@inproceedings{
koupa{\"\i}2024boosting,
title={Boosting Generalization in Parametric {PDE} Neural Solvers through Adaptive Conditioning},
author={Armand Kassa{\"\i} Koupa{\"\i} and Jorge Mifsut Benet and Yuan Yin and Jean-No{\"e}l Vittaut and Patrick Gallinari},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=GuY0zB2xVU}
}
Solving parametric partial differential equations (PDEs) presents significant challenges for data-driven methods due to the sensitivity of spatio-temporal dynamics to variations in PDE parameters. Machine learning approaches often struggle to capture this variability. To address this, data-driven approaches learn parametric PDEs by sampling a very large variety of trajectories with varying PDE parameters. We first show that incorporating conditioning mechanisms for learning parametric PDEs is essential and that among them, \textit{adaptive conditioning}, allows stronger generalization. As existing adaptive conditioning methods do not scale well with respect to the number of parameters to adapt in the neural solver, we propose GEPS, a simple adaptation mechanism to boost GEneralization in Pde Solvers via a first-order optimization and low-rank rapid adaptation of a small set of context parameters. We demonstrate the versatility of our approach for both fully data-driven and for physics-aware neural solvers. Validation performed on a whole range of spatio-temporal forecasting problems demonstrates excellent performance for generalizing to unseen conditions including initial conditions, PDE coefficients, forcing terms and solution domain. *Project page*: https://geps-project.github.io
Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioning
Armand Kassaï Koupaï Jorge Mifsut Benet Yuan Yin Jean-Noël Vittaut Patrick Gallinari