Advection Augmented Convolutional Neural Networks

TL;DR

This paper introduces a physically inspired neural network architecture that augments CNNs with advection to improve long-range information propagation and explainability in space-time sequence prediction tasks.

Contribution

The authors propose a novel semi-Lagrangian push operator to incorporate advection into CNNs, mimicking Reaction-Advection-Diffusion equations for better physical modeling.

Findings

Enhanced long-range information propagation in predictions.

Improved explainability of the neural network model.

Effective performance on multiple spatio-temporal datasets.

Abstract

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.