AI Advances in Solving Inverse PDE Problems Reviewed

A recent article on arXiv (2605.16966) examines the application of artificial intelligence in addressing inverse partial differential equation (PDE) challenges, a crucial area in scientific inquiry relevant to fields like medical imaging, geophysics, materials science, and aerodynamics. The authors begin by outlining the fundamental formulation, significant obstacles, and conventional numerical principles associated with inverse PDE issues. They categorize the discipline into three primary segments: inverse problems, inverse design, and control problems. For each segment, they discuss methodological frameworks and evaluate notable contemporary techniques. Additionally, the paper highlights various applications in both scientific and industrial sectors, aiming to present a thorough overview of recent developments and showcasing AI's potential to deduce hidden factors, create designs, or regulate physical states.