The field of wave scattering and inverse problems is witnessing significant developments, driven by innovative numerical methods and theoretical frameworks. Researchers are exploring new approaches to tackle high-frequency wave problems, complex geometries, and multiscale challenges. Notably, the use of neural networks, domain decomposition techniques, and semiclassical analysis is gaining traction. These advancements have the potential to improve the accuracy and efficiency of simulations in various fields, including acoustics, electromagnetism, and seismic analysis.

Some noteworthy papers in this area include: The paper on Bifurcations in Interior Transmission Eigenvalues, which develops a theoretical framework for identifying non-smooth spectral behavior in the interior transmission eigenvalue problem. The work on the modified Physics-Informed Hybrid Parallel Kolmogorov--Arnold and Multilayer Perceptron Architecture, which proposes a novel neural network architecture for solving high-frequency multiscale problems. The Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems, which enables the approximation of internal partial differential equation solutions in media with unknown reflectivity and loss distributions.