Inverse Problems: Modelling and Simulation

Alemdar Hasanov Hasanoğlu is a professor of mathematics at Kocaeli University in Türkiye.Roman Novikov is a Directeur de recherche at CNRS-Centre National de la Recherche Scientifique at École polytechnique CMAP-Centre de Mathématiques Appliquées, France.Karel Van Bockstal is a post-doctoral researcher (Ghent Analysis & PDE Center) at the Department of Mathematics: Analysis, Logic and Discrete Mathematics of Ghent University, Belgium.

• - Part I: Detection Methods.- 1. Determination of cavities in nonlinear parabolic systems arising from electrophysiology.- 2. Source detection on a network: numerical considerations.- 3. Resonator-Based Mass Detection in Nanostructures.- 4. Exploring instabilities of inverse problem solvers with low-dimensional manifolds.- 5. The multifrequency topological derivative method as a data processing tool in nondestructive testing.- 6. Motion Detection in Diffraction Tomography.- Part II: Geometric Inverse Problems.- 7. Survey on Broken Ray Transforms.- 8. Inverse Problems for Twisted Geodesic Flows.- 9. Applications of momentum ray transforms in inverse problems.- Part III: Inverse and Control Problems in Vibrating Structures.- 10. On the use of a roving harmonic load to locate cracks in shear deformable beam.- 11. Identification of out-of-plane loads over Timoshenko beams.- 12. Inverse Source Problems of Damped Vibrating Beam and Plate Models.- Part IV: Inverse Problems and Imaging.- 13. Higher order autocorrelations.- 14. Inverse Problems in Image Restoration.- 15. A Counterexample to Convergence for Multiscale.- 16. Three-dimensional brassiere design for electrical impedance tomography and numerical conductivity reconstructions in EIDORS.- 17. Permittivity Estimation Using Plasmonics.- Part V: Inverse problems and Regularisation.- 18. On Fourier Phase Retrieval by Differential Intensity Measurements in Finite Dimensions.- 19. Bi-level regularization via iterative mesh refinement for aeroacoustics.- Part VI: Inverse Problems for Fractional Equations.- 20. The Inverse Problem for the Fractional Conductivity.- 21. Inverse problems for simultaneous determination of source terms and several scalar parameters of fractional diffusion equations.- 22. A local uniqueness theorem for the fractional Schr¨odinger equation on closed Riemannian manifolds.- 23. Time-fractional diffusion equations of piecewise constant time-varying order.- Part VII: Inverse Problems for PDEs.- 24. A global optimum-informed greedy algorithm for A-optimal experimental design.- 25. Multi-dimensional operators with Sonine kernels.- 26. Numerical Reconstruction of Orders in Coupled Systems of Subdiffusion Equations.- 27. Inverse problems for a wave equation with an interface.- 28. New derivation of relaxation tensor for anisotropic extended Burgers model.- 29. Inverse Problems for Screens.- 30. Shearlet localization operator and microlocal analysis.- 31. Strong Unique Continuation for the Damped Wave.- Part VIII: Inverse Scattering Problems.- 32. Reduced Order Lippmann-Schwinger-Lanczos Inverse Scattering Method.- 33. Transparent scatterers and transmission eigenvalues.- 34. On passive inverse obstacle scattering problems with Neumann and Robin boundary conditions.- 35. New series representations and reconstruction techniques in coefficient inverse problems.- 36. A method to extrapolate the data for the inverse magnetisation problem with a planar sample.- 37. Lippmann-Schwinger-Lanczos approach for inverse scattering problem of Schrödinger equation in the resonance frequency domain.- Part IX: Machine Learning.- 38. Quantum-inspired classification algorithms.- Part X: Radon Transforms and Applications.- 39. Geometry of domains and algebraic type of their Radon transforms.- 40. Remarks on the Interior Problem for the Radon transform.- 41. Range conditions for some divergent-beam transforms.- 42. Super-resolution reconstruction from truncated Hankel transform.- Part XI: Stochastic Problems and Bayesian Inversion.- 43. Inverse stochastic variational formulation for a control economic equilibrium problem.- 44. Sampling in Bayesian inversion accelerated by surrogate models.