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Calorimetry with Deep Learning: Particle Simulation and Reconstruction for Collider Physics
Dawit Belayneh, Federico Carminati, Amir Farbin, Benjamin Hooberman, Gulrukh Khattak, Miaoyuan Liu, Junze Liu, Dominick Olivito, Vitória Barin Pacela, Maurizio Pierini, Alexander Schwing, Maria Spiropulu, Sofia Vallecorsa, Jean-Roch Vlimant, Wei Wei, Matt Zhang
TL;DR
Collider experiments face growing computational demands from detailed detector simulation and particle reconstruction. This paper trains neural networks on simulated calorimeter showers, using an end-to-end reconstruction model and a generative shower model. The authors report competitive performance with short execution times and potential simulation speedups, while identifying limitations in shower-edge modeling and geometry resampling.
Problem
Detailed detector simulation and event reconstruction are computationally intensive as collider data volumes and detector complexity increase.
Method
The paper trains an end-to-end network for particle identification and energy measurement and a GAN for generating calorimeter showers from particle conditions.
Results
The models achieve competitive performance with short execution times, including a potential simulation speedup of over 4,000 times for one event-simulation aspect.
Takeaways & Limitations
A single GPU-friendly deep-learning strategy can support fast calorimeter shower simulation and simultaneous particle reconstruction across collider-detector use cases.
Takeaways & Limitations
Geometry resampling omits detector characteristics such as depth information and gaps, while the generative model overestimates sparse energy deposits at shower edges.
Abstract
from arXiv · showhide
Using detailed simulations of calorimeter showers as training data, we investigate the use of deep learning algorithms for the simulation and reconstruction of particles produced in high-energy physics collisions. We train neural networks on shower data at the calorimeter-cell level, and show significant improvements for simulation and reconstruction when using these networks compared to methods which rely on currently-used state-of-the-art algorithms. We define two models: an end-to-end reconstruction network which performs simultaneous particle identification and energy regression of particles when given calorimeter shower data, and a generative network which can provide reasonable modeling of calorimeter showers for different particle types at specified angles and energies. We investigate the optimization of our models with hyperparameter scans. Furthermore, we demonstrate the applicability of the reconstruction model to shower inputs from other detector geometries, specifically ATLAS-like and CMS-like geometries. These networks can serve as fast and computationally light methods for particle shower simulation and reconstruction for current and future experiments at particle colliders.
1 Overview
Collider experiments need computationally efficient methods for particle reconstruction and detailed detector simulation as data volumes and detector granularity increase. This work applies neural networks to both tasks using calorimeter-cell data.
- Calorimeter cells record energy depositions as voxelized images characteristic of a primary particle’s type and energy.
- Higher collision rates and finer detector voxelization will increase data volumes and computational demands for real-time reconstruction.
- Detailed GEANT4 detector simulations are CPU intensive and consume roughly half of ATLAS computing resources.
- The paper trains an end-to-end reconstruction network and a GAN that generates calorimeter-cell shower images.
- The study uses fully simulated data and extends earlier simplified studies to more realistic particle energies and incident angles.
- The models are intended to preserve traditional-method accuracy while reducing computing resources and execution time.
2 Dataset
The datasets represent calorimeter showers from four particle types across broad energies and incident angles, with task-specific windows and filtering designed to make reconstruction challenging. The selected cases target difficult electron–pion and photon–neutral-pion distinctions.
- Dataset construction: Full-detector simulations are converted into ECAL and HCAL 3D energy-deposit arrays centered on each shower barycenter.
- Dataset construction: The study simulates electrons, photons, charged pions, and neutral pions with energies from 10 to 510 GeV and varied incident angles.
- Dataset construction: The GEN dataset uses a 51 × 51 × 25 ECAL window, while the REC dataset uses a smaller 25 × 25 × 25 slice.
- Task-dependent filtering: REC filtering retains electron–charged-pion showers with HCAL/ECAL < 0.1 because larger ratios make classification comparatively easy.
- Task-dependent filtering: High-energy neutral pions are challenging because their two-photon showers become collimated and can resemble a single photon.
- Model inputs: The networks receive ECAL and HCAL arrays directly, while expert features support alternative benchmark algorithms.
3 Benchmark Tasks
The paper benchmarks two machine-learning tasks: reconstructing particle identity and energy from detector hits, and simulating detector responses from incoming-particle information. It emphasizes end-to-end, multi-task reconstruction and fast generative simulation.
- Benchmark tasks: Particle reconstruction determines particle nature and momentum from raw detector hits.
- Benchmark tasks: Particle simulation generates stochastic detector responses from generator-level incoming-particle information.
- Motivation: Accelerating both tasks could reduce resource use and execution time in large-scale collider experiments.
- Simulation: The generative model is trained on electron ECAL showers to produce 51 × 51 × 25 energy-deposit arrays from energy and flight direction.
- Reconstruction: The reconstruction model treats calorimeter data as a 3D image and jointly performs particle identification and energy measurement.
- Reconstruction: The reconstruction study targets electron–charged-pion and photon–neutral-pion classification, including merged high-momentum neutral-pion showers.
4 Generative Model
The 3DGAN generates calorimeter showers conditioned on particle energy and direction, using adversarial, regression, energy, and pixel-distribution objectives. Its outputs reproduce key shower observables and offer substantial simulation speedups, while overestimating sparse edge deposits.
- Model architecture: 3DGAN generates 3D ECAL energy-deposit images from particle energy, flight direction, and a latent random vector, while its discriminator distinguishes generated from GEANT4 showers.The generator and discriminator use 3D convolutional architectures operating on voxelized calorimeter data.
- Training objective: The generator loss combines adversarial classification with primary-energy, incident-angle, total-energy, and pixel-intensity-distribution terms.These weighted terms provide feedback on conditioning and compare generated energy deposits with target distributions.
- Results: 3DGAN reproduces sampling-fraction behavior across the energy spectrum and matches energy-shape distributions, including their changes with incident angle.The comparisons cover hit counts, energy deposited along x, y, and z, and additional width and longitudinal-deposition observables.
- Limitations: 3DGAN describes the distribution core well but overestimates energy deposited in sparse cells near the volume edges.This is the principal reported mismatch in the shower-shape comparisons.
- Results: The GAN simulates one particle in about 13 ms on a CPU and 4 ms on a GPU, compared with about 17 seconds for GEANT4 on a CPU.For this event-simulation component, the reported potential speedup is over 4,000 times.
5 End-to-End Particle Reconstruction
The paper evaluates end-to-end neural networks that jointly classify particles and regress their energies from calorimeter-cell data, comparing dense, convolutional, and GoogLeNet architectures with traditional baselines. Neural models outperform the BDT for classification, while regression performance is broadly similar across neural architectures and varies with particle type and detector geometry.
- The reconstruction model jointly performs particle classification and energy regression from ECAL and HCAL calorimeter-cell arrays and total deposited energies.
- The study compares dense, 3D convolutional, and GoogLeNet architectures against feature-based BDT and linear-regression baselines.
- Classification performance: The GN model achieves the best classification performance on both particle-identification problems, while all neural models outperform the BDT.
- Classification performance: Classification accuracy remains effective across a wide range of particle energies and incident angles, with photon-versus-neutral-pion performance worsening at higher energies.
- Energy regression: The DNN, CNN, and GN models perform similarly for energy regression except that GN is worse on charged pions; charged-pion regression is also worse for the benchmark baselines.
- Other detector geometries: The resampling study cannot represent detector effects beyond geometry, including CMS energy-resolution improvements and second-order effects such as detector gaps.
- Other detector geometries: For ATLAS-like and CMS-like classification, the performance ranking remains GN, CNN, then DNN, with all three outperforming the BDT.
- Other detector geometries: On ATLAS-like geometries, DNN and CNN match the BDT in bias and surpass it in resolution, whereas CMS-like resampling yields no neural-network improvement in regression resolution.
6 Conclusion and Future Work
The paper presents deep-learning methods for calorimeter simulation and reconstruction that operate on detailed detector data and support multiple reconstruction tasks. It reports competitive performance, short execution time, GPU-friendly computation, and applicability to fully simulated detector data and future detector studies.
- Deep-learning methods can outperform traditional, resource-consuming techniques for calorimeter shower simulation and particle reconstruction.
- The proposed methods combine competitive performance with short execution time and GPU-friendly computation.
- The study uses a fully accurate GEANT4 simulation of a complete detector and a single architecture optimized through a hyperparameter scan for multiple tasks.
- The authors identify similar solutions as useful for current and future particle detectors.
- Calorimeter window size affects sample storage, training speed, and the maximum GPU batch size, motivating explicit window-size studies.
B End-to-end reconstruction of the ECAL showers produced by the 3DGAN
The reconstruction tool was applied to 3DGAN and GEANT4 calorimeter images to assess energy regression and particle classification. Energy means agreed reasonably, while GAN resolution was broader; classification accuracy was close to 100% for both inputs.
- 3DGAN validation: The reconstruction network was run on 3DGAN outputs and compared with its response on Monte Carlo data to validate GAN image quality.The comparison used the same 3D CNN reconstruction tool described for the reconstruction task.
- Energy regression: 2213 electron events per image type were used for the predicted-versus-true energy comparison of GAN and GEANT images.The plot compares predictions produced by the reconstruction tool for GAN and GEANT images.
- Energy regression: Energy predictions showed reasonable agreement in the mean, but GAN images had broader resolution than GEANT4 images.The comparison concerns the energy resolution obtained from the two image sources.
- Particle classification: Classification accuracy was close to 100% for both GAN and GEANT4 events.The result is reported for the electron-versus-charged-pion classification shown in Figure 22.
- Baseline comparison: The baseline classification model used Boosted Decision Trees because they process high-level features and optimize cut-based classification in multidimensional input space.The baseline features included shower-characterization variables such as R9, the energy fraction in a 3x3 window around the shower barycenter.
D Energy Regression Baseline
The paper establishes linear regression and XGBoost as energy-regression baselines, then evaluates feature choices, particle-dependent performance, and training-set scope. XGBoost improves resolution relative to linear regression but cannot extrapolate beyond its training-energy range.
- Linear regression: Linear regression predicts particle energy from total ECAL and HCAL energies using E = a · E_ECAL + b · E_HCAL + c.The fitted resolution function is plotted over the energy range for each particle type.
- Feature choices: Adding the mean z coordinate to ECAL and HCAL total energies improved electron energy resolution, particularly at high energy.For π±, ECAL x-direction RMS, HCAL-plane RMS, and HCAL mean z were additional useful variables.
- Training selection: About 0.5% of π± events had almost no reconstructed energy and were removed when raw ECAL+HCAL energy was below 30% of generated energy.The authors state that including these events adversely affected training.
- XGBoost results: XGBoost achieved relative resolutions of about 6–8% at the lowest energies and 1.0–1.1% at the highest energies for electrons, photons, and π0.These values are reported for the XGBoost regression baseline.
- XGBoost results: XGBoost improved resolution by about a factor of two at low energy and three to four at high energy compared with baseline linear regression.The passage reports these factors for the electron, photon, and π0 comparison.
- Scope and alternative: Because tree algorithms generally do not extrapolate, XGBoost cannot be used for energy values outside its training range without extending that range or changing algorithms.A small DNN achieved similar performance, matching the BDT at high energy while differing slightly elsewhere.
E GoogLeNet Model Architecture Details
The GoogLeNet-based architecture processes calorimeter inputs through inception modules, pooling, dense layers, and repeated auxiliary kinematic inputs. Its design is documented alongside energy-regression comparison figures and the final five-value output layer.
- Inception modules: The GoogLeNet architecture uses inception modules whose four branches are concatenated after separate convolution and pooling operations.The branches include convolutions with 1×1×1, 3×3×3, and 5×5 kernels, plus a max-pooling branch.
- Regression comparisons: Figures 25–27 compare bias and resolution versus true energy for linear regression and XGBoost predictions across particle types and electron feature sets.The figures include fixed-angle linear-regression results and comparisons between regression methods.
- Architecture specification: The architecture details are presented as the full layer specification for the GoogLeNet-based model.The surrounding text explicitly introduces the listed components as full details for each layer.
- Input processing: The network applies instance normalization to ECAL input, a 3D convolution to 192 channels, two inception modules, and 3D max pooling.The listed sequence precedes flattening and concatenation with additional inputs.
- Dense layers: After flattening, the architecture concatenates φ, η, total ECAL energy, and total HCAL energy before a 1024-output dense layer with ReLU.The same auxiliary input values are concatenated again before the final layer.
- Outputs: A final dense layer outputs five values, matching the output dimensionality used by the other two models.The architecture description identifies this as the final output stage.
F Use of HCAL in Classification
The study tests whether HCAL cell-level information is needed for classification by comparing training curves with and without HCAL cells. It also uses skip connections to provide total calorimeter energies directly to the network.
- HCAL ablation: Ten training sessions with HCAL information and ten without HCAL were averaged to produce classification training curves.The comparisons use the best-performing DNN architecture and are shown for electron/charged-pion and photon/neutral-pion classification.
- Classification curves: Figures 28 and 29 report accuracy and loss curves for electron/charged-pion and photon/neutral-pion classification with and without HCAL cells.The captions specify the particle pairs and the best DNN architecture used.
- Skip connections: Skip connections provide total ECAL and HCAL energies to both the first dense layer and the final output layer.The authors report improved CNN convergence time and performance with this design choice.
H Training for Regression Using Energy Summed in z
Using energy summed across z-layers reduces the input relative to full cell information, but full cell-level inputs perform better overall. At fixed 90° incidence, neural architectures and baselines perform with great accuracy.
- Input representation: Energy summed in z performs better than XGBoost at high energies but worse than full cell-level information.The comparison uses DNN regression inputs formed either from z-layer sums or the complete cell-energy array.
- Architecture studies: Skip connections are evaluated for CNN electron energy predictions using bias and resolution versus true energy.The comparison is presented in Figure 30.
- Fixed-angle regression: At fixed 90° incidence, all neural architectures and baseline algorithms perform with great accuracy.These results are shown for electron, charged-pion, photon, and neutral-pion regression.
- Fixed-angle regression: Figure 33 compares the XGBoost baseline with the best CNN model across all particle types on fixed-angle samples.The comparison summarizes bias and resolution as functions of true energy.
J Regression performance training on a different particle type
The study tests whether regression models trained on one particle type transfer to other particle types and examines photon-conversion effects. Electron-trained models match the resolution of models trained on photons or neutral pions, whereas charged pions remain poorly described.
- Cross-particle training: Electron-trained DNN and CNN models achieve the same resolution as CNN models trained directly on photons or π0, with slightly larger bias in some cases.The comparisons concern predictions for photon and π0 energies.
- Input representation: The input comparison evaluates DNN electron predictions using either z-layer energy sums or full cell information.This provides a representation-level comparison alongside the particle-transfer studies.
- Cross-particle limitations: Models trained on electrons, photons, or π0 do not describe π± well because charged pions produce hadronic showers with substantial HCAL energy.The other particle types deposit almost all of their energy in the ECAL.
- Photon conversions: Converted photons have worse resolution below around 100 GeV because the resulting e+e− pair forms two calorimeter showers instead of one.The photon sample contains about 9% converted photons.
- Photon conversions: For CNN and DNN models, converted photons also show worse low-energy bias when training includes the full photon sample.XGBoost retains the same resolution for converted photons when trained on the full sample.
K Regression Studies with Large Sample Windows
Large-window studies show that input-window size is a major regression design choice, with wider windows helping low-energy and broad showers but increasing computational costs. The section evaluates these effects across particle types and regression models.
- Dataset and windows: The studies use approximately 800,000 events per particle type, split two-thirds for training and one-third for testing.The full windows contain 51x51x25 ECAL and 11x11x60 HCAL samples.
- Window-size optimization: For energies above 150 GeV, minimum windows of 25x25 ECAL and 5x5 HCAL achieve best performance, while below 150 GeV the optimal windows are 51x51 and 11x11.The larger low-energy windows are attributed to wider showers.
- Window-size optimization: Larger windows increase file size and memory use, and make training take about 5 times longer per epoch.These are the stated practical drawbacks of the larger input configuration.
- Charged-pion regression: For π±, the wider 51x51 ECAL and 11x11 HCAL window improves the lowest-energy resolution by about a factor of 2 over the smaller window.Charged-pion showers are wider than those of the other particle types, especially at low energies.
- Regression comparisons: The section compares regression bias and resolution across electrons, charged pions, photons, and neutral pions using the listed figures.The figures include fixed-angle results, CNN-versus-XGBoost comparisons, particle-transfer tests, conversion splits, and window-size scans.
- Window-size comparisons: DNN window-size studies plot bias and resolution versus true energy, while π± studies compare CNN and DNN results across calorimeter window sizes.These figures isolate how the input window affects energy prediction.