GEPS: Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioning - Sorbonne Université
Conference Papers Year : 2024

GEPS: Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioning

Abstract

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. $\textit{Project page}$: https://geps-project.github.io
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hal-04764272 , version 1 (03-11-2024)

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Armand Kassaï Koupaï, Jorge Mifsut Benet, Yuan Yin, Jean-Noël Vittaut, Patrick Gallinari. GEPS: Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioning. Thirty-eight Conference on Neural Information Processing Systems (NeurIPS 2024), Dec 2024, Vancouver, Canada. ⟨hal-04764272⟩
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