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Mathematical Theory and Simulation Algorithms for Inverse Problems

Submission Deadline: 31 May 2025 View: 21 Submit to Special Issue

Guest Editors

Prof. Chih-Wen Chang

Email: cwchang@nuu.edu.tw

Affiliation: Department of Mechanical Engineering, National United University, Miaoli 360302, Taiwan

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Research Interests: Computer-aided Analysis, Smart Manufacturing, Artificial Intelligence Algorithms, Numerical Engineering Analysis, Computational Mechanics, Parameter Identification, Energy Engineering

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Prof. Ming-Fong Tsai

Email: mingfongtsai@gmail.com

Affiliation: Department of Electronic Engineering, National United University, Miaoli, Taiwan

Homepage:

Research Interests: Artificial Intelligence Algorithms, Intelligent Networks, Embedded Systems 

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Summary

Inverse problems are presently becoming more and more important in many fields of science and engineering and they typically result in mathematical models that are not well-posed in the sense of mathematician Hadamard. In other words, it means that one or more of the following properties do not hold: for all admissible data, a solution exists; for all admissible data, the solution is unique; the solution depends continuously on the data. Problems that fail to meet these prerequisites are said to be ill-posed. Inverse problems have been revealed as an unknown property of an object from their experimentation or observation. Inverse problems can also be defined as problems where all results are found when a part of them is known, and some boundaries or reasons may linger unknown. Such problems are much more difficult to solve than direct ones.

 

Inverse problems conform to the CMES journal's ideology as they are the opposite of the associated forward issue.

 

Inverse problems have a wide range of applications, including mechanics, heat conduction, acoustics, communication theory, signal processing, optics, semiconductors, medical imaging, nondestructive testing, physics, systems biology, finance, robotics, computer vision, radar, remote sensing, oceanography, thermoelastics, geophysics, and groundwater.

 

This Special Issue of CMES concentrates on the present mathematical theory and simulation regarding inverse problems and how they relate to their applications in engineering and science.


Keywords

inverse problems; numerical analysis; mathematical modeling; fractional problems; ordinary/partial differential equations; meshless methods; applications

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