Comparison of three recent discrete stochastic inversion methods and influence of the prior choice by Juda, Przemysław, Straubhaar, Julien, Renard, Philippe

“…In such cases, solving a categorical inverse problem is an important step in subsurface modeling. …”
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Determination of a nonlinear source term in a diffusion equation with final observations by Gongsheng Li, Yichen Ma, Kaitai Li

“…This paper deals with an inverse problem of determining a nonlinear source term in a quasilinear diffusion equation with overposed final observations. …”
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Shape Reconstruction for Unsteady Advection-Diffusion Problems by Domain Derivative Method by Wenjing Yan, Jian Su, Feifei Jing

“…By the parametric method, a regularized Gauss-Newton scheme is employed to the shape inverse problem. Numerical examples indicate that the proposed algorithm is feasible and effective for the practical purpose.…”
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Numerical algorithm for solving parabolic identification problem with mixed boundary condition by Charyyar Ashyralyyev, Tazegul Ashyralyyeva

“…Numerical algorithm for solving this inverse problem are proposed. Stability estimates for difference schemes are established. …”
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Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem by Lung-Hui Chen

“…We consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. …”
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OPTIMIZATION METHOD OF DYNAMIC LOAD IDENTIFICATION BASED ON GENETIC ALGORITHM by XI ZhuYou, YAN YunJu, CHANG XiaoTong

“…In the proposed method,the dynamics inverse problem was converted into the structural dynamics analysis and calculation,this can overcome the disadvantages of illconditioned matrix inverse,accumulated error and sensitive to initial conditions,etc. …”
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Application of finite-difference methods to parameter identification of agroecological models by Natalija Juščenko, Vitalijus Denisov

“… A typical parameter identification problem arisen in agroecological modeling is described and a finite difference method to solve an appropriate inverse problem is proposed. The method sup­poses the direct solution of an initial-boundary problem by finite difference scheme and then uses a non-linear optimization routine for parameter estimation. …”
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Regularization of Inverse Initial Problem for Conformable Pseudo-Parabolic Equation with Inhomogeneous Term by L. D. Long, Reza Saadati

“…Our paper is the first work to investigate the inverse problem for conformable parabolic equations in such spaces. …”
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Inverse Estimates for Nonhomogeneous Backward Heat Problems by Tao Min, Weimin Fu, Qiang Huang

“…We investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. …”
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Uniqueness in Inverse Electromagnetic Conductive Scattering by Penetrable and Inhomogeneous Obstacles with a Lipschitz Boundary by Fenglong Qu

“…The well posedness of the direct problem is established by the variational method. The inverse problem is also considered in this paper. Under certain assumptions, a uniqueness result is obtained for determining the shape and location of the obstacle and the corresponding surface parameter λ(x) from the knowledge of the near field data, assuming that the incident fields are electric dipoles located on a large sphere with polarization p∈ℝ3. …”
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Bioluminescence in cancer research - Applications and challenges by Shrikant B. Mali

“…Reconstruction approaches, whether mathematical or AI-based, seek to solve the inverse problem based on optical characteristics and tissue behaviour. …”
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On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients by A. De Cezaro

“…In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. …”
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Structural Damage Detection Based on Modal Parameters Using Continuous Ant Colony Optimization by Aditi Majumdar, Bharadwaj Nanda, Dipak Kumar Maiti, Damodar Maity

“…A method is presented to detect and quantify structural damages from changes in modal parameters (such as natural frequencies and mode shapes). An inverse problem is formulated to minimize the objective function, defined in terms of discrepancy between the vibration data identified by modal testing and those computed from analytical model, which then solved to locate and assess the structural damage using continuous ant colony optimization algorithm. …”
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Nouvelle méthodologie d’analyse bayésienne du report des voix et de l’abstention lors du deuxième tour des élections by Girondot, Marc

“…The information from the counts of the first and second rounds is used to model voter behavior as an inverse problem solved using a Bayesian approach. It is then possible to estimate the flow of votes between the first and the second round with very good precision and to provide the objective bases which will serve for an objective political or sociological analysis.…”
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Determining interaction directionality in complex biochemical networks from stationary measurements by N. Leibovich

“…Abstract Revealing interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Some methods may reveal undirected network topology, e.g., using node-node correlation. …”
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Quantitative estimating size of deep defects in multi-layered structures from eddy current NDT signals using improved ant colony algorithm by Bo Ye, Ming Li, Gefei Qiu, Jun Dong, Fang Zeng

“…The method uses a finite element forward model to simulate the underlying physical process and an improved ant colony algorithm (IACA) to solve the inverse problem. Experiments are carried out. The performance comparison between the IACA method and the least square method is shown. …”
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Bayesian Analysis for a Fractional Population Growth Model by Francisco J. Ariza-Hernandez, Jorge Sanchez-Ortiz, Martin P. Arciga-Alejandre, Luis X. Vivas-Cruz

“…We implement the Bayesian statistical inversion theory to obtain the solution for an inverse problem of growth data, using a fractional population growth model. …”
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Calibration of the Volatility in Option Pricing Using the Total Variation Regularization by Yu-Hua Zeng, Shou-Lei Wang, Yu-Fei Yang

“…Identifying the implied volatility is a typical PDE inverse problem. In this paper, based on the total variation regularization strategy, a bivariate total variation regularization model is proposed to estimate the implied volatility. …”
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A Test Matrix for an Inverse Eigenvalue Problem by G. M. L. Gladwell, T. H. Jones, N. B. Willms

“…An explicit solution of a spring-mass inverse problem incorporating the test matrix is provided.…”
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GPU-Accelerated Finite Element Method for Modelling Light Transport in Diffuse Optical Tomography by Martin Schweiger

“…The forward model is the computationally most expensive component of iterative methods for image reconstruction in diffuse optical tomography, and performance optimisation of the forward solver is therefore crucial for improving the efficiency of the solution of the inverse problem. The GPU forward solver uses a CUDA implementation that evaluates on the graphics hardware the sparse linear system arising in the finite element formulation of the diffusion equation. …”
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