# Particle Cloud Generation with Message Passing Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2106.11535 · HTML: https://mlsanity.com/paper/2106.11535/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 65 references that are in the map.
- First posted on arXiv 22 Jun 2021.

## Builds on (most cited first, 29 of 29)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows](https://mlsanity.com/paper/1906.12320/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules](https://mlsanity.com/paper/1906.00957/) (2019)
- [Pros and Cons of GAN Evaluation Measures: New Developments](https://mlsanity.com/paper/2103.09396/) (2021)
- [Discrete Point Flow Networks for Efficient Point Cloud Generation](https://mlsanity.com/paper/2007.10170/) (2020)
- [Point Cloud GAN](https://mlsanity.com/paper/1810.05795/) (2018)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [Image Augmentations for GAN Training](https://mlsanity.com/paper/2006.02595/) (2020)
- [ParticleNet: Jet Tagging via Particle Clouds](https://mlsanity.com/paper/1902.08570/) (2019)
- [Symmetry-Aware Actor-Critic for 3D Molecular Design](https://mlsanity.com/paper/2011.12747/) (2020)
- [Learning Particle Physics by Example: Location-Aware Generative Adversarial Networks for Physics Synthesis](https://mlsanity.com/paper/1701.05927/) (2017)
- [Jet-Images -- Deep Learning Edition](https://mlsanity.com/paper/1511.05190/) (2015)
- [Implicit competitive regularization in GANs](https://mlsanity.com/paper/1910.05852/) (2019)
- [Simulation-based inference methods for particle physics](https://mlsanity.com/paper/2010.06439/) (2020)
- [Rethinking Sampling in 3D Point Cloud Generative Adversarial Networks](https://mlsanity.com/paper/2006.07029/) (2020)
- [Data Augmentation at the LHC through Analysis-specific Fast Simulation with Deep Learning](https://mlsanity.com/paper/2010.01835/) (2020)

## Built on by (most cited first, 30 of 46)

- [Particle Transformer for Jet Tagging](https://mlsanity.com/paper/2202.03772/) (2022)
- [CaloClouds: Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2305.04847/) (2023)
- [Evaluating generative models in high energy physics](https://mlsanity.com/paper/2211.10295/) (2022)
- [PC-JeDi: Diffusion for Particle Cloud Generation in High Energy Physics](https://mlsanity.com/paper/2303.05376/) (2023)
- [EPiC-GAN: Equivariant Point Cloud Generation for Particle Jets](https://mlsanity.com/paper/2301.08128/) (2023)
- [CaloClouds II: Ultra-Fast Geometry-Independent Highly-Granular Calorimeter Simulation](https://mlsanity.com/paper/2309.05704/) (2023)
- [Deep Generative Models for Detector Signature Simulation: A Taxonomic Review](https://mlsanity.com/paper/2312.09597/) (2023)
- [EPiC-ly Fast Particle Cloud Generation with Flow-Matching and Diffusion](https://mlsanity.com/paper/2310.00049/) (2023)
- [New directions for surrogate models and differentiable programming for High Energy Physics detector simulation](https://mlsanity.com/paper/2203.08806/) (2022)
- [Comparison of Point Cloud and Image-based Models for Calorimeter Fast Simulation](https://mlsanity.com/paper/2307.04780/) (2023)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flows](https://mlsanity.com/paper/2405.20407/) (2024)
- [Explaining machine-learned particle-flow reconstruction](https://mlsanity.com/paper/2111.12840/) (2021)
- [Graph Neural Networks in Particle Physics: Implementations, Innovations, and Challenges](https://mlsanity.com/paper/2203.12852/) (2022)
- [Attention to Mean-Fields for Particle Cloud Generation](https://mlsanity.com/paper/2305.15254/) (2023)
- [Locality-Sensitive Hashing-Based Efficient Point Transformer with Applications in High-Energy Physics](https://mlsanity.com/paper/2402.12535/) (2024)
- [Selectively increasing the diversity of GAN-generated samples](https://mlsanity.com/paper/2207.01561/) (2022)
- [PC-Droid: Faster diffusion and improved quality for particle cloud generation](https://mlsanity.com/paper/2307.06836/) (2023)
- [Flow Matching Beyond Kinematics: Generating Jets with Particle-ID and Trajectory Displacement Information](https://mlsanity.com/paper/2312.00123/) (2023)
- [Diffusion map particle systems for generative modeling](https://mlsanity.com/paper/2304.00200/) (2023)
- [PIPPIN: Generating variable length full events from partons](https://mlsanity.com/paper/2406.13074/) (2024)
- [RINO: Renormalization Group Invariance with No Labels](https://mlsanity.com/paper/2509.07486/) (2025)
- [Multiband VAE: Latent Space Alignment for Knowledge Consolidation in Continual Learning](https://mlsanity.com/paper/2106.12196/) (2021)
- [Generalizing to new geometries with Geometry-Aware Autoregressive Models (GAAMs) for fast calorimeter simulation](https://mlsanity.com/paper/2305.11531/) (2023)
- [Machine Learning methods for simulating particle response in the Zero Degree Calorimeter at the ALICE experiment, CERN](https://mlsanity.com/paper/2306.13606/) (2023)
- [Do graph neural networks learn traditional jet substructure?](https://mlsanity.com/paper/2211.09912/) (2022)
- [Induced Generative Adversarial Particle Transformers](https://mlsanity.com/paper/2312.04757/) (2023)
- [Jet Discrimination with Quantum Complete Graph Neural Network](https://mlsanity.com/paper/2403.04990/) (2024)
- [BUFF: Boosted Decision Tree based Ultra-Fast Flow matching](https://mlsanity.com/paper/2404.18219/) (2024)
- [Evidential Deep Learning for Uncertainty Quantification and Out-of-Distribution Detection in Jet Identification using Deep Neural Networks](https://mlsanity.com/paper/2501.05656/) (2025)

## Abstract (arXiv)

In high energy physics (HEP), jets are collections of correlated particles produced ubiquitously in particle collisions such as those at the CERN Large Hadron Collider (LHC). Machine learning (ML)-based generative models, such as generative adversarial networks (GANs), have the potential to significantly accelerate LHC jet simulations. However, despite jets having a natural representation as a set of particles in momentum-space, a.k.a. a particle cloud, there exist no generative models applied to such a dataset. In this work, we introduce a new particle cloud dataset (JetNet), and apply to it existing point cloud GANs. Results are evaluated using (1) 1-Wasserstein distances between high- and low-level feature distributions, (2) a newly developed Fr'echet ParticleNet Distance, and (3) the coverage and (4) minimum matching distance metrics. Existing GANs are found to be inadequate for physics applications, hence we develop a new message passing GAN (MPGAN), which outperforms existing point cloud GANs on virtually every metric and shows promise for use in HEP. We propose JetNet as a novel point-cloud-style dataset for the ML community to experiment with, and set MPGAN as a benchmark to improve upon for future generative models. Additionally, to facilitate research and improve accessibility and reproducibility in this area, we release the open-source JetNet Python package with interfaces for particle cloud datasets, implementations for evaluation and loss metrics, and more tools for ML in HEP development.