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Generating and refining particle detector simulations using the Wasserstein distance in adversarial networks
Martin Erdmann, Lukas Geiger, Jonas Glombitza, David Schmidt
TL;DR
Training deep networks on simulations that differ from data distributions is a longstanding issue. The paper uses Wasserstein adversarial networks to generate energy-conditioned detector patterns and refine simulated traces; in its air-shower example, refinement improves energy reconstruction bias and resolution.
Problem
Training deep networks with simulations that differ from data distributions is a longstanding machine-learning issue.
Source: §2.4 · p. 4Method
WGANs generate detector patterns conditioned on energy labels and refine simulated signal traces to approximate data distributions.
Source: §2.3 · p. 3, §2.4 · p. 4Results
Small refinements of signal traces improve reconstruction of primary particle energy with respect to both energy bias and energy resolution.
Source: §6 · p. 8Takeaways & Limitations
Generated detector patterns follow the given shower energy in the air-shower example.
Source: §6 · p. 8Data traces are unlabeled and have no direct relation to generated traces, which use different random seeds.
Source: §2.4 · p. 4, §5 · p. 7
Abstract
from arXiv · showhide
We use adversarial network architectures together with the Wasserstein distance to generate or refine simulated detector data. The data reflect two-dimensional projections of spatially distributed signal patterns with a broad spectrum of applications. As an example, we use an observatory to detect cosmic ray-induced air showers with a ground-based array of particle detectors. First we investigate a method of generating detector patterns with variable signal strengths while constraining the primary particle energy. We then present a technique to refine simulated time traces of detectors to match corresponding data distributions. With this method we demonstrate that training a deep network with refined data-like signal traces leads to a more precise energy reconstruction of data events compared to training with the originally simulated traces.
1 Introduction
The paper applies Wasserstein adversarial training to detector simulations, generating spatial signal patterns conditioned on physics labels and refining simulated traces toward data distributions. It uses cosmic-ray air showers to illustrate these tasks and evaluates how refinement affects energy reconstruction.
1 Introduction
- AC-GANs condition generated images on class labels [9], while WGANs use Wasserstein distance to improve training stability and avoid mode collapse [10] [11].Source: §1 · p. 1
- Deep learning and GAN applications in particle physics include data analysis and fast generation of jet kinematics and calorimeter showers.Source: §1 · p. 1
- The paper proposes generating two-dimensional detector signal patterns for a given physics label, a task with broad particle- and astroparticle-detector applications.The example is cosmic-ray air showers producing signals in ground-based detector stations.Source: §1 · pp. 1–2
- Small refinements of simulated signal traces are evaluated by comparing energy reconstruction after training on original versus refined simulations.The paper treats the data as simulated for simplicity.Source: §1 · p. 2
2 Adversarial network architectures
The section presents Wasserstein adversarial training as a more stable basis than cross-entropy GAN training, then extends it to physics-conditioned generation and detector-signal refinement.
2 Adversarial network architectures
- Wasserstein distance improves training stability over cross-entropy GAN training, and mode collapse was not observed with this distance.Cross-entropy training can be delicate and produce restricted-phase-space outputs.Source: §2 · p. 2
2.1 Adversarial training with the Wasserstein distance
- WGAN approximates Wasserstein-1 distance with a critic approximating 1-Lipschitz functions; gradient penalty enforces the constraint, and alternating updates train critic and generator.The critic's expectation-score difference measures similarity between data and generated events.Source: §2.1 · pp. 2–3
2.2 Physics conditioning of the generator
- Physics conditioning appends labels to random noise and adds a constrainer-based label-reconstruction penalty weighted by κ; the constrainer is supervised on labeled data.The constrainer reconstructs the corresponding observable from generated data.Source: §2.2 · p. 3
2.3 Generating signal patterns using an energy label
- For cosmic-ray detector patterns, the generator takes noise and an energy label, whose distribution follows the air-shower simulation, while AixNet reconstructs signal-pattern energy.The energy label conditions patterns to follow primary particle energy as reconstructed by the constrainer.Source: §2.3 · pp. 3–4
2.4 Refining simulated signal traces to match data
- The refiner maps simulated detector time traces to same-dimensional modified traces, with small modifications and a similarly profiled energy-label distribution; refined traces are evaluated through energy reconstruction.The data traces used for adversarial training are unlabeled and have no direct event-level relation to the simulated traces.Source: §2.4 · p. 4
3 Simulated data for training and evaluation
The study uses simulated cosmic-ray air showers in a ground-based water-Cherenkov detector array, with a second simulation set deliberately altered to differ from the data set.
3 Simulated data for training and evaluation
- The simulations model vertical showers with fixed shower-maximum depth in water-Cherenkov detectors on a 1500 m-spaced hexagonal grid at 1400 m elevation.The setup is also described as a granular calorimeter with a single readout layer.Source: §3 · p. 4
- Air showers combine muons from pion decays and delayed electromagnetic-cascade particles, whose different arrival times and transverse distributions produce different trace shapes.The data simulation assigns about 30% of energy to muons and 70% to the electromagnetic cascade.Source: §3 · pp. 4–5
- The data set contains 105 proton events spanning 1–100 EeV, each represented by 9 × 9 detectors with 80 time-bin amplitudes.Event energies follow a flat distribution.Source: §3 · p. 5
- The comparison simulation uses the same conditions but reverses the muon/electromagnetic energy fractions from 30/70 to 70/30 and halves absolute noise and event fluctuations.The reduced noise reflects an assumed underestimation of noise in detector simulations.Source: §3 · p. 5
4 Energy constrained spatial signal pattern
A WGAN generates detector signal patterns from random input and an energy label, while a simultaneously trained constrainer evaluates their reconstructed energy. By 95 epochs, patterns show expected spatial and energy-related structure, and reconstructed energies correlate distinctly with input labels.
4 Energy constrained spatial signal pattern
- After 1 training epoch, generated detector-signal patterns labeled Elabel = 10, 30, 70, and 100 EeV differ from typical shower patterns, and their sizes do not agree with energy labels.Source: §4 · p. 5
- After 95 epochs, patterns show central hotspots, weaker outlying signals, local neighbor correlations, and larger patterns and total signals at higher energies.These properties are described as matching expectations.Source: §4 · p. 5
- A distinct correlation between input energy and constrainer-reconstructed energy across 5000 generated events shows that generated patterns relate to the given particle energy.The comparison is shown in Fig. 3.Source: §4 · p. 6, Figure 3 · p. 6
- The critic's approximate Wasserstein distance converges slowly toward zero while its gradient penalty decreases, providing a similarity measure for generated and data events.The loss components are shown in Fig. 4a.Source: §4 · p. 6, Figure 4 · p. 6
- The constrainer's supervised training loss reflects improving reconstruction performance, and its validation loss shows no sign of overtraining.Source: §4 · p. 6
- During generator training, the constrainer loss decreases considerably, with the patterns showing energy-related conditioning only in later epochs.The loss curves are shown in Fig. 4c.Source: §4 · p. 6, Figure 4 · p. 6
5 Network training with refined signal traces
Refining simulated detector traces improves data-event energy reconstruction compared with training on original simulations, although it remains below the simulation-to-simulation benchmark. The section also shows that the refiner moves simulated traces toward data traces while a residual distribution difference remains.
5 Network training with refined signal traces
- The study refines simulated detector traces to match unlabeled data-like traces, then uses the refined traces to train AixNet on detector-signal amplitudes for primary-energy reconstruction.The evaluation compares networks trained on original or refined simulated traces.Source: §5 · pp. 6–7
- For a 69 EeV event, the refiner makes the largest-signal and neighboring-detector simulated traces more like their corresponding data traces.The original largest-signal simulation rises faster than data because its muon component is overestimated.Source: §5 · p. 7, Figure 5 · p. 7
- Refined-trace training yields lower energy bias and improved energy resolution than original-simulation training, but reconstruction remains worse than the simulation-to-simulation benchmark.The comparison evaluates data events with AixNet trained on refined simulated traces versus original simulated traces.Source: §5 · p. 7
- The critic loss converges as refined traces better resemble data, yet its nonzero distance indicates residual differences that are sufficiently small for energy reconstruction.The loss is described as a similarity measure between refined and data traces.Source: §5 · p. 7
6 Conclusion
The conclusion reports that Wasserstein-distance adversarial training transfers distributions between datasets in two detector-simulation applications. Generated patterns follow a specified shower energy, and refining simulated traces improves data-event energy reconstruction over original-simulation training.
6 Conclusion
- Unsupervised transfer of probability distributions between datasets works well with the Wasserstein distance in the two investigated detector-simulation variants.The example represents spatially distributed ground-based water-Cherenkov detectors as single-layer calorimeter simulations.Source: §6 · pp. 7–8
- Generated detector-response patterns follow the specified energy constraint, with generated events exhibiting the given shower energy.The example uses ground-based water-Cherenkov air-shower simulations as single-layer calorimeter simulations.Source: §6 · p. 8
- Small refinements to simulated traces improve primary-energy reconstruction for air-shower data events in both energy bias and energy resolution.The conclusion compares training on refined traces with training on originally simulated traces.Source: §6 · p. 8
A Appendix
The appendix provides tables describing the generator, critic, and refiner network architectures used in the WGAN applications.
A Appendix
- Table 1 describes the generator network used to generate signal patterns in the WGAN.The supplied caption identifies the network's role, not its architecture details.Source: Table 1 · p. 10
- Table 2 describes the critic network used in the WGAN for signal-pattern generation.The supplied caption identifies the network's role, not its architecture details.Source: Table 2 · p. 10
- Table 3 describes the refiner network used in the WGAN for refining signal traces.The supplied caption identifies the network's role, not its architecture details.Source: Table 3 · p. 10