Hierarchical Graph Representation for IceCube Event Graph Classification

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This repository contains the model architecture and training setup for dimuon event classification in IceCube using graph neural network algorithms. In particular, the model is comprised of the three following deep learning algorithms (with reference to the original papers):

• Graph Convolutional Neural Network - Paper: Semi-Supervised Classification with Graph Convolutional Networks

• Graph Attention Networks - Paper: Graph Attention Networks

• Hierarchical Graph Pooling - Paper: Hierarchical Graph Representation Learning with Differentiable Pooling

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The following diagrams summarizes the components and the full model architecture used in the classification network.

Affine Transformation in Graph Convolutions	Message Passing Framework using Attention Mechanism

One Graph Convolution block with edge attention

Hierarchical Pooling Mechanism using DiffPool (from paper)

Physics Informed Edge Attention

The following equation defines the elements in the adjacency matrix based on Gaussian kernel based edge attention:

$$e_{ij} = N\cdot \exp\left[-\left(\frac{d^2_{ij}}{\sigma^2_d}+\frac{(1-\vert \cos\theta_{ij}\vert)^2}{\sigma_{\theta}^2}\right)\right]$$

Full Model Architecture

For a summarized details of the model and its application in the IceCube project, check out the research poster

Instruction on general use and application of the model in other fields is coming soon..