Advection Augmented Convolutional Neural Networks (ADR-Net)

Authors: Niloufar Zakariaei, Siddharth Rout, Eldad Haber, Moshe Eliasof

Conference: 38th Annual Conference on Neural Information Processing Systems (NeurIPS 2024)

Preprint: ArXiv

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Abstract

Many problems in the physical sciences involve the prediction of space-time sequences, such as weather forecasting, disease propagation, and video prediction. Traditional approaches using Convolutional Neural Networks (CNNs) combined with time-prediction mechanisms often struggle with long-range information propagation and lack explainability. To address these issues, we propose a novel architecture that augments CNNs with advection using a semi-Lagrangian push operator. This operator enables the non-local transformation of information, which is particularly beneficial in problems requiring rapid information transport across an image. We combine this operator with reaction and diffusion components to form a network that mirrors the Reaction-Advection-Diffusion (ADR) equation. We demonstrate the superior performance of this approach on various spatio-temporal datasets.

Key Contributions

1. Advection-Augmented Architecture: We introduce a physically inspired network that augments CNNs with a semi-Lagrangian push operator to model advection, allowing for non-local information transport.

2. ADR Process: The network mimics the Reaction-Advection-Diffusion equation to solve spatio-temporal prediction problems, offering explainability by linking neural operations to known physical processes.

3. Performance: Our ADRNet outperforms traditional CNN architectures in scenarios requiring the transport of features over long distances, such as weather prediction and traffic flow analysis.

Model Overview

• Advection Component: Moves information across an image using the semi-Lagrangian method, overcoming the limitations of local convolutional operations.
• Diffusion and Reaction Components: Modeled as standard CNN layers, these components perform smoothing and local feature updates.
• Operator Splitting: Inspired by differential equation solvers, our model divides the ADR process into three steps—advection, diffusion, and reaction—to improve efficiency and stability.

Datasets

We evaluate the ADR-Net on several spatio-temporal datasets:

• Shallow Water Equation (SWE): Derived from Navier-Stokes equations.
• CloudCast: Satellite imagery for weather prediction.
• Moving MNIST: Synthetic video prediction dataset.
• KITTI: Benchmark dataset for video prediction in autonomous driving.

Citation

If you use this work in your research, please cite:

@InProceedings{ADR-CNN2024,
  title={Advection Augmented Convolutional Neural Networks},
  author={Niloufar Zakariaei, Siddharth Rout, Eldad Haber, Moshe Eliasof},
  booktitle={Neural Information Processing Systems (NeurIPS)},
  year={2024}
}