  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.
