Advection Augmented Convolutional Neural Networks
This work addresses the challenge of long-range information propagation and explainability in space-time prediction tasks, such as weather forecasting and disease analysis, with an incremental improvement over existing CNN-based methods.
The authors tackled the problem of predicting space-time sequences in physical sciences by introducing a physically inspired architecture that augments CNNs with advection using a novel semi-Lagrangian push operator, complemented by Reaction and Diffusion components, and demonstrated its effectiveness on spatio-temporal datasets.
Many problems in physical sciences are characterized by the prediction of space-time sequences. Such problems range from weather prediction to the analysis of disease propagation and video prediction. Modern techniques for the solution of these problems typically combine Convolution Neural Networks (CNN) architecture with a time prediction mechanism. However, oftentimes, such approaches underperform in the long-range propagation of information and lack explainability. In this work, we introduce a physically inspired architecture for the solution of such problems. Namely, we propose to augment CNNs with advection by designing a novel semi-Lagrangian push operator. We show that the proposed operator allows for the non-local transformation of information compared with standard convolutional kernels. We then complement it with Reaction and Diffusion neural components to form a network that mimics the Reaction-Advection-Diffusion equation, in high dimensions. We demonstrate the effectiveness of our network on a number of spatio-temporal datasets that show their merit.