We show that AI foundation models that are pretrained on numerical solutions to a diverse corpus of partial differential equations can be adapted and fine-tuned to obtain skillful predictive weather emulators for the Martian atmosphere. We base our work on the Poseidon PDE foundation model for two-dimensional systems. We develop a method to extend Poseidon from two to three dimensions while keeping the pretraining information. Moreover, we investigate the performance of the model in the presence of sparse initial conditions. Our results make use of four Martian years (approx.~34 GB) of training data and a median compute budget of 13 GPU hours. We find that the combination of pretraining and model extension yields a performance increase of 34.4\% on a held-out year. This shows that PDEs-FMs can not only approximate solutions to (other) PDEs but also anchor models for real-world problems with complex interactions that lack a sufficient amount of training data or a suitable compute budget.

翻译：我们证明，通过对偏微分方程多样化数值解进行预训练的人工智能基础模型，可以经过适配与微调，获得对火星大气具有高预测技能的天气模拟器。本研究基于面向二维系统的Poseidon偏微分方程基础模型开展工作。我们提出了一种将Poseidon从二维扩展至三维的方法，同时保留其预训练信息。此外，我们探究了模型在稀疏初始条件下的性能表现。我们的实验结果利用了四个火星年（约34 GB）的训练数据及13 GPU小时的中位数计算预算。研究发现，预训练与模型扩展相结合可使模型在预留年份数据上的性能提升34.4%。这表明偏微分方程基础模型不仅能够逼近（其他）偏微分方程的解，还能作为锚定模型应用于那些训练数据不足、计算预算有限但具有复杂相互作用的现实问题。