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A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations

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applied mathematics and Mechanics(English Edition) 2023年第7期44卷 1199-1224页

作者： J.WU S.F.WANG P.PERDIKARIS Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA 19104U.S.A. Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA 19104U.S.A.

We propose a self-supervising learning framework for finding the dominant eigenfunction-eigenvalue pairs of linear and self-adjoint *** represent target eigenfunctions with coordinate-based neural networks and employ the Fourier positional encodings to enable the approximation of high-frequency *** formulate a self-supervised training objective for spectral learning and propose a novel regularization mechanism to ensure that the network finds the exact eigenfunctions instead of a space spanned by the ***,we investigate the effect of weight normalization as a mechanism to alleviate the risk of recovering linear dependent modes,allowing us to accurately recover a large number of *** effectiveness of our methods is demonstrated across a collection of representative benchmarks including both local and non-local diffusion operators,as well as high-dimensional time-series data from a video *** results indicate that the present algorithm can outperform competing approaches in terms of both approximation accuracy and computational cost.

关键词： spectral learning partial differential equation(PDE) neural network slow features analysis

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Fragmentation dynamics of electron-impact double ionization of helium

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Chinese Physics B 2023年第6期32卷 9-15页

作者：刘士炜叶地发刘杰 Beijing Computational Science Research Center Beijing 100193China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Graduate School China Academy of Engineering PhysicsBeijing 100193China HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China

We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 e V to 1 ke V for comparative study. At the lowest excess energy, i.e., close to the double-ionization threshold, it is found that the projectile momentum is totally transferred to the recoil-ion while the residual energy is randomly partitioned among the three outgoing electrons, which are then most probably emitted with an equilateral triangle configuration. Our results agree well with experiments as compared with early quantum-mechanical calculation as well as classical simulation based on a two-dimensional Bohr's model. Furthermore, by mapping the final momentum vectors event by event into a Dalitz plot,we unambiguously demonstrate that the ergodicity has been reached and thus confirm a long-term scenario conceived by Wannier. The time scale for such few-body thermalization, from the initial nonequilibrium state to the final microcanonical distribution, is only about 100 attoseconds. Finally, we predict that, with the increase of the excess energy, the dominant emission configuration undergoes a transition from equilateral triangle to T-shape and finally to a co-linear mode. The associated signatures of such configuration transition in the electron–ion joint momentum spectrum and triple-electron angular distribution are also demonstrated.

关键词： double ionization classical trajectory Monte Carlo simulation Wannier threshold law ergodicity

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STOCHASTIC CONTROLLED AVERAGING FOR FEDERATED LEARNING WITH COMMUNICATION COMPRESSION 12

STOCHASTIC CONTROLLED AVERAGING FOR FEDERATED LEARNING WITH ...

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12th International Conference on Learning Representations, ICLR 2024

作者： Huang, Xinmeng Li, Ping Li, Xiaoyun LinkedIn BellevueWA98004 United States The Graduate Group of Applied Mathematics and Computational Science The University of Pennsylvania United States

Communication compression has been an important topic in Federated Learning (FL) for alleviating the communication overhead. However, communication compression brings forth new challenges in FL due to the interplay of compression-incurred information distortion and inherent characteristics of FL such as partial participation and data heterogeneity. Despite the recent development, the existing approaches either cannot accommodate arbitrary data heterogeneity or partial participation, or require stringent conditions on compression. In this paper, we revisit the seminal stochastic controlled averaging method by proposing an equivalent but more efficient/simplified formulation with halved uplink communication costs, building upon which we propose two compressed FL algorithms, SCALLION and SCAFCOM, to support unbiased and biased compression, respectively. Both the proposed methods outperform the existing compressed FL methods in terms of communication and computation complexities. Moreover, SCALLION and SCAFCOM attain fast convergence rates under arbitrary data heterogeneity without any additional assumptions on compression errors. Experiments show that SCALLION and SCAFCOM outperform recent compressed FL methods under the same communication budget. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Stochastic systems

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Error Estimate of a New Conservative Finite Difference Scheme for the Klein-Gordon-Dirac System

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Numerical mathematics(Theory,Methods and Applications) 2023年第1期16卷 140-164页

作者： Shasha Bian Yue Cheng Boling Guo Tingchun Wang The Graduate School of China Academy of Engineering Physics Beijing 100088China School of Mathematics and Statistics Nanjing University of Information Science and TechnologyNanjing 210044China Institute of Applied Physics and Computational Mathematics Beijing 100088China

In this paper,we derive and analyze a conservative Crank-Nicolson-type finite difference scheme for the Klein-Gordon-Dirac(KGD)*** from the derivation of the existing numerical methods given in literature where the numerical schemes are proposed by directly discretizing the KGD system,we translate the KGD equations into an equivalent system by introducing an auxiliary function,then derive a nonlinear Crank-Nicolson-type finite difference scheme for solving the equivalent *** scheme perfectly inherits the mass and energy conservative properties possessed by the KGD,while the energy preserved by the existing conservative numerical schemes expressed by two-level’s solution at each time *** using energy method together with the‘cut-off’function technique,we establish the optimal error estimate of the numerical solution,and the convergence rate is O(τ^(2)+h^(2))in l∞-norm with time stepτand mesh size *** experiments are carried out to support our theoretical conclusions.

关键词： Klein-Gordon-Dirac equation nonlinear finite difference scheme conservation error analysis

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An Iterative Thresholding Method for the Minimum Compliance Problem

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Communications in computational Physics 2023年第4期33卷 1189-1216页

作者： Luyu Cen Wei Hu Dong Wang Xiaoping Wang Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNew JerseyUSA School of Science and Engineering The Chinese University of Hong KongShenzhenGuangdong 518172China Shenzhen International Center for Industrial and Applied Mathematics Shenzhen Research Institute of Big DataGuangdong 518172China

In this paper,we propose a simple energy decaying iterative thresholding algorithm to solve the two-phase minimum compliance *** material domain is implicitly represented by its characteristic function,and the problem is formulated into a minimization problem by the principle of minimum complementary *** prove that the energy is decreasing in each *** effective continuation schemes are proposed to avoid trapping into the local *** results on 2D isotropic linear material demonstrate the effectiveness of the proposed methods.

关键词： Minimum compliance convolution thresholding linear elasticity

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Hydrogen-Bonding Interactions from Nucleobase-Decorated Supramolecular Polymer: Synthesis, Self-Assembly and Biomedical Applications

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ACS Biomaterials science and Engineering 2024年第1期10卷 234-254页

作者： Ilhami, Fasih Bintang Birhan, Yihenew Simegniew Cheng, Chih-Chia Department of Natural Science Faculty of Mathematics and Natural Science Universitas Negeri Surabaya Surabaya60231 Indonesia Department of Chemistry College of Natural and Computational Sciences Debre Markos University Debre Markos00000 Ethiopia Graduate Institute of Applied Science and Technology National Taiwan University of Science and Technology Taipei10607 Taiwan

The fabrication of supramolecular materials for biomedical applications such as drug delivery, bioimaging, wound-dressing, adhesion materials, photodynamic/photothermal therapy, infection control (as antibacterial), etc. has grown tremendously, due to their unique properties, especially the formation of hydrogen bonding. Nevertheless, void space in the integration process, lack of feasibility in the construction of supramolecular materials of natural origin in living biological systems, potential toxicity, the need for complex synthesis protocols, and costly production process limits the actual application of nanomaterials for advanced biomedical applications. On the other hand, hydrogen bonding from nucleobases is one of the strategies that shed light on the blurred deployment of nanomaterials in medical applications, given the increasing reports of supramolecular polymers that promote advanced technologies. Herein, we review the extensive body of literature about supramolecular functional biomaterials based on nucleobase hydrogen bonding pertinent to different biomedical applications. It focuses on the fundamental understanding about the synthesis, nucleobase-decorated supramolecular architecture, and novel properties with special emphasis on the recent developments in the assembly of nanostructures via hydrogen-bonding interactions of nucleobase. Moreover, the challenges, plausible solutions, and prospects of the so-called hydrogen bonding interaction from nucleobase for the fabrication of functional biomaterials are outlined. © 2023 American Chemical Society

关键词： Hydrogen bonds

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A Gas-Kinetic Scheme for Collisional Vlasov-Poisson Equations in Cylindrical Coordinates

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Communications in computational Physics 2022年第8期32卷 779-809页

作者： Yi Wang Jiexing Zhang Guoxi Ni University of Science and Technology of China HefeiChina Graduate school of China Academy of Engineering Physics BeijingChina Institute of Applied Physics and computational mathematics BeijingChina

Many configurations in plasma physics are axisymmetric,it will be more convenient to depict them in cylindrical coordinates compared with Cartesian *** this paper,a gas-kinetic scheme for collisional Vlasov-Poisson equations in cylindrical coordinates is proposed,our algorithm is based on Strang *** equation is divided into two parts,one is the kinetic transport-collision part solved by multiscale gas-kinetic scheme,and the other is the acceleration part solved by a Runge-Kutta *** asymptotic preserving property of whole algorithm is proved and it’s applied on the study of charge separation problem in plasma edge and 1D Z-pinch *** results show it can capture the process fromnon-equilibrium to equilibrium state by Coulomb collisions,and numerical accuracy is obtained.

关键词： Vlasov-BGK-Poisson equations cylindrical coordinates gas-kinetic scheme asymptotic preserving property Coulomb collisions

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Correlations in interacting electron liquids: Many-body statistics and hyperuniformity

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Physical Review B 2024年第10期110卷 104201页

作者： Haina Wang Rhine Samajdar Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Materials Institute Program in Applied and Computational Mathematics

Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to ordinary liquids. The structure factor of disordered hyperuniform systems often obeys the scaling relation S(k)∼Bkα with B,α>0 in the limit k→0. Ground states of d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this paper, we systematically address these questions by deriving the analytical small-k behaviors (and, associated, α and B) of the total and spin-resolved structure factors of quasi-one-dimensional, two-dimensional, and three-dimensional electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our paper thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple

关键词： Electronic structure Quantum many-body systems Two-dimensional electron gas

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Local order metrics for many-particle systems across length scales

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Physical Review Research 2024年第3期6卷 033262页

作者： Charles Emmett Maher Salvatore Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics

Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in d-dimensional Euclidean space Rd across length scales is an outstanding challenge in physics, chemistry, and materials science. Since an infinite set of n-particle correlation functions is required to fully characterize a system, one must settle for a reduced set of structural information, in practice. We initiate a program to use the local number variance σN2(R) associated with a spherical sampling window of radius R (which encodes pair correlations) and an integral measure derived from it ΣN(Ri,Rj) that depends on two specified radial distances Ri and Rj. Across the first three space dimensions (d=1,2,3), we find these metrics can sensitively describe and categorize the degree of order/disorder of 41 different models of antihyperuniform, nonhyperuniform, disordered hyperuniform, and ordered hyperuniform many-particle systems at a specified length scale R. Using our local variance metrics, we demonstrate the importance of assessing order/disorder with respect to a specific value of R. These local order metrics could also aid in the inverse design of structures with prescribed length-scale-specific degrees of order/disorder that yield desired physical properties. In future work, it would be fruitful to explore the use of higher-order moments of the number of points within a spherical window of radius R [S. Torquato et al., Phys. Rev. X 11, 021028 (2021)] to devise even more sensitive order metrics.

关键词： Classical statistical mechanics

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Semi-analytical finite element method applied for characterizing micropolar fibrous composites

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applied mathematics and Mechanics(English Edition) 2024年第12期45卷 2147-2164页

作者： J.A.OTERO Y.ESPINOSA-ALMEYDA R.RODRIGUEZ-RAMOS J.MERODIO School of Engineering and Sciences Monterrey Institute of TechnologyEstado de Mexico 52926Mexico Institute of Engineering and Technology Autonomous University of Ciudad JuarezCiudad JuarezChihuahua 32310Mexico Postgraduate Program in Computational Modeling in Science and Technology Federal Fluminense UniversityRıo de Janeiro 27255-125Brazil Faculty of Mathematics and Computer Science University of HavanaLa Habana 10400Cuba Department of Mathematics Applied to ICT School of Informatics Systems EngineeringTechnical University of MadridMadrid 28031Spain

A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous *** framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact *** mathematical formulation of the local problems and the effective coefficients are presented by the *** local problems obtained from the AHM are solved by the FEM,which is denoted as the *** numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.

关键词： semi-analytical approach fiber-reinforced composite(FRC) effective property finite element method(FEM) asymptotic homogenization method(AHM) micropolar elasticity

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