Machine Learning Solutions for Inverse Problems: Part B

Machine Learning Solutions for Inverse Problems: Part B, Volume 27 in the Handbook of Numerical Analysis, continues the exploration of emerging approaches at the intersection of machine learning and inverse problem theory. This volume presents a collection of chapters addressing a wide range of contemporary topics, including deep image prior methods for computed tomography, data-consistent learning strategies, and unified frameworks for training and inversion in machine learning-based reconstruction methods.

Additional chapters examine learned regularization techniques, generative models for inverse problems, and the integration of deep learning with traditional computational frameworks such as full waveform inversion and PDE-based inverse modeling. The volume also discusses advances in self-supervised learning, data selection strategies, plug-and-play denoising methods, and diffusion models for solving imaging inverse problems.

Further contributions explore neural network representations, operator learning, and learned iterative schemes, along with theoretical perspectives on stability, approximation hardness, hallucinations, and trustworthiness in AI-driven inverse problem methodologies. Together, these chapters provide a comprehensive overview of current developments in machine learning approaches to inverse problems, offering valuable insights for researchers in numerical analysis, computational mathematics, and scientific computing.

• Presents the latest developments in machine learning approaches for solving inverse problems
• Explores modern techniques including deep learning, generative models, diffusion models, and operator learning
• Covers applications in imaging, tomography, and PDE-based inverse modeling
• Includes theoretical perspectives on stability, approximation hardness, and trustworthiness in AI for inverse problems
• Serves as a comprehensive reference for researchers in numerical analysis, computational mathematics, and scientific computing