Learning Physics from an Imperfect Ancestor: Joint Failure Mode Resolution for Neural Operators and PINNs

This paper addresses two critical failure modes in scientific machine learning for PDEs: neural operators degrade sharply outside their training distribution, while PINNs may converge to physically incorrect solutions when the governing residual admits multiple solutions. The authors propose a joint approach where an imperfect neural operator guides PINN training to avoid these pitfalls, combining the cost efficiency of neural operators with the label-free flexibility of physics-informed learning.