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Solving inverse problems using data-driven models. (English) Zbl 1429.65116
Summary: Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical-analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

MSC:
65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
65J22 Numerical solution to inverse problems in abstract spaces
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
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