# One-Shot Transfer Learning for Nonlinear ODEs

arXiv: https://arxiv.org/abs/2311.14931 · HTML: https://mlsanity.com/paper/2311.14931/

## 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 (most cited first, 8 of 8)

- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)
- [Physical Symmetries Embedded in Neural Networks](https://mlsanity.com/paper/1904.08991/) (2019)
- [Solving Differential Equations Using Neural Network Solution Bundles](https://mlsanity.com/paper/2006.14372/) (2020)
- [Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows](https://mlsanity.com/paper/2211.00214/) (2022)
- [Residual-based error bound for physics-informed neural networks](https://mlsanity.com/paper/2306.03786/) (2023)
- [Error-Aware B-PINNs: Improving Uncertainty Quantification in Bayesian Physics-Informed Neural Networks](https://mlsanity.com/paper/2212.06965/) (2022)

## Built on by (most cited first, 3 of 3)

- [Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space](https://mlsanity.com/paper/2501.12116/) (2025)
- [IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation](https://mlsanity.com/paper/2509.07245/) (2025)
- [Chebyshev-Augmented One-Shot Transfer Learning for PINNs on Nonlinear Differential Equations](https://mlsanity.com/paper/2605.01634/) (2026)

## 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.