Accurate high-altitude wind forecasting is important for air traffic control. And the large volume of data available for this task makes deep neural network-based models a possibility. However, special methods are required because the data is measured only sparsely: along the main aircraft trajectories and arranged sparsely in space, namely along the main air corridors. Several deep learning approaches have been proposed, and in this work, we show that Transformers can fit this data efficiently and are able to extrapolate coherently from a context set. We show this by an extensive comparison of Transformers to numerous existing deep learning-based baselines in the literature. Besides high-altitude wind forecasting, we compare competing models on other dynamical physical systems, namely those modelled by partial differential equations, in particular the Poisson equation and Darcy Flow equation. For these experiments, in the case where the data is arranged non-regularly in space, Transformers outperform all the other evaluated methods. We also compared them in a more standard setup where the data is arranged on a grid and show that the Transformers are competitive with state-of-the-art methods, even though it does not require regular spacing. The code and datasets of the different experiments will be made publicly available at publication time.

翻译：精确的高空风预报对于空中交通控制非常重要。 用于这项任务的大量数据使得基于深神经网络的模型成为可能。 但是,需要特殊的方法,因为这些数据的测量很少:在主要飞行器轨道上,在空间,即主要空气走廊上,安排得很少。 已经提出了几种深层次的学习方法, 在这项工作中,我们表明变换器能够有效地适应这些数据,并且能够从一个上下文集中连贯地推断出来。 我们通过将变换器与文献中现有的许多深层学习基线进行广泛的比较来显示这一点。 除了高空风预报,我们还比较其他动态物理系统上的竞争模型,即按部分差异方程,特别是Poisson方程和适量流动方程模拟的模型。 对于这些实验,如果数据是非经常性地在空间进行,变换器比其他所有经过评估的方法都好。 我们还在更标准的设置中比较了它们,其中将数据放在一个网格上,显示变换器与现有的大量深学习基线有竞争力。 尽管数据并不需要定期公布,但数据需要定期公布。