@inproceedings{
lei2023oneshot,
title={One-Shot Transfer Learning for Nonlinear {ODE}s},
author={Wanzhou Lei and Pavlos Protopapas and Joy Parikh},
booktitle={The Symbiosis of Deep Learning and Differential Equations III},
year={2023},
url={https://openreview.net/forum?id=mcIbqPMKCU}
}
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.
One-Shot Transfer Learning for Nonlinear ODEs
Wanzhou Lei Pavlos Protopapas Joy Parikh