Fully Differentiable Physics-informed Lagrangian Convolutional Neural Network for Precipitation Nowcasting

The task of precipitation nowcasting is often perceived as a computer vision problem. It is analogous to next frame video prediction - i.e. processing consecutive radar precipitation map frames and predicting the future ones. This makes convolutional neural networks (CNNs) a great fit for this task. In the recent years, the CNNs have become the de-facto state-of-the-art model for precipitation nowcasts.

However, a pure machine learning model has difficulties to capture accurately the underlying patterns in the data. Since the data behaves according to the known physical laws, we can incorporate this knowledge to train more accurate and trustworthy models.

We present a double U-Net model, combining a continuity-constrained Lagrangian persistence U-Net with an advection-free U-Net dedicated to capturing the precipitation growth and decay. In contrast to previous works, the combined model is fully differentiable, allowing us to fine-tune these models together in a data-driven way. We examine the learned Lagrangian mappings, along with a thorough quantitative and qualitative evaluation. The results of the evaluation will be provided in the presentation.