Data driven approaches for nonlinear inverse problems

The project aims to develop new techniques for solving complex inverse problems that arise in various scientific fields. In many real-world applications, such as medical imaging, geophysics, and material science, we often seek to recover the hidden properties of a system from indirect and noisy measurements. However, the inverse problems associated with these measurements are often nonlinear and ill-posed, making it challenging to obtain accurate and reliable solutions. The proposed project focuses on the use of data-driven methods to address these challenges. Data-driven methods refer to a class of techniques that rely on the analysis of large datasets to learn the underlying structure of the system and make predictions based on this learned knowledge. Specifically, the project aims to investigate the use of machine learning models to solve nonlinear inverse problems. The project involves the development of novel algorithms that can handle complex nonlinearities, account for uncertainties in the measurements, and generalize well to unseen data. The algorithms will be evaluated on a variety of benchmark problems and real-world applications, including medical imaging, seismic inversion, and material science. The ultimate goal of the project is to provide a new set of tools for solving challenging inverse problems that can lead to breakthroughs in various scientific fields.