Source-linked AI summary
Learning Particle Physics by Example: Location-Aware Generative Adversarial Networks for Physics Synthesis
Luke de Oliveira, Michela Paganini, Benjamin Nachman
TL;DR
High-energy physics requires computationally expensive simulations, motivating faster generative approaches. The paper introduces Location-Aware GANs for jet-image generation and finds realistic images with physically meaningful observable distributions, while identifying limitations for classifier training.
Problem
Precise high-energy-physics simulations are time- and CPU-intensive, motivating faster event-generation methods.
Method
The paper introduces Location-Aware Generative Adversarial Networks that learn generative models of simulated jet images using location-based architectural modifications.
Results
Qualitative and quantitative evaluations show realistic jet images whose observable distributions reproduce many features of Pythia images.
Takeaways & Limitations
Jet images provide a testing ground for GAN-based generation and a basis for further high-energy-physics simulation studies.
Takeaways & Limitations
GAN-generated images are not currently a viable exclusive substitute for Pythia images when training a classifier to discriminate Pythia images.
Abstract
from arXiv · showhide
We provide a bridge between generative modeling in the Machine Learning community and simulated physical processes in High Energy Particle Physics by applying a novel Generative Adversarial Network (GAN) architecture to the production of jet images -- 2D representations of energy depositions from particles interacting with a calorimeter. We propose a simple architecture, the Location-Aware Generative Adversarial Network, that learns to produce realistic radiation patterns from simulated high energy particle collisions. The pixel intensities of GAN-generated images faithfully span over many orders of magnitude and exhibit the desired low-dimensional physical properties (i.e., jet mass, n-subjettiness, etc.). We shed light on limitations, and provide a novel empirical validation of image quality and validity of GAN-produced simulations of the natural world. This work provides a base for further explorations of GANs for use in faster simulation in High Energy Particle Physics.
1 Introduction
High-energy physics relies on detailed simulations that are expensive at the required scale. The paper explores GANs for faster event generation by reproducing physically meaningful jet images.
- O(10^9) events/year must be simulated, making precise Geant4-based detector simulations time- and CPU-intensive.Existing approximations are faster but remain non-negligible and are not applicable to all physics applications.
- The paper develops GAN-based fast event generation for high-energy physics using jet images as a constrained starting point.Jet images represent idealized two-dimensional radiation patterns from high-energy quarks and gluons.
- Generated jet images are evaluated by whether they resemble simulated images in physically meaningful ways.The paper frames this as evidence for GANs’ future applications in physics simulation.
- The paper introduces dedicated GAN architectures for jet images and presents results alongside discussion of what the neural network learns.The architecture and results are described in Sections 4 and 5, respectively.
2 Dataset
Jet images encode calorimeter-like radiation patterns on a two-dimensional η × φ grid. The dataset applies clustering, trimming, centering, and kinematic selection while accounting for the images’ sparse structure.
- A jet image is a two-dimensional η × φ pixel grid representing the locations and energies of particles within a jet.It approximates a calorimeter without longitudinal segmentation.
- 0.1 × 0.1 η–φ cells form the calorimeter grid, with each cell’s energy equal to the sum of incident-particle energies.Positive-energy cells are assigned to jets using anti-kt clustering with R = 1.0.
- R = 0.3 kt subjets below 5% of the parent jet’s transverse momentum are dropped during trimming.This reduces underlying-event and pileup contributions.
- Jets are centered by translating constituents so the highest-pT subjet lies at the origin.The image uses a [−1.25, 1.25] × [−1.25, 1.25] rectangular grid with 0.1 × 0.1 pixels.
- Typical jet images are highly sparse, with approximately 10% occupancy and no smooth natural-image-like features.These properties motivate a dedicated GAN setup.
3 Generative Adversarial Networks
GANs learn a synthesized image distribution through an adversarial generator–discriminator game. The generator produces samples from latent inputs, while the discriminator distinguishes generated from real images during alternating optimization.
- I is the sample space of grayscale square images, while N denotes naturally occurring samples drawn from an unknown data distribution f.The target is the distribution the model aims to recover.
- The generator maps a latent vector z to synthesized examples S.Here z is sampled from a normal distribution with mean μ and variance σ^2.
- The discriminator maps an image I to a probability that it is fake or real.D(I) = 0 denotes fake and D(I) = 1 denotes real.
- The GAN loss contains terms for classifying generated samples as fake and data-distribution samples as real.The generator minimizes the loss and the discriminator maximizes it.
- Generator and discriminator updates alternate through gradient-descent steps during training.The players are typically non-convex, contributing to GAN training difficulty.
- Mini-batch discrimination and feature matching are described as methods that help avoid mode collapse.They let the discriminator use batch-level features and statistics, making single-output generation suboptimal for the generator.
4 Location-Aware Generative Adversarial Network(LAGANs)
LAGAN adapts GANs to sparse jet images by using location-specific processing, auxiliary signal/background classification, and training stabilizers. Its architecture combines convolutional and locally connected layers to model both location-dependent constituents and dispersed radiation.
- LAGAN modifies DCGAN to exploit jet-image symmetries while explicitly inducing location-based feature detection.
- The discriminator jointly distinguishes real from generated images and classifies boosted W bosons versus QCD to learn a conditional data distribution.
- The generator and discriminator use a convolutional layer followed by locally connected layers without weight sharing, with ReLU, batch normalization, minibatch discrimination, and label flipping supporting sparsity and stability.Minibatch discrimination was experimentally crucial for modeling high dynamic range and sparsity, while batch normalization and label flipping were essential for stability under large dynamic range.
- Preliminary experiments motivated location-specific layers for central constituents and convolutional processing for less location-specific, low-energy radiation.
- Locally connected layers use unique filters at each image patch, whereas convolutional layers share filters across locations.
- LAGAN uses a 200-dimensional Gaussian latent vector, class conditioning, and a 25 × 25 generated output trained end-to-end with alternating generator and discriminator updates.Training uses Adam, batch size 100, 40 epochs, and two NVIDIA Titan X GPUs.
5 Generating Jet Images with Adversarial Networks
The LAGAN model reproduces key physical properties and radiation patterns of Pythia jet images across broad intensity and observable ranges. Its validation also exposes limitations, including exaggerated pixel-level class differences and difficulty generating ambiguous images.
- 5.1 Image Content Quality Assessment: The generated distributions of image mass, pT, and τ21 nearly match Pythia, including the approximately 80 GeV signal-mass peak, while retaining comparable diversity.The W-boson mass peak emerges without being explicitly encouraged by the training or architecture.
- 5.1 Image Content Quality Assessment: The discriminator assigns P(real) approximately 1/2 to almost all generated images, with little mass or pT dependence except outside the training ranges for background.This stable confusion indicates convergence toward a point where generated and real images are difficult to distinguish by the discriminator.
- 5.1 Image Content Quality Assessment: Nearest-neighbor comparisons show realistic dispersion patterns without memorizing the training set, although the model is inadequate in very low-intensity regions.The low-intensity shortcoming is considered inconsequential because most important jet information is carried by higher-pT particles.
- 5.1 Image Content Quality Assessment: Average generated images approximate Pythia’s broad radiation patterns, with central-region pixel intensities differing by only a few percent.The generated images span multiple orders of magnitude while producing large, spread-out, roughly circular dispersion patterns.
- 5.1 Image Content Quality Assessment: Signal-background difference polarity is reproduced at the pixel level, but stronger generated magnitude differences suggest overestimated individual-pixel contributions to classification.The auxiliary classification setup can also make generated images easier to classify than Pythia images, limiting their use as an exclusive classifier training set.
6 Conclusions and Outlook
The paper introduces LAGAN for generating realistic jet images and positions it as a foundation for faster, broader GAN-based simulation in high energy physics.
- LAGAN learns a rich generative model of jet images and produces realistic-looking images under qualitative and quantitative evaluation.
- The architecture extends GAN methods to jet images, which differ significantly from natural images studied in prior GAN research.
- LAGAN is presented as a testing ground for fast generative models in high energy physics and future higher-dimensional image generation.
- Neural-network generation is identified as a promising avenue for computationally heavy simulation needs in high energy particle and nuclear physics.
A Additional Material
The additional figures compare Pythia and GAN images, discriminator labels, signal-background differences, and classifier correlations across real and generated samples.
- Figures 24 and 25 compare average Pythia and GAN signal or background images on log scale, alongside their linear-scale differences.
- Figures 26–29 compare average Pythia and GAN images labeled as real or fake, including linear-scale differences between labels.
- Figures 30 and 31 show signal-background differences for real and fake images produced by Pythia and the GAN.
- Figure 32 presents normalized confusion matrices for all images, Pythia images only, and GAN images only, relating discriminator outputs to the true physical process.
B Image Pre-processing
The preprocessing analysis examines information loss from transformations and identifies a fully preprocessed option that performs best across the reported metrics.
- Rotation about the jet axis in η−φ does not preserve jet mass, so preprocessing can alter physical information.
- Figure 33 quantifies information lost by preprocessing steps, with particular attention to the rotation step.
- The best fully preprocessed option for all metrics is Pix+Trans+Rotation(Cubic)+Renorm, which preserves total pixel intensity after rotation.
- A preprocessing step without information loss lies on the random-classifier line f(x) = 1/x in the Figure 33 ROC analysis.
- Figure 34 evaluates signal-background discrimination using jet mass and n-subjettiness after preprocessing.