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About this paper
Shaan Desai, Marios Mattheakis, Hayden Joy, Pavlos Protopapas, Stephen Roberts
A framework for one-shot transfer learning in Physics-Informed Neural Networks (PINNs) is introduced, enabling rapid, accurate solutions for families of linear differential equations by analytically computing the final layer weights. This approach drastically reduces inference times to milliseconds for thousands of linear ODEs and PDEs, offering substantial computational efficiency over training models from scratch.
Key insights
- A pre-trained PINN can learn a versatile 'latent space' of functions that effectively generalizes across a family of related differential equations.
- For linear systems, the PINN loss function becomes a convex quadratic with respect to the final layer weights, allowing for a direct analytical solution via matrix inversion.
- Freezing the hidden layers and only optimizing the final layer significantly accelerates solution finding, even for nonlinear problems where an analytical solution is not feasible.
Summary by alphaXiv.
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