# Optimising simulations for diphoton production at hadron colliders using amplitude neural networks

arXiv: https://arxiv.org/abs/2106.09474 · HTML: https://mlsanity.com/paper/2106.09474/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 96 references that are in the map.
- First posted on arXiv 17 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Learning Particle Physics by Example: Location-Aware Generative Adversarial Networks for Physics Synthesis](https://mlsanity.com/paper/1701.05927/) (2017)
- [GANplifying Event Samples](https://mlsanity.com/paper/2008.06545/) (2020)
- [LHC analysis-specific datasets with Generative Adversarial Networks](https://mlsanity.com/paper/1901.05282/) (2019)
- [i-flow: High-dimensional Integration and Sampling with Normalizing Flows](https://mlsanity.com/paper/2001.05486/) (2020)
- [Simulation of electron-proton scattering events by a Feature-Augmented and Transformed Generative Adversarial Network (FAT-GAN)](https://mlsanity.com/paper/2001.11103/) (2020)
- [Understanding Event-Generation Networks via Uncertainties](https://mlsanity.com/paper/2104.04543/) (2021)
- [Variational Autoencoders for Jet Simulation](https://mlsanity.com/paper/2009.04842/) (2020)
- [Lund jet images from generative and cycle-consistent adversarial networks](https://mlsanity.com/paper/1909.01359/) (2019)
- [Neural Network-Based Approach to Phase Space Integration](https://mlsanity.com/paper/1810.11509/) (2018)
- [Improved Neural Network Monte Carlo Simulation](https://mlsanity.com/paper/2009.07819/) (2020)
- [The use of Generative Adversarial Networks to characterise new physics in multi-lepton final states at the LHC](https://mlsanity.com/paper/2105.14933/) (2021)

## Built on by (most cited first, 9 of 9)

- [Lorentz-Equivariant Geometric Algebra Transformers for High-Energy Physics](https://mlsanity.com/paper/2405.14806/) (2024)
- [A Lorentz-Equivariant Transformer for All of the LHC](https://mlsanity.com/paper/2411.00446/) (2024)
- [Lorentz Local Canonicalization: How to Make Any Network Lorentz-Equivariant](https://mlsanity.com/paper/2505.20280/) (2025)
- [Scaling laws for amplitude surrogates](https://mlsanity.com/paper/2601.13308/) (2026)
- [Forecasting Generative Amplification](https://mlsanity.com/paper/2509.08048/) (2025)
- [Extrapolating Jet Radiation with Autoregressive Transformers](https://mlsanity.com/paper/2412.12074/) (2024)
- [Comparing Machine Learning and Interpolation Methods for Loop-Level Calculations](https://mlsanity.com/paper/2111.14788/) (2021)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [Event Generation with Parallel Langevin Sampling and Learned Stein Diagnostics](https://mlsanity.com/paper/2606.14854/) (2026)

## Abstract (arXiv)

Machine learning technology has the potential to dramatically optimise event generation and simulations. We continue to investigate the use of neural networks to approximate matrix elements for high-multiplicity scattering processes. We focus on the case of loop-induced diphoton production through gluon fusion and develop a realistic simulation method that can be applied to hadron collider observables. Neural networks are trained using the one-loop amplitudes implemented in the NJet C++ library and interfaced to the Sherpa Monte Carlo event generator where we perform a detailed study for 2→3 and 2→4 scattering problems. We also consider how the trained networks perform when varying the kinematic cuts effecting the phase space and the reliability of the neural network simulations.