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Chien-physics-informed neural networks for solving singularly perturbed boundary-layer problems

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Applied Mathematics and Mechanics(English Edition) 2024年第9期45卷 1467-1480页

作者： Long WANG Lei ZHANG Guowei HE The State Key Laboratory of Nonlinear Mechanics Institute of MechanicsChinese Academy of SciencesBeijing 100190China school of Engineering sciences University of Chinese Academy of SciencesBeijing 100049China

A physics-informed neural network(PINN)is a powerful tool for solving differential equations in solid and fluid ***,it suffers from singularly perturbed boundary-layer problems in which there exist sharp changes caused by a small perturbation parameter multiplying the highest-order *** this paper,we introduce Chien's composite expansion method into PINNs,and propose a novel architecture for the PINNs,namely,the Chien-PINN(C-PINN)*** novel PINN method is validated by singularly perturbed differential equations,and successfully solves the wellknown thin plate bending *** particular,no cumbersome matching conditions are needed for the C-PINN method,compared with the previous studies based on matched asymptotic expansions.

关键词： physics-informed neural network(PINN) singular perturbation boundarylayer problem composite asymptotic expansion

Diversity and ecological assembly process of aerobic anoxygenic phototrophic bacteria in a low irradiation area,Three Gorges Reservoir

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Journal of Environmental sciences 2024年第9期143卷 116-125页

作者： Lixin Huo Anran Ma Hong Liu Xingzu Wang Cheng Song Chongqing Institute of Green and Intelligent Technology Chinese Academy of SciencesChongqing 400714China Chongqing school University of Chinese Academy of SciencesCollege of Resources and EnvironmentChongqing 400714China Key Laboratory of Reservoir Aquatic Environment Chinese Academy of SciencesChongqing 400714China University of chinese academy of {2. Beijing 100049China

Aerobic anoxygenic phototrophic bacteria(AAPB)are significant bacterial groups in aquatic ecosystems,known for their rapid growth and photoheterotrophic ***,the distribution and ecological assembly process of AAPB in low irradiation freshwater basins remain unclear,warranting further *** this study,we present the diversity,abundance,spatial variations,ecological process,and community interaction of AAPB in sediment of Three Gorges Reservoir(TGR)under low *** findings demonstrate the dominant genera of AAPB community that exist in the TGR area also are appeared in different waters,with some regional ***,the concentration of pufM gene,an indicator for AAPB,maintains a consistently high numerical level ranging from(2.2.±0.44)×10^(4)to(9.98±0.30)×10^(7)gene copies/*** solar irradiation is suggested as the major factor affecting AAPB,it remains unclear whether and how AAPB differ between regions due to varying solar irradiation *** results show spatial differences between total bacteria and AAPB communities,with significant differences observed only in *** and environmental factor contributed less than 10%to the spatial difference of community,with sediment type and environmental factors being the key factors influencing microbial community *** stochastic process plays a dominant role in the aggregation and replacement of AAPB communities,among which the most contribution is dispersal *** AAPB network,Yoonia and Gemmobacter are the hubs for *** results valuable insights into the AAPB communities in TGR with low irradiation.

关键词： Three Gorges Reservoir(TGR) Aerobic anoxygenic phototrophic bacteria(AAPB) Bacterial community Null model Community assembly

Structure-Preserving Recurrent Neural Networks for a Class of Birkhoffian Systems

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Journal of Systems Science & Complexity 2024年第2期37卷 441-462页

作者： XIAO Shanshan CHEN Mengyi ZHANG Ruili TANG Yifa LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China school of Mathematics and Statistics Beijing Jiaotong UniversityBeijing 100044China

In this paper,the authors propose a neural network architecture designed specifically for a class of Birkhoffian systems—The Newtonian *** proposed model utilizes recurrent neural networks(RNNs)and is based on a mathematical framework that ensures the preservation of the Birkhoffian *** authors demonstrate the effectiveness of the proposed model on a variety of problems for which preserving the Birkhoffian structure is important,including the linear damped oscillator,the Van der Pol equation,and a high-dimensional *** with the unstructured baseline models,the Newtonian neural network(NNN)is more data efficient,and exhibits superior generalization ability.

关键词： Birkhoffian system k(z,t)-symplectic neural networks recurrent neural network

Synthesis methods and powder quality of titanium monocarbide

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chinese Journal of Chemical Engineering 2024年第8期72卷 10-18页

作者： Maoqiao Xiang Wenjun Ding Qinghua Dong Qingshan Zhu State Key Laboratory of Mesoscience and Engineering Institute of Process EngineeringChinese Academy of SciencesBeijing 100190China school of Chemical Engineering University of the Chinese Academy of SciencesBeijing 100049China Innovation academy for Green Manufacture Chinese Academy of SciencesBeijing 100190China

Titanium monocarbide(TiC),which is the most stable titanium-based carbide,has attracted considerable interest in the fields of energy,catalysis,and structural materials due to its excellent *** of high-quality TiC powders with low cost and high efficiency is crucial for industrial applications;however major challenges face its ***,the methods for synthesizing TiC powders based on a reaction system are *** analysis is focused on the underlying mechanisms by which synthesis methods affect the quality of ***,strategies for improving the synthesis of highquality powders are analyzed from the perspective of enhancing heat and mass transfer ***,the critical issues,challenges,and development trends of the synthesis technology and application of high-quality TiC powder are discussed.

关键词： Titanium carbide Synthesis methods Reaction engineering Reaction kinetics Powder technology

Review on synergistic damage effect of irradiation and corrosion on reactor structural alloys

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Nuclear Science and Techniques 2024年第3期35卷 109-141页

作者： Hui Liu Guan-Hong Lei He-Fei Huang Shanghai Institute of Applied Physics Chinese Academy of SciencesShanghai 201800China school of Nuclear Science and Technology University of Chinese Academy of SciencesBeijing 100049China

The synergistic damage effect of irradiation and corrosion of reactor structural materials has been a prominent research *** paper provides a comprehensive review of the synergistic effects on the third-and fourth-generation fission nuclear energy structural materials used in pressurized water reactors and molten salt *** competitive mechanisms of multiple influencing factors,such as the irradiation dose,corrosion type,and environmental temperature,are summarized in this *** approaches are proposed to alleviate the synergistic damage caused by irradiation and corrosion,thereby promoting in-depth research in the future and solving this key challenge for the structural materials used in reactors.

关键词： Irradiation and corrosion Synergistic effect Austenitic stainless steels Nickel-based alloys Reactors

Threshold Selection and Resource Allocation for Quantized Identification

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Journal of Systems Science & Complexity 2024年第1期37卷 204-229页

作者： WANG Ying LI Xin ZHAO Yanlong ZHANG Ji-Feng Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

This paper is concerned with the optimal threshold selection and resource allocation problems of quantized identification, whose aims are improving identification efficiency under limited resources. Firstly, the first-order asymptotically optimal quantized identification theory is extended to the weak persistent excitation condition. Secondly, the characteristics of time and space complexities are established based on the Cramér-Rao lower bound of quantized systems. On these basis, the optimal selection methods of fixed thresholds and adaptive thresholds are established under aperiodic signals, which answer how to achieve the best efficiency of quantized identification under the same time and space complexity. In addition, based on the principle of maximizing the identification efficiency under a given resource, the optimal resource allocation methods of quantized identification are given for the cases of fixed thresholds and adaptive thresholds, respectively, which show how to balance time and space complexity to realize the best identification efficiency of quantized identification.

关键词： Quantized output resource allocation system identification threshold selection.

Recursive Projected Filter Algorithm with Binary-Valued Observations

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Journal of Systems Science & Complexity 2024年第5期37卷 1832-1860页

作者： ZHANG Xiaoyan WANG Ying XUE Wenchao ZHAO Yanlong Key Laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

This paper focuses on the state estimate for a class of systems with both process noise and measurement noise under binary-valued observations,in which the Gaussian assumption on the predicted density of the state is not required.A recursive projected filter algorithm with time-varying thresholds is constructed to estimate the state under binary-valued *** time-varying thresholds are designed as the prediction value of the measurement,which can provide more information about the system *** convergence property is established with some suitable stability,boundedness and observability *** particular,the estimation error between state and estimate is proved to be asymptotically bounded in the mean-square sense,whose upper bound is related to the variance of process ***,the theoretical results are demonstrated via numerical examples of first-order and high-order systems.

关键词： Binary-valued observations convergence recursive filter time-varying thresholds

A Deep Learning Method for Computing Eigenvalues of the Fractional Schrödinger Operator

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Journal of Systems Science & Complexity 2024年第2期37卷 391-412页

作者： GUO Yixiao MING Pingbing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger *** proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the *** improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded *** authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger *** an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

关键词： Eigenvalue problem deep learning fractional Schrödinger operator isospectral problem

SEMI-PROXIMAL POINT METHOD FOR NONSMOOTH CONVEX-CONCAVE MINIMAX OPTIMIZATION

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Journal of Computational Mathematics 2024年第3期42卷 617-637页

作者： Yuhong Dai Jiani Wang Liwei Zhang LSEC ICMSECAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China school of Mathematical sciences Dalian University of TechnologyDalian 116024China

Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research *** there have been many numerical algorithms for solving smooth convex-concave minimax problems,numerical algorithms for nonsmooth convex-concave minimax problems are *** paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem.A semi-proximal point method(SPP)is proposed,in which a quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each *** construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly *** prove the global convergence of our algorithm under mild assumptions,without requiring strong convexity-concavity *** the locally metrical subregularity of the solution mapping,we prove that our algorithm has the linear rate of *** numerical results are reported to verify the efficiency of our algorithm.

关键词： Minimax optimization Convexity-concavity Global convergence Rate of con-vergence Locally metrical subregularity