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arXiv · 2311.14931

One-Shot Transfer Learning for Nonlinear ODEs

Wanzhou Lei·Pavlos Protopapas·Joy Parikh
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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.

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Wanzhou Lei, Pavlos Protopapas, Joy Parikh. 2023-11-25. One-Shot Transfer Learning for Nonlinear ODEs. https://arxiv.org/abs/2311.14931

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