Neural Networks for solving Inverse Problems. Applications in Materials Science and Medical Imaging

This thesis is a compound of various works of the author and coworkers on the application of neural networks and deep learning for solving inverse problems. The first application is in Materials Science. The development of new structural materials with desirable properties has become one of the most challenging tasks for engineers. We use Neural Networks to learn how the parameters influence the material properties and focus mainly on solving the corresponding inverse problem. Given desired properties, a material should have, we aim at finding the production parameters we need to obtain it. The second application is in Computed Tomography (CT), which is one of the most valuable technologies in modern medical imaging. It allows a non-invasive acquisition of the inside of the human body using X-rays. In this work, we examine the application of deep learning methods for the reconstruction of CT images in the context of a low-data regime.