The field of inverse analysis and imaging is moving towards the development of more efficient and accurate methods for solving complex problems. Researchers are focusing on improving the performance of Bayesian inverse analysis, particularly in high-dimensional spaces, by leveraging simpler and computationally cheaper models. Another area of focus is the development of new algorithms for image reconstruction in multispectral computed tomography, which can accurately and effectively reconstruct images in the presence of geometric inconsistencies. Furthermore, there is a growing interest in uncertainty quantification and the development of probabilistic models for discretization error in finite element methods. Notable papers in these areas include:

• A novel inference approach that leverages multi-fidelity models to solve Bayesian inverse problems in high-dimensional spaces.
• An accurate and fast image reconstruction algorithm for geometric-inconsistency multispectral CT.
• A method for estimating probability densities in multiple dimensions that takes into account detector sensitivity.
• A comparison of probabilistic models for discretization error in inverse problems, highlighting the benefits of the Bayesian finite element method.
• An improved finite element modeling method for triply periodic minimal surface structures, which exhibits superior mesh convergence and solution accuracy.