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Workshop: The Symbiosis of Deep Learning and Differential Equations -- III

One-Shot Transfer Learning for Nonlinear ODEs

Wanzhou Lei · Pavlos Protopapas · Joy Parikh

Keywords: [ perturbation method ] [ duffing equation ] [ ODEs ] [ nonlinear ] [ transfer learning ] [ One-shot ]


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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