Michael Hintermüller - Böcker

Machine Learning Solutions for Inverse Problems: Part A, Volume 26 in the Handbook of Numerical Analysis, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Data-Driven Approaches for Generalized Lasso Problems, Implicit Regularization of the Deep Inverse Prior via (Inertial) Gradient Flow, Generalized Hardness of Approximation, Hallucinations, and Trustworthiness in Machine Learning for Inverse Problems, Energy-Based Models for Inverse Imaging Problems, Regularization Theory of Stochastic Iterative Methods for Solving Inverse Problems, and more.Other sections cover Advances in Identifying Differential Equations from Noisy Data Observations, The Complete Electrode Model for Electrical Impedance Tomography: A Comparative Study of Deep Learning and Analytical Methods, Learned Iterative Schemes: Neural Network Architectures for Operator Learning, Jacobian-Free Backpropagation for Unfolded Schemes with Convergence Guarantees, and Operator Learning Meets Inverse Problems: A Probabilistic PerspectiveProvides the authority and expertise of leading contributors from an international board of authorsPresents the latest release in the Handbook of Numerical Analysis seriesUpdated release includes the latest information on the Machine Learning Solutions for Inverse Problems

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 problemsExplores modern techniques including deep learning, generative models, diffusion models, and operator learningCovers applications in imaging, tomography, and PDE-based inverse modelingIncludes theoretical perspectives on stability, approximation hardness, and trustworthiness in AI for inverse problemsServes as a comprehensive reference for researchers in numerical analysis, computational mathematics, and scientific computing

This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017.

This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017.

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems.

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems.