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  • Open Access


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

    Jiepeng Yao1,2, Zhanjia Peng1,2, Jingjing Liu1,2, Chengxiao Fan1,2, Zhongyi Wang1,2,3, Lan Huang1,2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2243-2265, 2023, DOI:10.32604/cmes.2023.028101

    Abstract In the establishment of differential equations, the determination of time-varying parameters is a difficult problem, especially for equations related to life activities. Thus, we propose a new framework named BioE-PINN based on a physical information neural network that successfully obtains the time-varying parameters of differential equations. In 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 networks. In this paper, taking the electrophysiological differential… More >

  • Open Access


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

    Chih-Wen Chang*

    CMC-Computers, Materials & Continua, Vol.73, No.1, pp. 433-451, 2022, DOI:10.32604/cmc.2022.027021

    Abstract 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 study. Even 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 available. We 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 functions. The unknown nonlinear large external force can be recuperated via back-substitution of the… More >

  • Open Access


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

    Jianghui Zhu1,3, Xiaotong Chang2, Xueli Zhang2, Yutai Su2, Xu Long2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.3, pp. 1719-1735, 2022, DOI:10.32604/cmes.2022.019140

    Abstract The estimation of the disturbance input acting on a vehicle from its given responses is an inverse problem. To 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 profile. The capabilities of this methodology in the presence of noise are numerically demonstrated. Moreover, to reduce the influence of the driving speed on the estimation results, a method of choosing… More >

  • Open Access


    Mechanics Based Tomography Using Camera Images

    Sevan Goenezen1,*, Ping Luo1, Baik Jin Kim1, Maulik Kotecha1, Yue Mei2,3

    Molecular & Cellular Biomechanics, Vol.16, Suppl.2, pp. 46-48, 2019, DOI:10.32604/mcb.2019.07348

    Abstract It is well known that the mechanical properties of tissues may vary spatially due to changing tissue types or due to inherent tissue disease. For example, the biomechanical properties are known to vary throughout blood vessels [1]. Diseases such as cancers may also lead to locally altered mechanical properties, thus allow a preliminary diagnosis via finger palpation. Quantifying the mechanical property distribution of tissues for a given constitutive equation will allow to characterize the biomechanical response of tissues. This may help to 1) predict disease progression, 2) diagnose diseases that alter the biomechanics of the tissue, e.g., skin cancers, breast… More >

  • Open Access


    Application of Numerical Methods to Elasticity Imaging

    Benjamin Castaneda, Juvenal Ormachea, Paul Rodríguez, Kevin J. Parker§

    Molecular & Cellular Biomechanics, Vol.10, No.1, pp. 43-65, 2013, DOI:10.3970/mcb.2013.010.043

    Abstract Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the viscoelastic properties of tissue in order to provide clinically useful information. As a result, several modalities of elasticity imaging, mostly based on ultrasound but also on magnetic resonance imaging and optical coherence tomography, have been proposed and applied to a number of… More >

  • Open Access


    An Optimal Multi-Vector Iterative Algorithm in a Krylov Subspace for Solving the Ill-Posed Linear Inverse Problems

    Chein-Shan Liu 1

    CMC-Computers, Materials & Continua, Vol.33, No.2, pp. 175-198, 2013, DOI:10.3970/cmc.2013.033.175

    Abstract An optimal m-vector descent iterative algorithm in a Krylov subspace is developed, of which the m weighting parameters are optimized from a properly defined objective function to accelerate the convergence rate in solving an ill-posed linear problem. The optimal multi-vector iterative algorithm (OMVIA) is convergent fast and accurate, which is verified by numerical tests of several linear inverse problems, including the backward heat conduction problem, the heat source identification problem, the inverse Cauchy problem, and the external force recovery problem. Because the OMVIA has a good filtering effect, the numerical results recovered are quite smooth with small error, even under… More >

  • Open Access


    Artificial Neural Network Methods for the Solution of Second Order Boundary Value Problems

    Cosmin Anitescu1, Elena Atroshchenko2, Naif Alajlan3, Timon Rabczuk3,*

    CMC-Computers, Materials & Continua, Vol.59, No.1, pp. 345-359, 2019, DOI:10.32604/cmc.2019.06641

    Abstract We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy. In this procedure, a coarse grid of training points is used at the initial training stages, while more points are added at later stages based on the value of the residual at a larger set of evaluation points. This method increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth. Numerical results are presented for benchmark problems for scalar-valued PDEs, namely Poisson and Helmholtz equations, as well as for an inverse… More >

  • Open Access


    Optimally Generalized Regularization Methods for Solving Linear Inverse Problems

    Chein-Shan Liu1

    CMC-Computers, Materials & Continua, Vol.29, No.2, pp. 103-128, 2012, DOI:10.3970/cmc.2012.029.103

    Abstract In order to solve ill-posed linear inverse problems, we modify the Tikhonov regularization method by proposing three different preconditioners, such that the resultant linear systems are equivalent to the original one, without dropping out the regularized term on the right-hand side. As a consequence, the new regularization methods can retain both the regularization effect and the accuracy of solution. The preconditioned coefficient matrix is arranged to be equilibrated or diagonally dominated to derive the optimal scales in the introduced preconditioning matrix. Then we apply the iterative scheme to find the solution of ill-posed linear inverse problem. Two theorems are proved… More >

  • Open Access


    A Combined Sensitive Matrix Method and Maximum Likelihood Method for Uncertainty Inverse Problems

    W. Zhang1, X. Han1,2, J. Liu1, Z. H. Tan1

    CMC-Computers, Materials & Continua, Vol.26, No.3, pp. 201-226, 2011, DOI:10.3970/cmc.2011.026.201

    Abstract The uncertainty inverse problems with insufficiency and imprecision in the input and/or output parameters are widely existing and unsolved in the practical engineering. The insufficiency refers to the partly known parameters in the input and/or output, and the imprecision refers to the measurement errors of these ones. In this paper, a combined method is proposed to deal with such problems. In this method, the imprecision of these known parameters can be described by probability distribution with a certain mean value and variance. Sensitive matrix method is first used to transform the insufficient formulation in the input and/or output to a… More >

  • Open Access


    Meshless Local Petrov-Galerkin Mixed Collocation Method for Solving Cauchy Inverse Problems of Steady-State Heat Transfer

    Tao Zhang1,2, Yiqian He3, Leiting Dong4, Shu Li1, Abdullah Alotaibi5, Satya N. Atluri2,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.6, pp. 509-533, 2014, DOI:10.3970/cmes.2014.097.509

    Abstract In this article, the Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method is developed to solve the Cauchy inverse problems of Steady- State Heat Transfer In the MLPG mixed collocation method, the mixed scheme is applied to independently interpolate temperature as well as heat flux using the same meshless basis functions The balance and compatibility equations are satisfied at each node in a strong sense using the collocation method. The boundary conditions are also enforced using the collocation method, allowing temperature and heat flux to be over-specified at the same portion of the boundary. For the inverse problems where noise is… More >

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