One-Shot Transfer Learning for Nonlinear ODEs
W Lei, P Protopapas, J Parikh - arXiv preprint arXiv:2311.14931, 2023 - arxiv.org
W Lei, P Protopapas, J Parikh
arXiv preprint arXiv:2311.14931, 2023•arxiv.orgWe 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 …
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 …
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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