Using graph neural networks to reconstruct charged pion showers in the CMS High Granularity Calorimeter
- Aamir, M. et al
- arXiv:2406.11937
 | A picture of the CE-E, CE-H, and AHCAL prototypes setup mounted on a concrete platform in the H2 experimental area of the CERN SPS. |
 | A picture of the CE-E, CE-H, and AHCAL prototypes setup mounted on a concrete platform in the H2 experimental area of the CERN SPS. |
 | Simulated geometry of the CE-E, CE-H and AHCAL detector prototypes depicting the position of active layers and absorbing material. |
 | Simulated geometry of the CE-E, CE-H, and AHCAL detector prototypes depicting the position of active layers and absorbing material. |
 | Schematic of the operation of the GNN based dynamic reduction network used in this analysis. |
 | This schematic illustrates the GNN-based dynamic reduction network. The $x_i$ represents rechits, with red edges showing their connections in the latent space which are updated during graph convolution (in magenta). In the graph clustering stage, small circles indicate clusters, and nodes within as blue dots. Final predictions are produced after passing through the output neural network. |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | A few input features used for training DRN, namely distributions of number of rechits (top left), $x$ and $y$ coordinates of rechits (top right), distribution of energy measured in individual rechits (bottom left), and distribution of rechit energies versus their depth in $z$ (bottom right). |
 | Comparison of distribution of energy obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) for pions with incident energy of 100 GeV. |
 | Comparison of distribution of energy obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) for pions with incident energy of 100 GeV. |
 | Comparison of distribution of energy obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) for pions with incident energy of 100 GeV. |
 | Comparison of distribution of energy obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) for pions with incident energy of 100 GeV. |
 | Comparison of distribution of energy obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) for pions with incident energy of 100 GeV. |
 | Comparison of distribution of energy obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) for pions with incident energy of 100 GeV. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as a function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as a function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as a function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as a function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as a function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as function of incident pion energy. |
 | Comparison of resolution (upper row) and response (bottom row) obtained in training and validation datasets for the models DRN (E) (left), DRN (E,z) (middle), and DRN (E,x,y,z) (right) as a function of incident pion energy. |
 | Distributions of energies predicted using different DRN models for 20 GeV (left) and 200 GeV (right) pions. |
 | Distributions of energies predicted using different DRN models for 20 GeV (left) and 200 GeV (right) pions. |
 | Distributions of energies predicted using different DRN models for 20 GeV (left) and 200 GeV (right) pions. |
 | Distributions of energies predicted using different DRN models for 20 GeV (left) and 200 GeV (right) pions. |
 | Resolution (top, left), ratio of resolution to DRN (E,x,y,z) (top, right), and response (bottom) as function of pion energy obtained from the three models trained with different features and the WS method in simulation. |
 | Resolution (top, left), ratio of resolution to DRN (E,x,y,z) (top, right), and response (bottom) as function of pion energy obtained from the three models trained with different features and the WS method in simulation. |
 | Resolution (top, left), ratio of resolution to DRN (E,x,y,z) (top, right), and response (bottom) as function of pion energy obtained from the three models trained with different features and the WS method in simulation. |
 | Resolution (top, left), ratio of resolution to DRN (E,x,y,z) (top, right), and response (bottom) as function of pion energy obtained from the three models trained with different features and the WS method in simulation. |
 | Resolution (top, left), ratio of resolution to DRN (E,x,y,z) (top, right), and response (bottom) as function of pion energy obtained from the three models trained with different features and the WS method in simulation. |
 | Resolution (top, left), ratio of resolution to DRN (E,x,y,z) (top, right), and response (bottom) as function of pion energy obtained from the three models trained with different features and the WS method in simulation. |
 | Distributions of rechit energies in units of MIPs (left) and rechit energies as function of depth in the detector (right). |
 | Distributions of rechit energies in units of MIPs (left) and rechit energies as function of depth in the detector (right). |
 | Distributions of rechit energies in units of MIPs (left) and rechit energies as function of depth in the detector (right). |
 | Distributions of rechit energies in units of MIPs (left) and rechit energies as function of depth in the detector (right). |
 | Resolution curves obtained with the models DRN(E), DRN(E[MIPs]), DRN(E[MIPs],Flag). By including a flag indicating in which subsection of the calorimeter the rechit belongs to, the resolution obtained with DRN(E) is recovered. |
 | Resolution curves obtained with the models DRN(E), DRN(E[MIPs]), DRN(E[MIPs],Flag). By including a flag indicating in which subsection of the calorimeter the rechit belongs, the resolution obtained with DRN(E) is recovered. |
 | Comparison of resolution using rechit energies given in GeV or MIPs with only longitudinal (left) and both transverse and longitudinal (right) coordinates. |
 | Comparison of resolution using rechit energies given in GeV or MIPs with only longitudinal (left) and both transverse and longitudinal (right) coordinates. |
 | Comparison of resolution using rechit energies given in GeV or MIPs with only longitudinal (left) and both transverse and longitudinal (right) coordinates. |
 | Comparison of resolution using rechit energies given in GeV or MIPs with only longitudinal (left) and both transverse and longitudinal (right) coordinates. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Distribution of energy predicted by the DRN model on hadron showers generated by pions of true energy 20 GeV (top, left), 50 GeV (top, right), 100 GeV (bottom, left), and 200 GeV (bottom, right) in beam test HGCAL prototype detector and its simulation. The model is trained using the simulated flat energy sample in the same detector setup. |
 | Comparison of resolution (left) and response (right) for pion showers reconstructed in beam test data and simulation using DRN model and WS method. |
 | Comparison of resolution (left) and response (right) for pion showers reconstructed in beam test data and simulation using DRN model and WS method. |
 | Comparison of resolution (left) and response (right) for pion showers reconstructed in beam test data and simulation using DRN model and WS method. |
 | Comparison of resolution (left) and response (right) for pion showers reconstructed in beam test data and simulation using DRN model and WS method. |
 | Energy reconstructed using WS method (top panel) and DRN(E,x,y,z) model (lower panel) for pions of energy 50 GeV (left) and 200 GeV (right) as a function of fraction of energy carried by $\pi^0$s in a given shower. |
 | Energy reconstructed using WS method (top panel) and DRN(E,x,y,z) model (lower panel) for pions of energy 50 GeV (left) and 200 GeV (right) as a function of the fraction of energy carried by $\pi^0$s in a given shower. |
 | Energy reconstructed using WS method (top panel) and DRN(E,x,y,z) model (lower panel) for pions of energy 50 GeV (left) and 200 GeV (right) as a function of fraction of energy carried by $\pi^0$s in a given shower. |
 | Energy reconstructed using WS method (top panel) and DRN(E,x,y,z) model (lower panel) for pions of energy 50 GeV (left) and 200 GeV (right) as a function of the fraction of energy carried by $\pi^0$s in a given shower. |
 | Schematic of standalone geometry of expected HGCAL configuration. |
 | Schematic of standalone geometry of expected HGCAL configuration. |
 | Resolution (left) and response (right) predicted by DRN(E), DRN(E,z) and DRN(E x y z) in the full HGCAL setup in simulation. |
 | Resolution (left) and response (right) predicted by DRN(E), DRN(E,z) and DRN(E x y z) in the full HGCAL setup in simulation. |
 | Resolution (left) and response (right) predicted by DRN(E), DRN(E,z) and DRN(E x y z) in the full HGCAL setup in simulation. |
 | Resolution (left) and response (right) predicted by DRN(E), DRN(E,z) and DRN(E x y z) in the full HGCAL setup in simulation. |
 | Distributions of of energy reconstructed in full HGCAL and beam test setups using DRN(E,x,y,z) for pions with energies 20 GeV (left) and 200 GeV (right). |
 | Distributions of energy reconstructed in full HGCAL and beam test setups using DRN(E,x,y,z) for pions with energies 20 GeV (left) and 200 GeV (right). |
 | Distributions of of energy reconstructed in full HGCAL and beam test setups using DRN(E,x,y,z) for pions with energies 20 GeV (left) and 200 GeV (right). |
 | Distributions of energy reconstructed in full HGCAL and beam test setups using DRN(E,x,y,z) for pions with energies 20 GeV (left) and 200 GeV (right). |
 | Comparison of energy resolution (left) and response (right) in full HGCAL and beam test setups using DRN(E,x,y,z). |
 | Comparison of energy resolution (left) and response (right) in full HGCAL and beam test setups using DRN(E,x,y,z). |
 | Comparison of energy resolution (left) and response (right) in full HGCAL and beam test setups using DRN(E,x,y,z). |
 | Comparison of energy resolution (left) and response (right) in full HGCAL and beam test setups using DRN(E,x,y,z). |