Solving time-dependent parametric partial differential equations (PDEs) is challenging, as models must adapt to variations in parameters such as coefficients, forcing terms, and boundary conditions. Data-driven neural solvers either train on data sampled from the PDE parameters distribution in the hope that the model generalizes to new instances or rely on gradient-based adaptation and meta-learning to implicitly encode the 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 trajectories or preceding states. This approach enables Zebra to flexibly handle arbitrarily sized context inputs and supports uncertainty quantification through the sampling of multiple solution trajectories. We evaluate Zebra across a variety of challenging PDE scenarios, demonstrating its adaptability, robustness, and superior performance compared to existing approaches.

本研究解决了在求解时变参数偏微分方程（PDE）时面临的模型适应性挑战。通过引入一种新颖的生成自回归变换器Zebra，该方法利用上下文信息进行预训练和推断，免去梯度适应的需要。结果表明，Zebra在多种复杂PDE场景中展现出更强的适应性和鲁棒性，相比现有方法具有显著的性能提升。

斑马：用于求解参数偏微分方程的上下文和生成预训练