# High-precision regressors for particle physics

arXiv: https://arxiv.org/abs/2302.00753 · HTML: https://mlsanity.com/paper/2302.00753/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 53 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Highway Networks](https://mlsanity.com/paper/1505.00387/) (2015)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Unsupervised and Semi-supervised Learning with Categorical Generative Adversarial Networks](https://mlsanity.com/paper/1511.06390/) (2015)
- [Deeply learned face representations are sparse, selective, and robust](https://mlsanity.com/paper/1412.1265/) (2014)
- [CaloFlow: Fast and Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2106.05285/) (2021)
- [CaloFlow II: Even Faster and Still Accurate Generation of Calorimeter Showers with Normalizing Flows](https://mlsanity.com/paper/2110.11377/) (2021)
- [Variational Autoencoders for Anomalous Jet Tagging](https://mlsanity.com/paper/2007.01850/) (2020)
- [GANplifying Event Samples](https://mlsanity.com/paper/2008.06545/) (2020)
- [Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines](https://mlsanity.com/paper/1610.02746/) (2016)
- [Unbiased Monte Carlo Cluster Updates with Autoregressive Neural Networks](https://mlsanity.com/paper/2105.05650/) (2021)
- [New directions for surrogate models and differentiable programming for High Energy Physics detector simulation](https://mlsanity.com/paper/2203.08806/) (2022)
- [Lund jet images from generative and cycle-consistent adversarial networks](https://mlsanity.com/paper/1909.01359/) (2019)
- [Improved Neural Network Monte Carlo Simulation](https://mlsanity.com/paper/2009.07819/) (2020)
- [A machine learning approach for efficient multi-dimensional integration](https://mlsanity.com/paper/2009.06697/) (2020)

## Abstract (arXiv)

Monte Carlo simulations of physics processes at particle colliders like the Large Hadron Collider at CERN take up a major fraction of the computational budget. For some simulations, a single data point takes seconds, minutes, or even hours to compute from first principles. Since the necessary number of data points per simulation is on the order of 109 - 1012, machine learning regressors can be used in place of physics simulators to significantly reduce this computational burden. However, this task requires high-precision regressors that can deliver data with relative errors of less than 1% or even 0.1% over the entire domain of the function. In this paper, we develop optimal training strategies and tune various machine learning regressors to satisfy the high-precision requirement. We leverage symmetry arguments from particle physics to optimize the performance of the regressors. Inspired by ResNets, we design a Deep Neural Network with skip connections that outperform fully connected Deep Neural Networks. We find that at lower dimensions, boosted decision trees far outperform neural networks while at higher dimensions neural networks perform significantly better. We show that these regressors can speed up simulations by a factor of 103 - 106 over the first-principles computations currently used in Monte Carlo simulations. Additionally, using symmetry arguments derived from particle physics, we reduce the number of regressors necessary for each simulation by an order of magnitude. Our work can significantly reduce the training and storage burden of Monte Carlo simulations at current and future collider experiments.