One-Shot Transfer Learning for Nonlinear ODEs
This addresses the problem of efficiently solving specific nonlinear ODEs for researchers in computational physics or applied mathematics, but it appears incremental as it builds on existing PINN and transfer learning techniques.
The paper tackles solving nonlinear ODEs with a single polynomial term by combining perturbation methods and one-shot transfer learning with PINNs, achieving a closed-form solution for new instances within the same class, as demonstrated on the Duffing equation.
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.