One-Shot Transfer Learning for Nonlinear ODEs
Wanzhou Lei Pavlos Protopapas Joy Parikh
We introduce a generalizable approach that combines perturbation method and
one-shot transfer learning to solve nonlinear ODEs with a single polynomial
term, using Physics-Informed Neural Networks (PINNs). Our method transforms
non-linear ODEs into linear ODE systems, trains a PINN across varied
conditions, and offers a closed-form solution for new instances within the same
non-linear ODE class. We demonstrate the effectiveness of this approach on the
Duffing equation and suggest its applicability to similarly structured PDEs and
ODE systems.