One-Shot Transfer Learning for Nonlinear ODEs

Wanzhou Lei, Pavlos Protopapas, Joy Parikh

Keywords: nonlinear, ODEs, transfer learning, one-shot, perturbation method, duffing equation

TL;DR: We introduce a generalizable approach that combines perturbation method and one-shot transfer learning to solve nonlinear ODEs, using Physics-Informed Neural Networks (PINNs).

Abstract: 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.

Submission Number: 15