How AI is solving hidden-cause problems in physics and engineering

Inverse PDE problems ask: given observations, what hidden parameters or designs produced them? This survey organizes recent AI approaches into three categories: inverse problems (inferring causes from data), inverse design (optimizing structure for desired outcomes), and control (managing physical states). Applications span medical imaging, geophysics, aerodynamics, and thermal systems. The review identifies emerging challenges including physics-informed architectures, handling sparse real-world data, quantifying uncertainty, and developing foundation models for inverse problems.