Gen Nakamura is currently Harim Professor at Inha University, S. Korea, and Professor Emeritus of Hokkaido University, Japan. Roland Potthast currently leads the division for data assimilation at the German Meteorological Service, Frankfurt/Offenbach, with a part-time professorship in mathematics at the University of Reading, UK.

• 1 Introduction 2 Functional analytic tools 3 Approaches to regularization 4 A stochastic view of inverse problems 5 Dynamical systems inversion and data assimilation 6 Programming of numerical algorithms and useful tools 7 Neural field inversion and kernel reconstruction 8 Simulation of waves and fields 9 Nonlinear operators 10 Analysis: uniqueness, stability and convergence questions 11 Source reconstruction and magnetic tomography 12 Field reconstruction techniques 13 Sampling methods 14 Probe methods 15 Analytic continuation tests 16 Dynamical sampling and probe methods 17 Targeted observations and meta-inverse problems

Gen Nakamura is currently Harim Professor at Inha University, S. Korea, and Professor Emeritus of Hokkaido University, Japan. Roland Potthast currently leads the division for data assimilation at the German Meteorological Service, Frankfurt/Offenbach, with a part-time professorship in mathematics at the University of Reading, UK.

• 1 Introduction 2 Functional analytic tools 3 Approaches to regularization 4 A stochastic view of inverse problems 5 Dynamical systems inversion and data assimilation 6 Programming of numerical algorithms and useful tools 7 Neural field inversion and kernel reconstruction 8 Simulation of waves and fields 9 Nonlinear operators 10 Analysis: uniqueness, stability and convergence questions 11 Source reconstruction and magnetic tomography 12 Field reconstruction techniques 13 Sampling methods 14 Probe methods 15 Analytic continuation tests 16 Dynamical sampling and probe methods 17 Targeted observations and meta-inverse problems