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A Newton type iterative method for heat-conduction inverse problems

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Applied Mathematics and Mechanics(English Edition) 2007年第4期28卷 531-539页

作者：贺国强孟泽红 Department of Mathematics Shanghai UniversityShanghai 200444P. R. China

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.

关键词： inverse problems nonlinear ill-posed operator equations Newton type method implicit iterative method iteration stopping rule

Weak optimal inverse problems of interval linear programming based on KKT conditions

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Applied Mathematics(A Journal of Chinese Universities) 2021年第3期36卷 462-474页

作者： LIU Xiao JIANG Tao LI Hao-hao School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China Hangzhou College of Commerce Zhejiang Gongshang UniversityHangzhou 310018China School of Data Sciences Zhejiang University of Finance and EconomicsHangzhou 310018China.

In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT ***,the problem is precisely ***,by adjusting the minimum change of the current cost coefficient,a given weak solution can become ***,an equivalent characterization of weak optimal inverse IvLP problems is ***,the problem is simplified without adjusting the cost coefficient of null variable.

关键词： interval linear programming inverse problems KKT conditions weak optimal solution

A Stochastic Collocation Approach to Bayesian Inference in inverse problems

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Communications in Computational Physics 2009年第9期6卷 826-847页

作者： Youssef Marzouk Dongbin Xiu Department of Aeronautics&Astronautics Massachusetts Institute of TechnologyCambridgeMA 02139USA Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA

We present an efficient numerical strategy for the Bayesian solution of inverse *** collocation methods,based on generalized polynomial chaos(gPC),are used to construct a polynomial approximation of the forward solution over the support of the prior *** approximation then defines a surrogate posterior probability density that can be evaluated repeatedly at minimal computational *** ability to simulate a large number of samples from the posterior distribution results in very accurate estimates of the inverse solution and its associated *** with high accuracy of the gPC-based forward solver,the new algorithm can provide great efficiency in practical applications.A rigorous error analysis of the algorithm is conducted,where we establish convergence of the approximate posterior to the true posterior and obtain an estimate of the convergence *** is proved that fast(exponential)convergence of the gPC forward solution yields similarly fast(exponential)convergence of the *** numerical strategy and the predicted convergence rates are then demonstrated on nonlinear inverse problems of varying smoothness and dimension.

关键词： inverse problems Bayesian inference stochastic collocation generalized polynomial chaos uncertainty quantification

ERROR ESTIMATES FOR THE RECURSIVE LINEARIZATION OF inverse MEDIUM problems

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Journal of Computational Mathematics 2010年第6期28卷 725-744页

作者： Gang Bao Faouzi Triki Department of Mathematics Michigan State University East Lansing MI 48824-1027 USA LMC-IMAG Universite Joseph Fourier I B.P. 53 38041 Grenoble Cedex 9 France

This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, inverse problems 13（1997）, pp.253-282] is established for solving the acoustic inverse scattering problem.

关键词： Recursive linearization Tikhonov regularization inverse problems Convergence analysis.

Deep Guided Attention Network for Joint Denoising and Demosaicing in Real Image

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Chinese Journal of Electronics 2024年第1期33卷 303-312页

作者： Tao ZHANG Ying FU Jun ZHANG School of Computer Science and Technology Beijing Institute of Technology Advanced Reasearch Institute of Multidisciplinary Science Beijing Institute of Technology

Denoising(DN) and demosaicing(DM) are the first crucial stages in the image signal processing pipeline. Recently, researches pay more attention to solve DN and DM in a joint manner, which is an extremely undetermined inverse problem. Existing deep learning methods learn the desired prior on synthetic dataset, which limits the generalization of learned network to the real world data. Moreover, existing methods mainly focus on the raw data property of high green information sampling rate for DM, but occasionally exploit the high intensity and signalto-noise(SNR) of green channel. In this work, a deep guided attention network(DGAN) is presented for real image joint DN and DM(JDD), which considers both high SNR and high sampling rate of green information for DN and DM, respectively. To ease the training and fully exploit the data property of green channel, we first train DN and DM sub-networks sequentially and then learn them jointly, which can alleviate the error accumulation. Besides, in order to support the real image JDD, we collect paired raw clean RGB and noisy mosaic images to conduct a realistic dataset. The experimental results on real JDD dataset show the presented approach performs better than the state-of-the-art methods, in terms of both quantitative metrics and qualitative visualization.

关键词： Training Visualization inverse problems Green products Noise reduction Pipelines Signal processing

Undersea Buried Pipeline Reconstruction Based on the Level Set and inverse Multiquadric Regularization Method

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Journal of Ocean University of China 2022年第1期21卷 101-112页

作者： SHANG Wenjing XUE Wei XU Yidong MAKAROV Sergey B LI Yingsong College of Information and Communication Engineering Harbin Engineering UniversityHarbin 150001China Key Laboratory of Advanced Marine Communication and Information Technology Ministry of Industry and Information TechnologyHarbin 150001China Yantai Research Institute and Graduate School of Harbin Engineering University Yantai 264006China Institute of Physics Nanotechnology and TelecommunicationsHigher School of Applied Physics and Space TechnologiesPeter the Great St.Petersburg Polytechnic UniversitySt.Petersburg 195251Russia

The electric inversion technique reconstructs the subsurface medium distribution from acquired *** the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance,are detected and located in a contactless ***,the process of accurately reconstructing the shape of the target object is challenging because electric inversion is a nonlinear and ill-posed *** this work,we present an inverse multiquadric(IMQ)regularization method based on the level set function for reconstructing buried *** the case of locating underwater objects,the unknown inversion area is split into two parts,the background and the pipeline with known *** geometry of the pipeline is represented based on the level set function for achieving a noiseless inversion *** obtain a binary image,the IMQ is used as the regularization term,which‘pushes’the level set function away from *** also provide an appropriate method to select the bandwidth and regularization parameters for the IMQ regularization term,resulting in reconstructed images with sharp *** simulation results and analysis show that the proposed method performs better than classical inversion methods.

关键词： inverse problems level set function inverse multiquadric regularization method buried pipeline

A Time-Varying Parameter Estimation Method for Physiological Models Based on Physical Information Neural Networks

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Computer Modeling in Engineering & Sciences 2023年第12期137卷 2243-2265页

作者： Jiepeng Yao Zhanjia Peng Jingjing Liu Chengxiao Fan Zhongyi Wang Lan Huang College of Information and Electrical Engineering China Agricultural UniversityBeijing100083China Key Laboratory of Agricultural Information Acquisition Technology(Beijing) Ministry of AgricultureBeijing100083China Key Laboratory of Modern Precision Agriculture System Integration Research Ministry of EducationBeijing100083China

In the establishment of differential equations,the determination of time-varying parameters is a difficult problem,especially for equations related to life ***,we propose a new framework named BioE-PINN based on a physical information neural network that successfully obtains the time-varying parameters of differential *** the proposed framework,the learnable factors and scale parameters are used to implement adaptive activation functions,and hard constraints and loss function weights are skillfully added to the neural network output to speed up the training convergence and improve the accuracy of physical information neural *** this paper,taking the electrophysiological differential equation as an example,the characteristic parameters of ion channel and pump kinetics are determined using *** results demonstrate that the numerical solution of the differential equation is calculated by the parameters predicted by BioE-PINN,the RootMean Square Error(RMSE)is between 0.01 and 0.3,and the Pearson coefficient is above 0.87,which verifies the effectiveness and accuracy of ***,realmeasuredmembrane potential data in animals and plants are employed to determine the parameters of the electrophysiological equations,with RMSE 0.02-0.2 and Pearson coefficient above *** conclusion,this framework can be applied not only for differential equation parameter determination of physiological processes but also the prediction of time-varying parameters of equations in other fields.

关键词： Physics-informed neural network differential equation bioelectrical signals inverse problems

A Meshless Method for Retrieving Nonlinear Large External Forces on Euler-Bernoulli Beams

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Computers, Materials & Continua 2022年第10期73卷 433-451页

作者： Chih-Wen Chang Department of Mechanical Engineering National United UniversityMiaoli360302Taiwan

We retrieve unknown nonlinear large space-time dependent forces burdened with the vibrating nonlinear Euler-Bernoulli beams under varied boundary data,comprising two-end fixed,cantilevered,clamped-hinged,and simply supported conditions in this *** though some researchers used several schemes to overcome these forward problems of Euler-Bernoulli beams;however,an effective numerical algorithm to solve these inverse problems is still not *** cope with the homogeneous boundary conditions,initial data,and final time datum for each type of nonlinear beam by employing a variety of boundary shape *** unknown nonlinear large external force can be recuperated via back-substitution of the solution into the nonlinear Euler-Bernoulli beam equation when we acquire the solution by utilizing the boundary shape function scheme and deal with a smallscale linear system to gratify an additional right-side boundary *** the robustness and accuracy,we reveal that the current schemes are substantiated by comparing the recuperated numerical results of four instances to the exact forces,even though a large level of noise up to 50%is burdened with the overspecified *** current method can be employed in the online real-time computation of unknown force functions in space-time for varied boundary supports of the vibrating nonlinear beam.

关键词： inverse problems nonlinear Euler-Bernoulli beams ill-posed problems nonlinear space-time dependent force boundary shape functions

A Novel Method for the Reconstruction of Road Profiles from Measured Vehicle Responses Based on the Kalman Filter Method

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Computer Modeling in Engineering & Sciences 2022年第3期130卷 1719-1735页

作者： Jianghui Zhu Xiaotong Chang Xueli Zhang Yutai Su Xu Long School of Automation Northwestern Polytechnical UniversityXi’an710072China School of Mechanics Civil Engineering&ArchitectureNorthwestern Polytechnical UniversityXi’an710072China Chinese Flight Test Establishment Xi’an710089China

The estimation of the disturbance input acting on a vehicle from its given responses is an inverse *** overcome some of the issues related to ill-posed inverse problems,this work proposes a method of reconstructing the road roughness based on the Kalman filter method.A half-car model that considers both the vehicle and equipment is established,and the joint input-state estimation method is used to identify the road *** capabilities of this methodology in the presence of noise are numerically ***,to reduce the influence of the driving speed on the estimation results,a method of choosing the calculation frequency is proposed.A road vibration test is conducted to benchmark the proposed method.

关键词： Road profile reconstruction inverse problems precise integration Kalman filter spatial resolution