AI tackles one of math's most brutal problems: Inverse PDEs - Phys.org

The approach avoids recursive automatic differentiation, a computationally expensive component of traditional methods. The engineers report that the method stabilises the optimisation loop and is efficient, scalable, and generalisable.

Inverse PDEs are used in fields such as medical imaging and geophysics to infer unknown parameters from observed data. They are difficult because they require repeatedly solving forward PDEs, which is computationally prohibitive. The new method eliminates the need for recursive differentiation, potentially reducing computational load. The researchers published results on benchmark problems demonstrating the method's effectiveness.

The development represents an advance in applying AI to scientific computing. However, the method's performance on real-world, high-dimensional problems remains to be demonstrated. The work was published in a peer-reviewed journal and has been covered by Phys.org.