： Zhang, Lei Liu, Bin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan430074 China

This paper considers a stochastically perturbed Keller-Segel-Navier-Stokes (KS-SNS) system arising from the biomathematics in two dimensions, where the diffusion of fluid is expressed by a fractional Laplacian with an exponent in [1/2, 1]. Our main result demonstrates that, under appropriate assumptions, the Cauchy problem of the KS-SNS system has a unique global probabilistically strong and analytically weak solution, which also confirms that the quadratic logistic source authentically contributes to the global existence of solutions. First, a three-layer approximate system is introduced, this system seems to be new in the studying of chemotaxis-fluid model and it enables one to construct approximate solutions in regular Hilbert spaces Hs(R2). Second, to accomplish the convergence progressively, a series of crucial entropy-energy inequalities for the approximations are derived, whose derivation strongly depends on the fine structure of the system and requires a novel strategy to adapt to the appearance of fractional dissipation and the unboundedness of domain. Third, based on these uniform bounds, we establish the existence of global martingale weak solutions by virtue of a stochastic compactness method. Finally, by applying the Littlewood-Paley theory, we show that the pathwise uniqueness holds for these martingale solution. As a by-product, a few interpolation inequalities in Besov spaces are obtained, which seems to be new and may have their own interest. Copyright © 2023, The Authors. All rights reserved.

关键词： Stochastic systems

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Incomplete crossing and semi-topological horseshoes

arXiv

引用

arXiv 2025年

作者： Cheng, Junfeng Yang, Xiao-Song School of Mathematics and Statistics 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

This paper enriches the topological horseshoe theory using finite subshift theory in symbolic dynamical systems, and develops an elementary framework addressing incomplete crossing and semi-horseshoes. Two illustrative examples are provided: one from the perturbed Duffing system and another from a polynomial system proposed by Chen, demonstrating the prevalence of semi-horseshoes in chaotic systems. Moreover, the semi-topological horseshoe theory enhances the detection of chaos and improves the accuracy of topological entropy estimation. Copyright © 2025, The Authors. All rights reserved.

关键词： Topology

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An Optimization Method for Renewable Energy and Energy Storage Capacity Allocation Based on Temporal Production Simulation 7

An Optimization Method for Renewable Energy and Energy Stora...

引用

7th IEEE Conference on Energy Internet and Energy System Integration, EI2 2023

作者： Du, Hongbo Li, Chi Chen, Liang Zhang, Jinping Kou, Caixia College of Sciences Beijing University of Posts and Telecommunications Beijing China National Key Laboratory of Renewable Energy Grid-Integration China Electric Power Research Institute Beijing China Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

ISBN: (纸本)9798350345094

With the rapid expansion of large-scale renewable energy bases in China, optimizing the allocation of renewable energy and energy storage capacity is crucial for improving system efficiency. In this paper, a joint optimal configuration method of wind-photovoltaic-energy storage capacity based on time series production simulation is proposed for renewable energy transmission base. Its aim is to minimize the total investment cost of the system under certain constraints about the proportion of renewable energy power generation, renewable energy utilization rate, conventional thermal power operation, energy storage power station operation, ultra-high voltage direct current (UHVDC) regulation and power transmission. To handle the nonlinear constraints, linearization is achieved by introducing integer variables. For the complex operation constraints of conventional thermal power and UHVDC channel, a simplified modeling method of start-stop cycle and adjustment cycle is proposed, which can effectively reduce the number of integer variables and improve the solving efficiency. The effectiveness of the proposed method is tested on the data of a renewable energy base in Northwest China. © 2023 IEEE.

关键词： Energy utilization

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A New Multi-point Stepsize Gradient Method for Optimization 5th

A New Multi-point Stepsize Gradient Method for Optimization

引用

5th International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOV 2020

作者： Huang, Yakui Dai, Yu-Hong Liu, Xin-Wei Institute of Mathematics Hebei University of Technology Tianjin300401 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

ISBN: (纸本)9783030720391

The Barzilai-Borwein (BB) gradient method, which employs two-point stepsizes computed by the information of two consecutive iterations, is efficient in solving large-scale unconstrained optimization. In this paper, motivated by the success of BB method and the multi-point stepsize proposed by Dai and Fletcher (Mathematical Programming, 2006, 106: 403–421), we develop a new efficient gradient method, called MPSG, which adaptively uses the Dai-Fletcher long stepsize and Dai-Fletcher short stepsize. The R-linear convergence of MPSG for general n-dimensional strictly convex quadratic functions is established. By making use of two modified multi-point stepsizes and nonmonotone line searches, MPSG is extended to solve general unconstrained optimization. Moreover, the proposed MPSG method is further generalized for solving extreme eigenvalue problems. Numerical experiments on quadratic optimization, general unconstrained optimization and extreme eigenvalue problems demonstrate the efficiency of our method. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Gradient methods

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Cascaded adaptive aberration-eliminating multimode fiber imaging

引用

Advanced Photonics 2025年第02期 135-143页

作者： Zhong Wen Qilin Deng Quanzhi Li Yizhou Tan Jingshan Zhong Chiming Zhang Jiahe Zhang Clemens F.Kaminski Ying Gu Xu Liu Qing Yang Zhejiang University College of Optical Science and Engineering State Key Laboratory of Extreme Photonics and Instrumentation Zhejiang University International Research Center for Advanced Photonics Zhejiang University ZJU-Hangzhou Global Scientific and Technological Innovation Center Chinese PLA General Hospital The First Medical Center Department of Laser Medicine Chinese PLA General Hospital Hainan HospitalLaser Medicine Center Zhejiang Laboratory Research Center for Intelligent Manufacturing Computing University of Cambridge Department of Chemical Engineering and Biotechnology

In vivo microscopic imaging inside a biological lumen such as the gastrointestinal tract, respiratory airways, or within blood vessels has faced significant technological challenges for decades. A promising candidate technology is the multimode fiber(MMF) endoscope, which enables minimally invasive diagnostics at a resolution reaching the cellular level. However, for in vivo imaging applications deep inside a biological lumen, sample-induced aberrations and the dynamic dispersion in the MMF make the MMF endoscope a chaotic system with many unknowns, where multiple minor fluctuations can couple and compound into intractable problems. We introduce a dynamically encoding, cascaded, optical, and ultrathin polychromatic light-field endoscopy(DECOUPLE) to tackle this challenge. DECOUPLE includes an adaptive aberration correction that can accurately track and control MMF behavior in the spatial-frequency domain to compensate for chaos introduced during complex dynamic imaging processes. We demonstrate the flexibility and practicality of DECOUPLE for noninvasive volumetric imaging in two colors for light passing through various highly aberrating samples including 120-μm-thick onion epidermal slices and 80-μm-thick layers of fat emulsions. To summarize, we represent a significant step toward practical in vivo imaging deep within biological tissue.

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The Exploration of Neural Collapse under Imbalanced Data

arXiv

引用

arXiv 2024年

作者： Liu, Haixia School of Mathematics and Statistics Institute of Interdisciplinary Research for Mathematics and Applied Science Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Hubei Wuhan China

Neural collapse, a newly identified characteristic, describes a property of solutions during model training. In this paper, we explore neural collapse in the context of imbalanced data. We consider the L-extended unconstrained feature model with a bias term and provide a theoretical analysis of global minimizer. Our findings include: (1) Features within the same class converge to their class mean, similar to both the balanced case and the imbalanced case without bias. (2) The geometric structure is mainly on the left orthonormal transformation of the product of L linear classifiers and the right transformation of the class-mean matrix. (3) Some rows of the left orthonormal transformation of the product of L linear classifiers collapse to zeros and others are orthogonal, which relies on the singular values of Ŷ = (IK − 1/Nn1TK)D, where K is class size, n is the vector of sample size for each class, D is the diagonal matrix whose diagonal entries are given by √n. Similar results are for the columns of the right orthonormal transformation of the product of class-mean matrix and D. (4) The i-th row of the left orthonormal transformation of the product of L linear classifiers aligns with the i-th column of the right orthonormal transformation of the product of class-mean matrix and D. (5) We provide the estimation of singular values about Ŷ . Our numerical experiments support these theoretical *** Codes ***, *** Copyright © 2024, The Authors. All rights reserved.

关键词： Linear transformations

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Quasiperiodic Symmetric Tilt FCC Grain Boundaries

arXiv

引用

arXiv 2024年

作者： Zou, Wenwen Zhang, Juan Xu, Jie Jiang, Kai 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 LSEC NCMIS Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we investigate [110] symmetric tilt FCC grain boundaries (GBs) by a recently developed approach for quasiperiodic interfaces using the Landau-Brazovskii model. On special tilt angles associated with quadratic algebraic numbers, quasiperiodic GBs exhibit generalized Fibonacci substitution rules. The transition mechanism from quasiperiodic GBs to periodic GBs is explored through sphere offsets and spectral coalescence. We also propose an accurate method to calculate the GB energy for arbitrary tilt angle and analyze the factors affecting the GB energy. The revealing GB energy change is continue along with tilt angle except periodic GBs. © 2024, CC BY-NC-SA.

关键词： Grain boundaries

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Quantized Constant-Envelope Waveform Design for Massive MIMO DFRC Systems

arXiv

引用

arXiv 2024年

作者： Wu, Zheyu Liu, Ya-Feng Chen, Wei-Kun Masouros, Christos The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The School of Mathematics and Statistics Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China The Department of Electronic and Electrical Engineering University College London Torrington Place LondonWC1E 7JE United Kingdom

Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances. Copyright © 2024, The Authors. All rights reserved.

关键词： Mean square error

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