fccml-thesis

Graph Neural Networks for Particle Physics

Machine Learning in Particle Physics: Graph Neural Networks for Jet Clustering at the Future Circular Collider

• Akanksha Ahuja
• St Hugh’s College,
• University of Oxford

Abstract

We present an interdisciplinary project in Particle Physics and Computer Sci- ence by applying novel data processing techniques, modern data analysis and integrating them with advanced machine learning. Our objective is to develop a novel methodology to perform final state particle classification, based on its origin of decay in the event of two leptons (electron and positron) colliding at the FCC-ee detector, a future circular detector, proposed at CERN in the coming decades. Based on the classification of the final state, as decaying from the Higgs Boson, or Z Boson, we group the particles of the same class together: jet clustering. Traditional techniques use sequential recombination methods for jet clustering. A wide variety of graph machine learning architectures, using diverse graph representations, specifically targeting generated level simulations, have been recently explored in the literature and have offered promising results. However, there has been limited exploration of the application of graph neural networks in jet clustering, as most relevant work has been carried out in pile-up mitigation, reconstruction of the calorimeter, and jet tagging. Our research project is the first to build a supervised node classification for jet clustering in an electron-positron collision within an inductive learning setup on a simulation dataset. Each event collision is represented as a graph, whereas the final state particles (observed at the detector) are represented as nodes. We aim to develop three new graph representations based on existing literature reviews, implement a baseline for comparison among the eight different graph neural network models, and evaluate the best model parameters through multiple empirical experiments. Our key findings report an increased performance against the established baseline, the most suitable network depth, the best performing GNN architectures, graph processing scheme, and edge-generation scheme. Our work highlights the way forward for further exploration and research to enhance jet clustering algorithms for the future circular collider

Acknowledgements:

• Prof Daniela Bortoletto, University of Oxford
• Prof Phil Blunsom, University of Oxford
• Dr Michele Selvaggi, CERN
• Dr Loukas Gouskos, CERN

Experiment 1.x: Data processing, analysis, visualisation

• Builds the 3 graph datasets for two processing schemes: fixed size graph data sets and variable size datasets: fcc_experiment_1.x_both_fixed_and_variable_sized_graphs.ipynb
• Builds the 3 graph datasets and saves graphs as torch objects fcc_experiment_1_x_save_variable_graphs_as_torch_data_objects.ipynb
• Visualisation of Node Metrics for Event ID:9 and Global Metrics of 100 Graphs fccml_experiment_1_x_graph_metrics_for_100_events_and_node_metrics_for_event_id_9_visualisation.ipynb

Experiment 2.x GCN

Network Depth

• Model Training and Testing on GCN-2 on Fixed and Variable Sized Graphs and explanations of node predictions using GNNExplainer fcc_experiment_2_x_model_GCNX_2.ipynb

• Model Training and Testing of GCN-16 on Variable Sized Graphs across 3 datasets fcc_experiment_2_x_model_final_GCNX_16_32_on_variable_sized.ipynb

• Model Training and Testing of On GCN-4 and GCN-8 on Variable Sized Graphs across 3 datasets fcc_experiment_2_x_model_final_GCNX_4_8_on_variable_sized.ipynb

• Model Performance of GCN-16 across 3 datasets fcc_experiment_2_x_model_performance_GCNX_16.ipynb

• Model Performance of GCN-4 across 3 datasets fcc_experiment_2_x_model_performance_GCNX_4.ipynb

• Model Performance of GCN-8 across 3 datasets fcc_experiment_2_x_model_performance_GCNX_8.ipynb

• Model Performance of GCN-2 across 3 datasets fcc_experiment_2_x_model_performance_GCNX_2.ipynb

• Model Performance by calculating the sum of 4 predicted properties and sum of 4 true properties of each of the clustered particles: H, Z and others separately in the test dataset and returning their MSE and MAE scores across each class for the 3 graph datasets created. fcc_experiment_2_x_model_GCNX_2_calculate_sum_of_mom_x_on_colab_save_physics_performance_metrics.ipynb

Hyperparameters

• Model Training and Testing on GCN-2 on the KNN dataset: Hyperparameter Dropout fcc_experiment_2_x_model_GCNX_2_hyperparameters_dropout_0_1_0_2_0_3_0_4_0_5.ipynb

• Model Training and Testing on GCN-2 on the KNN dataset: Hidden Channels fcc_experiment_2_x_model_GCNX_2_hyperparameters_hidden_channels_10_16_32_64_128.ipynb

• Model Training and Testing on GCN-2 on the KNN dataset: Learning Rate fcc_experiment_2_x_model_GCNX_2_hyperparameters_lr_0_1_to_0_00001.ipynb

• Model Training and Testing on GCN-2 on the KNN dataset: Non-linearity fcc_experiment_2_x_model_GCNX_2_hyperparameters_non_linearity_elu_selu_gelu_leaky_relu_tanh.ipynb

• Model Training and Testing on GCN-2 on the KNN dataset: Optimizers fcc_experiment_2_x_model_GCNX_2_hyperparameters_optimizer_adam_sgd_rmsprop.ipynb

• Model Training and Testing on GCN-2 on the KNN dataset: Weight Decay fcc_experiment_2_x_model_GCNX_2_hyperparameters_wd_0_5_to_0_00005.ipynb

• Model Performance of GCN-2 dropout fcc_experiment_2_x_model_performance_GCNX_2_hyperparameters_dropout_0_1_0_2_0_3_0_4_0_5.ipynb

• Model Performance of GCN-2 hidden channels fcc_experiment_2_x_model_performance_GCNX_2_hyperparameters_hidden_channels_10_16_32_64_128.ipynb

• Model Performance of GCN-2 Learning Rate fcc_experiment_2_x_model_performance_GCNX_2_hyperparameters_lr_0_1_to_0_00001.ipynb

• Model Performance of GCN-2 Non Linearity fcc_experiment_2_x_model_performance_GCNX_2_hyperparameters_non_linearity_elu_selu_gelu_leaky_relu_tanh.ipynb

• Model Performance of GCN-2 optimizers fcc_experiment_2_x_model_performance_GCNX_2_hyperparameters_optimizer_adam_sgd_rmsprop.ipynb

• Model Performance of GCN-2 Weight decay fcc_experiment_2_x_model_performance_GCNX_2_hyperparameters_wd_0_5_to_0_00005.ipynb

Dataset Size

• Model Training and Testing on GCN-2 on various dataset sizes: fcc_experiment_2_x_model_GCNX_2_on_20_40_60_80_percentage_of_dataset.ipynb

• Model Performance of 20% of dataset fcc_experiment_2_x_model_performance_GCN_20_percent_dataset.ipynb

• Model Performance of 40% of dataset fcc_experiment_2_x_model_performance_GCN_40_percent_dataset.ipynb

• Model Performance of 60% of dataset fcc_experiment_2_x_model_performance_GCN_60_percent_dataset.ipynb

• Model Performance of 80% of dataset fcc_experiment_2_x_model_performance_GCN_80_percent_dataset.ipynb

Experiment 3.x ChebNet

• Model Training and Testing of ChebNet-2 and ChebNet-4 on Variable Sized Graphs across 3 datasets fcc_experiment_3_x_model_ChebNet_2_4.ipynb

• ChebNet-2 with k=3, 4 on all 3 datasets fcc_experiment_3_x_model_ChebNet_2_hyperparameters_k_3_4.ipynb

• Model performance of ChebNet-2 on all 3 datasets fcc_experiment_3_x_model_performance_ChebX_2.ipynb

• Model performance ChebNet-2 with k=3, 4 on all 3 datasets fcc_experiment_3_x_model_performance_ChebX_2_hyperparameters_k_3_4.ipynb

• Model performance of ChebNet-4 on all 3 datasets fcc_experiment_3_x_model_performance_ChebX_4.ipynb

Experiment 4.x SAGE

• Model Training and Testing of SAGE-2 and SAGE-4 on Variable Sized Graphs across 3 datasets fcc_experiment_4_x_model_SAGE_2_4.ipynb

• Model Performance of SAGE-2 across 3 datasets fcc_experiment_4_x_model_performance_SAGE_2.ipynb

• Model Performance of SAGE-4 across 3 datasets fcc_experiment_4_x_model_performance_SAGE_4.ipynb

Experiment 5.x TAGCN

• Model Training and Testing of TAGCN-2 and TAGCN-4 on Variable Sized Graphs across 3 datasets fcc_experiment_5_x_model_TAGCN_2_4.ipynb

• Model Performance TAGCN-2 on all datasets fcc_experiment_5_x_model_performance_TAGCN_2.ipynb

• Model Performance of TAGCN-4 across all datasets fcc_experiment_5_x_model_performance_TAGCN_4.ipynb

Experiment 6.x GAT

• Model Training and Testing of GAT-2 and GAT-4 on Variable Sized Graphs across 3 datasets fcc_experiment_6_x_model_GAT_2_4.ipynb

• Model Training and Testing GAT-2 with different heads on KNN dataset fcc_experiment_6_x_model_GAT_2_hyperparameters_heads_2_4_6_8_10.ipynb

• Model performance of GAT-2 across 3 datasets fcc_experiment_6_x_model_performance_GAT_2.ipynb

• Model performance of GAT-2 with different heads on KNN dataset fcc_experiment_6_x_model_performance_GAT_2_hyperparameters_heads_2_4_6_8_10.ipynb

• Model performance of GAT-4 across 3 datasets fcc_experiment_6_x_model_performance_GAT_4.ipynb

Experiment 7.x GIN

• Model Training and Testing of GIN-2 and GIN-4 on Variable Sized Graphs across 3 datasets fcc_experiment_7_x_model_GIN_2_4.ipynb

• Model performance of GIN-2 across 3 datasets fcc_experiment_7_x_model_performance_GIN_2.ipynb

• Model performance GIN-4 across 3 datasets fcc_experiment_7_x_model_performance_GIN_4.ipynb

Experiment 8.x JK

• Model Training and Testing of JK-2 and JK-4 on Variable Sized Graphs across 3 datasets fcc_experiment_8_x_model_JK_2_4.ipynb

• Model Performance of JK-2 across 3 datasets fcc_experiment_8_x_model_performance_JK_2.ipynb

• Model Performance ofJK-4 across 3 datasets fcc_experiment_8_x_model_performance_JK_4.ipynb

Experiment 9.x superGAT

• Model training and testing of superGAT-2 and superGAT-4 on all datasets fcc_experiment_9_x_model_superGAT_2_4.ipynb

• Model training and testing of superGAT-2: different attentions and heads on KNN dataset fcc_experiment_9_x_model_superGAT_2_hyperparameters_attention_MX_SD_head_2_4_8.ipynb

• Model Performance of superGAT-2 on all datasets fcc_experiment_9_x_model_performance_superGAT_2.ipynb

• Model Performance of superGAT-2: different attentions and heads on KNN dataset fcc_experiment_9_x_model_performance_superGAT_2_hyperparameters_heads_2_4_6_8_10.ipynb

• Model Performance of superGAT-4 on all datasets fcc_experiment_9_x_model_performance_superGAT_4.ipynb

Experiment 10.x MLP

• Model Training and Testing on MLP-2, MLP-4, MLP-8 on Variable Sized Graphs using only node features fcc_experiment_10_x_model_MLP_2_4_8.ipynb

• Model performance of MLP-2, MLP-4, MLP-8 on Variable Sized Graphs using event accuracy fcc_experiment_10_x_model_performance_MLP_2_4_8.ipynb