One-Shot Transfer Learning for Nonlinear ODEs
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Abstract (arXiv)
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.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 8 of its 16 references that are in the map. First posted on arXiv 25 Nov 2023.
Builds on
8 of 16 references.
References · 8
- 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
- 2019DeepXDE: A deep learning library for solving differential equationscited by 619
- 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
- 2019Physical Symmetries Embedded in Neural Networkscited by 40
- 2020Solving Differential Equations Using Neural Network Solution Bundlescited by 21
- 2022Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flowscited by 12
- 2023Residual-based error bound for physics-informed neural networkscited by 9
- 2022Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networkscited by 4
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Citing papers per year: 2025: 2; 2026: 1.
3 papers.