One-Shot Transfer Learning for Nonlinear ODEs

TL;DR

This paper presents a novel one-shot transfer learning method using Physics-Informed Neural Networks to efficiently solve nonlinear ODEs by transforming them into linear systems, enabling quick adaptation to new problem instances.

Contribution

It introduces a generalizable approach combining perturbation and transfer learning with PINNs for nonlinear ODEs, providing a closed-form solution for new cases within the same class.

Findings

Effective on the Duffing equation

Transforms nonlinear ODEs into linear systems

Applicable to similar PDEs and ODEs

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.