PINNs in More General Geometry
For researchers in computational geometry, this is an incremental application of existing PINN methods to geometric problems.
This paper introduces PINN architecture principles for differential geometry problems, demonstrating their use via three works. No concrete numerical results are provided.
Neural architectures trained with losses inspired by differential conditions are the basis for PINN models. Since many constructions in differential geometry may be framed as minimisation of a differential functional, these functionals can be coded as loss functions to align the AI loss-minimisation goal with that of solving the geometric problem. This contribution to the Recent Progress in Computational String Geometry workshop proceedings introduces the PINN architecture defining principles, motivates how they are well suited for problems in differential geometry, and demonstrates their use via summaries of three works at this intersection.