One-Shot Transfer Learning for Nonlinear 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.
Cite
Text
Lei et al. "One-Shot Transfer Learning for Nonlinear ODEs." NeurIPS 2023 Workshops: DLDE, 2023.Markdown
[Lei et al. "One-Shot Transfer Learning for Nonlinear ODEs." NeurIPS 2023 Workshops: DLDE, 2023.](https://mlanthology.org/neuripsw/2023/lei2023neuripsw-oneshot/)BibTeX
@inproceedings{lei2023neuripsw-oneshot,
title = {{One-Shot Transfer Learning for Nonlinear ODEs}},
author = {Lei, Wanzhou and Protopapas, Pavlos and Parikh, Joy},
booktitle = {NeurIPS 2023 Workshops: DLDE},
year = {2023},
url = {https://mlanthology.org/neuripsw/2023/lei2023neuripsw-oneshot/}
}