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AN ACCELERATION STRATEGY FOR RANDOMIZE-THEN-OPTIMIZE SAMPLING VIA DEEP NEURAL NETWORKS

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Journal of Computational Mathematics 2021年第6期39卷 848-864页

作者： liang yan Tao Zhou School of Mathematics Southeast UniversityNanjing210096China Nanjing Center for Applied Mathematics Nanjing211135China LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO can be computationally intensive forcomplexity problems due to repetitive evaluations of the expensive forward model and itsgradient. In this work, we present a novel goal-oriented deep neural networks (DNN) surrogate approach to substantially reduce the computation burden of RTO. In particular,we propose to drawn the training points for the DNN-surrogate from a local approximatedposterior distribution – yielding a flexible and efficient sampling algorithm that convergesto the direct RTO approach. We present a Bayesian inverse problem governed by ellipticPDEs to demonstrate the computational accuracy and efficiency of our DNN-RTO approach, which shows that DNN-RTO can significantly outperform the traditional RTO.

关键词： Bayesian inverse problems Deep neural network Markov chain Monte Carlo

Sensor management of LEO constellation based on covariance control

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Journal of Systems Engineering and Electronics 2019年第2期30卷 393-401页

作者： QIN Zheng liang yan'gang College of Aerospace Science and Engineering National University of Defense Technology

This paper studies the multi-sensor management problem for low earth orbit(LEO) infrared warning constellation used to track a midcourse missile. A covariance control approach, which selects sensor combinations or subset based on the difference between the desired covariance matrix and the actual covariance of each target, is used for sensor management, including some matrix metrics to measure the differentia between two covariance matrices. Besides, to meet the requirements of the space based warning system, the original covariance control approach is improved. Simulation results demonstrate that the covariance control approach is able to provide a better tracking performance by providing a well-designed desired covariance and balance tracking performance goals with system demands.

关键词： sensor management covariance control target tracking accuracy LEO constellation

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

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Journal of Systems Engineering and Electronics 2019年第3期30卷 535-544页

作者： liang yan’gang QIN Zheng College of Aerospace Science and Engineering National University of Defense Technology

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

关键词： layout optimization satellite multi-objective optimization Pareto front multi-attribute decision making

Study of Deuteron Separation Energy Based on Bayesian Neural Network Approach

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原子能科学技术 2023年第4期57卷 721-728页

作者： XING Kang liang yan SUN Xiaojun College of Physics and Technology Guangxi Normal UniversityGuilin 541004China Guangxi Key Laboratory of Nuclear Physics and Technology Guangxi Normal UniversityGuilin 541004China

Deuteron separation energy is not only the basis for validating the nuclear mass models and nucleon-nucleon interaction potential,but also can determine the stability of a nuclide to certain *** neural network(BNN)approach,which has strong predictive power and can naturally give theoretical errors of predicted values,had been successfully applied to study the different kinds of separations except the deuteron *** this paper,several typical nuclear mass models,such as macroscopic model BW2,macroscopic-microscopic model WS4,and microscopic model HFB-31,are chosen to study the deuteron separation energy combining BNN *** root-mean-square deviations of these models are partly *** addition,the inclusion of physical parameters related to the pair and shell effects in the input layer can further improve the theoretical accuracy for the deuteron separation *** results show that the theoretical predictions are more reliable as more physical features of BNN approach are included.

关键词： Bayesian neural network deuteron separation energy pair and shell effects

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Generalized Christoffel Functions for Power Orthogonal Polynomials

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 819-832页

作者： Xie TAO yan liang Guangdong Country Garden School College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)(Ministry of Education of China)Hunan Normal University

In this paper we extend the Christoffel functions to the case of power orthogonal *** existence and uniqueness as well as some properties are given.

关键词： generalized Christoffel function existence uniqueness gaussian quadrature formula Christoffel number

Global Existence and Pointwise Estimates of Solutions to Generalized Benjamin-Bona-Mahony Equations in Multi Dimensions

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Chinese Annals of Mathematics,Series B 2014年第4期35卷 659-668页

作者： Hongmei XU yan liang College of Science Hohai University

This paper is concerned with the global existence and pointwise estimates of solutions to the generalized Benjamin-Bona-Mahony equations in all space *** using the energy method, Fourier analysis and pseudo-differential operators, the global existence and pointwise convergence rates of the solution are obtained. The decay rate is the same as that of the heat equation and one can see that the solution propagates along the characteristic line.

关键词： Cauchy problem Generalized Benjamin-Bona-Mahony equations Multidimensions Global existence Pointwise estimates

Single-photon detection and its applications

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Science China(Physics,Mechanics & Astronomy) 2014年第7期57卷 1218-1232页

作者： liang yan ZENG HePing Shanghai Key Laboratory of Modern Optical System Engineering Research Center of Optical Instrument and System Ministry of Education School of Optical-Electrical and Computer Engineering University of Shanghai for Science and Technology State Key Laboratory of Precision Spectroscopy East China Normal University

A single-photon detector is an extremely sensitive device capable of registering photons,offering essential technical support for optics quantum information *** review herein our recent experimental progress in the development and application of single-photon detection *** based on advanced self-differencing,low-pass filtering,frequency up-conversion and photon-number-resolving are introduced for attaining high-speed,high-efficiency,low-noise single-photon detection at infrared *** advantages of high-speed single-photon detection are discussed in some applications,such as the laser ranging and quantum key *** photon-number-resolving detection is shown to support efficient quantum random number generation.

关键词： quantum optics photodetection avalanche photodiode frequency up-conversion

A Non-Intrusive Reduced Basis EKI for Time Fractional Diffusion Inverse Problems

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Acta Mathematicae Applicatae Sinica 2020年第1期36卷 183-202页

作者： Feng-lian yanG liang yan College of Science Hohai UniversityNanjing 210098China School of Mathematics Southeast UniversityNanjing210096China

In this study,we consider an ensemble Kalman inversion(EKI)for the numerical solution of time fractional diffusion inverse problems(TFDIPs).Computational challenges in the EKI arise from the need for repeated evaluations of the forward *** address this challenge by introducing a non-intrusive reduced basis(RB)method for constructing surrogate models to reduce computational *** this method,a reduced basis is extracted from a set of full-order snapshots by the proper orthogonal decomposition(POD),and a doubly stochastic radial basis function(DSRBF)is used to learn the projection *** DSRBF is carried out in the offline stage with a stochastic leave-one-out cross-validation algorithm to select the shape parameter,and the outputs for new parameter values can be obtained rapidly during the online *** to the complete decoupling of the offline and online stages,the proposed non-intrusive RB method–referred to as POD-DSRBF–provides a powerful tool to accelerate the EKI approach for *** demonstrate the practical performance of the proposed strategies through two nonlinear time-fractional diffusion inverse *** numerical results indicate that the new algorithm can achieve significant computational gains without sacrificing accuracy.

关键词： fractional differential equations ensemble Kalman inversion surrogate modeling reduced basis method

Bainite isothermal transformation of Si–Mn–Mo alloy by phase structure factor calculation under different rare earth contents

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Rare Metals 2014年第4期33卷 427-432页

作者： yan-liang Yi Yi-Long liang Qi-Bing Tan The Key Laboratory for Mechanical Behavior and Microstructure of Materials School of Materials and MetallurgyGuizhou University

The effect of rare earth （RE） on bainite trans- formation mechanism is not yet unified in the academia. Therefore, further studying the effect of RE on bainite transformation mechanism will have important guiding significance for the development of bainite steels. In this paper, using differential dilatometer （DIL805A/D）, heat treatment was performed and C-curve was drawn. The effect of phase structure factor on bainite transformation under two different fractions of RE in Si-Mn-Mo bainite steels was investigated by the empirical electron theory （EET） of solids, molecules, dilatometry, and metallogra- phy. Experimental results show that RE makes Fe-C- RE segregation structural unit of Si-Mn-Mo bainite steels increase, i.e., the values of phase structure factor （na, FDC） increase, and delay bainite transformation due to the drag effect resulting from the segregation of RE ferrite island interphase and the retardation of RE to carbon diffusion in Si-Mn-Mo bainite steels. Beside this, C-curve is shifted to right and down, and microstructures of bainite ferrite and substructures are finer.

关键词： Phase structure factor C-curve Substructure Rare earths