A Study on Deep Learning Methods for Inverse Scattering Problems

This project aims to explore the application of deep learning methods to inverse scattering problems, addressing the limitations of traditional numerical methods when dealing with nonlinearity, ill-posedness, and data uncertainty. Based on the mathematical model of the inverse scattering problem, the project will design an innovative deep learning framework that integrates physical principles with data-driven approaches to improve model accuracy, generalization capability, and computational efficiency. Specifically, the project will develop neural network architectures tailored to inverse scattering, utilizing multi-frequency iterative strategies and Bayesian inference to progressively enhance reconstruction accuracy and model robustness. Additionally, by analyzing approximation, generalization, and optimization errors in depth, we will explore effective approaches for error control and uncertainty quantification in operator learning. The anticipated outcomes of the project will have broad
applications in medical imaging, geophysical exploration, autonomous driving, and related industries, driving technological innovation. This project will also contribute a solid theoretical and practical foundation for further advancements in inverse scattering, enhancing China's international influence in this field.