Communication Dans Un Congrès Année : 2024

Zebra: In-Context Generative Pretraining for Solving Parametric PDEs

Louis Serrano
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Armand Kassaï Koupaï
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Thomas Wang
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Pierre Erbacher
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Résumé

Solving time-dependent parametric partial differential equations (PDEs) is challenging for data-driven methods, as these models must adapt to variations in parameters such as coefficients, forcing terms, and initial conditions. State-of-the-art neural surrogates perform adaptation through gradient-based optimization and meta-learning to implicitly encode the variety of dynamics from observations. This often comes with increased inference complexity. Inspired by the in-context learning capabilities of large language models (LLMs), we introduce Zebra, a novel generative auto-regressive transformer designed to solve parametric PDEs without requiring gradient adaptation at inference. By leveraging in-context information during both pre-training and inference, Zebra dynamically adapts to new tasks by conditioning on input sequences that incorporate context example trajectories. As a generative model, Zebra can be used to generate new trajectories and allows quantifying the uncertainty of the predictions. We evaluate Zebra across a variety of challenging PDE scenarios, demonstrating its adaptability, robustness, and superior performance compared to existing approaches.

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hal-05234209 , version 1 (04-09-2025)

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Louis Serrano, Armand Kassaï Koupaï, Thomas Wang, Pierre Erbacher, Patrick Gallinari. Zebra: In-Context Generative Pretraining for Solving Parametric PDEs. ICML 2025, Jul 2025, Vancouver (BC), Canada. ⟨10.48550/arXiv.2410.03437⟩. ⟨hal-05234209⟩
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