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.

中文翻译：

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使用数据驱动模型解决逆问题

最近对逆问题的研究旨在为将数据驱动模型（尤其是基于深度学习的模型）与物理分析模型中包含的特定领域知识结合起来建立数学上连贯的基础。重点是解决不适定逆问题，这些问题是自然科学、医学和生命科学以及工程和工业应用中许多具有挑战性的应用的核心。这份调查报告旨在说明数据驱动的逆问题中的一些主要贡献。