Manuscript Topics

Inverse problems and their applications in the fields of imaging and material science constitute a crucial area of research. This domain focuses on the retrieval of unknown properties or parameters from observed data, or designing of specific materials to achieve spcial outcomes. In imaging, inverse problems play a pivotal role in developing advanced techniques for reconstructing high-resolution images from limited or noisy data. This includes applications in medical imaging, such as computed tomography (CT) and magnetic resonance imaging (MRI), where inverse problems are used to reconstruct internal structures of the body from external measurements. Similarly, in seismic imaging, inverse problems are employed to create detailed maps of the Earth's interior from seismic wave data. In material science, inverse problems are utilized to deduce material properties, such as conductivity, permeability, and elasticity, from experimental measurements. This is particularly important in the development of new materials and the understanding of material behavior under various conditions. For instance, inverse problems can be used to analyze the microstructure of materials and predict their macroscopic properties, which is essential for applications ranging from aerospace engineering to biomedical devices.

The range of pertinent topics for this Special Issue encompasses, but is not exhaustive of, the following:
• Theoretical frameworks and methodologies for tackling inverse problems in mathematical physics;
• Practical applications of inverse problems spanning nondestructive evaluation, seismic imaging, medical imaging, and materials science;
• Exploration of uniqueness and stability attributes of solutions to inverse problems;
• Numerical approaches for solving inverse problems, incorporating iterative procedures, optimization algorithms, and regularization methodologies;
• Emerging advancements and innovative strategies in the realm of inverse problems and numerical computation;
• Inverse problems examined within specific mathematical physics contexts, such as stratified media, impedance, gravimetry, and thermal conduction;
• Mathematical analysis for metamaterials and related applications;
• Deep learning methodologies for addressing inverse problems or numerical computation in mathematical physics, encompassing neural network designs, training paradigms, and applications across diverse domains.

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