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Quantum control based on three forms of Lyapunov functions

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Chinese Physics B 2024年第4期33卷 216-222页

作者：俞国慧杨洪礼 coll.ge of mathematics and systems science Shandong University of Science and TechnologyQingdao 266590China

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state *** this paper, the specific control laws under the three forms are *** is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test *** calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing ***, a unified form of the control laws under the three forms is given.

关键词： quantum system Lyapunov function particle swarm optimization simulated annealing algorithms quantum control

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

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Journal of systems science & Complexity 2024年第5期37卷 2132-2156页

作者： FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu School of mathematics Statistics and Mechanics Beijing University of Technology Academy of mathematics and systems science Chinese Academy of Sciences

In recent years, Kriging model has gained wide popularity in various fields such as space geology, econometrics, and computer experiments. As a result, research on this model has *** this paper, the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method, with consideration for the model uncertainty. The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method. First, the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction ***, the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models. The effectiveness of the proposed method is verified through numerical analyses.

关键词： Asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging

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 Science Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

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 observations. The time-varying thresholds are designed as the prediction value of the measurement, which can provide more information about the system state. The convergence property is established with some suitable stability,boundedness and observability conditions. In 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 noise. Finally, 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

Deciphering and integrating invariants for neural operator learning with various physical mechanisms

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National science Review 2024年第4期11卷 111-122页

作者： Rui Zhang Qi Meng Zhi-Ming Ma Academy of mathematics and systems science Chinese Academy of Sciences(CAS) Microsoft Research

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation(PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose the physical invariant attention neural operator(PIANO) to decipher and integrate the physical invariants for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional *** to existing techniques, PIANO can reduce the relative error by 13.6%–82.2% on PDE forecasting tasks across varying coefficients, forces or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO.

关键词： neural operator PDE solver contrastive learning physical invariants

Physical informed memory networks for solving PDEs:implementation and applications

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Communications in Theoretical Physics 2024年第2期76卷 51-61页

作者： Jiuyun Sun Huanhe Dong Yong Fang coll.ge of mathematics and systems science Shandong University of Science and TechnologyQingdao 266590China

With the advent of physics informed neural networks(PINNs),deep learning has gained interest for solving nonlinear partial differential equations(PDEs)in recent *** this paper,physics informed memory networks(PIMNs)are proposed as a new approach to solving PDEs by using physical laws and dynamic behavior of *** the fully connected structure of the PINNs,the PIMNs construct the long-term dependence of the dynamics behavior with the help of the long short-term memory ***,the PDEs residuals are approximated using difference schemes in the form of convolution filter,which avoids information loss at the neighborhood of the sampling ***,the performance of the PIMNs is assessed by solving the Kd V equation and the nonlinear Schr?dinger equation,and the effects of difference schemes,boundary conditions,network structure and mesh size on the solutions are *** show that the PIMNs are insensitive to boundary conditions and have excellent solution accuracy even with only the initial conditions.

关键词： nonlinear partial differential equations physics informed memory networks physics informed neural networks numerical solution

On the convergence of tracking differentiator with multiple stochastic disturbances

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science China(Information sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG School of mathematics and Big Data Foshan University School of mathematics and Statistics Central South University Academy of mathematics and systems science Chinese Academy of Sciences systems Engineering Institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances

Forward to the Special Topic on“Solving Differential Equations with Deep Learning”

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Journal of systems science & Complexity 2024年第2期37卷 389-390页

作者： YAN Zhenya Academy of mathematics and systems science Chinese Academy of SciencesBeijing 100190China

The concept of artificial intelligence(AI)was first presented at the Dartmouth SummerResearch Project on AI hosted by McCarthy and Minsky in *** that,the developmentof AI has experienced ups and downs due to some limited conditions including intelligentcomputing techniques,computer and hardware and software^([1,2]).In particular,with the rapidof deep artificial neural networks,machine learning(ML)and deep learning(DL)techniques^([3,4])have been applied in many fields of science and engineering,including machine translation,image recognition,genomics,scientific computing and atmospheric science,etc^([5]).

关键词： has artificial hardware

Dynamic Analysis of the Multi-state Reliability System with Priority Repair Discipline

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 665-694页

作者： Aihemaitijiang YUMAIER Ehmet KASIM coll.ge of mathematics and systems science Xinjiang UniversityUrumqi 830046China

This paper considers a multi-state repairable system that is composed of two classes of components,one of which has a priority for ***,we investigate the well-posedenss of the system by applying the operator semigroup ***,using Greiner’s idea and the spectral properties of the corresponding operator,we obtain that the time-dependent solution of the system converges strongly to its steady-state solution.

关键词： multi-state system C0-semigroup Dirichlet operator well-posedness asymptotic behavior

Density peak clustering using tensor network

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science China(Information sciences) 2024年第3期67卷 321-322页

作者： Xiao SHI Yun SHANG Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences National Center for mathematics and Interdisciplinary sciences Key Laboratory of ManagementDecision and Information SystemsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tens... 详细信息

关键词： Tensors