Accurate Extrinsic Prediction of Physical Systems Using Transformers

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.