The method of perturbation and curriculum learning in Physics-Informed Neural Networks

The talk introduced Perturbative Learning PINNs (PL-PINNs), which train a neural network to learn only the correction $\psi$ to a known base solution $v$, writing the total solution as $u=v+\psi$. The core method is a continuation-based training strategy that gradually shifts the problem from a simple, solvable regime to the complex, nonlinear target problem, thereby avoiding poor local minima. A hybrid scaling strategy was also detailed, allowing the method to transition from high, perturbation-level accuracy in simple cases to flexible, adaptive learning in highly nonlinear regimes. Overall, PL-PINNs solve challenging nonlinear problems, like the Gross–Pitaevskii equation, more efficiently and robustly than standard PINNs.