# Neural Network-Based Approach to Phase Space Integration

arXiv: https://arxiv.org/abs/1810.11509 · HTML: https://mlsanity.com/paper/1810.11509/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2018.

## Built on by (most cited first, 10 of 10)

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- [Convolutional L2LFlows: Generating Accurate Showers in Highly Granular Calorimeters Using Convolutional Normalizing Flows](https://mlsanity.com/paper/2405.20407/) (2024)
- [Optimising simulations for diphoton production at hadron colliders using amplitude neural networks](https://mlsanity.com/paper/2106.09474/) (2021)
- [Bayesian Modelling of Multivalued Power Curves from an Operational Wind Farm](https://mlsanity.com/paper/2111.15496/) (2021)
- [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)
- [BitHEP -- The Limits of Low-Precision ML in HEP](https://mlsanity.com/paper/2504.03387/) (2025)
- [Flow Annealed Importance Sampling Bootstrap meets Differentiable Particle Physics](https://mlsanity.com/paper/2411.16234/) (2024)
- [Event Generation with Parallel Langevin Sampling and Learned Stein Diagnostics](https://mlsanity.com/paper/2606.14854/) (2026)

## Abstract (arXiv)

Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized to perform this task. The algorithm has been applied to several examples of direct relevance for particle physics, including situations with non-trivial features such as sharp resonances and soft/collinear enhancements. Excellent performance has been demonstrated in all examples, with the properly trained NN achieving unweighting efficiencies of between 30% and 75%. In contrast to traditional Monte Carlo algorithms such as VEGAS, the NN-based approach does not require that the phase space coordinates be aligned with resonant or other features in the cross section.