[Paper Review] (Machine) Learning amplitudes for faster event generation

Fady Bishara, Marc Montull|arXiv (Cornell University)|Jan 1, 2019

Scientific Computing and Data ManagementDecision Sciences34 citations

TL;DR

This paper proposes replacing exact quantum field theory amplitudes in Monte Carlo event generators with trained machine learning regressors to drastically accelerate event generation. Using XGBoost to predict the loop-induced gg → ZZ process, the method achieves sub-0.1% accuracy with prediction speeds ~1,000× faster than traditional tools, using only ~7 minutes of training and models under 30 MB in size.

ABSTRACT

We propose to replace the exact amplitudes used in Monte Carlo event generators for trained machine learning regressors, with the aim of speeding up the evaluation of slow amplitudes. As a proof of concept, we study the process $gg→ZZ$, whose leading-order amplitude is loop induced. We show that gradient boosting machines like xgboost can predict the fully differential distributions with errors below 0.1%, and with prediction times $O(10^3)$ faster than the evaluation of the exact function. This is achieved with training times $∼ 23$ $minutes$ and regressors of size $≲ 22$ $Mb$. We also find that xgboost performs well over the entire phase space, while interpolation gives much larger errors in regions where the function is peaked. These results suggest a possible new avenue to speed up Monte Carlo event generators.

Motivation & Objective

• Address the growing computational bottleneck of higher-order quantum field theory amplitudes in Monte Carlo event generation.
• Reduce evaluation times for loop-induced processes like gg → ZZ, which are slow and hinder precision physics.
• Explore whether ML can replace exact amplitude calculations without sacrificing accuracy.
• Demonstrate a practical, lightweight ML framework for integration into existing HEP event generators.
• Enable faster phenomenological studies and searches for new physics by accelerating amplitude evaluation.

Proposed method

• Train XGBoost gradient boosting machines on pre-computed exact amplitudes from OpenLoops for the gg → ZZ process.
• Use 18 million uniformly distributed phase space points in √s and cosθ to train and test the regressor.
• Partition phase space into 10 sub-regions based on amplitude peak structure to improve local accuracy.
• Optimize hyperparameters (n_estimators=200, max_depth=50, learning_rate=0.1) via small grid search.
• Use a single CPU core for training, achieving <7 minutes training time.
• Store trained models in <30 MB, enabling fast distribution and deployment.

Experimental results

Research questions

• RQ1 Can ML regressors accurately predict complex, loop-induced amplitudes like gg → ZZ with sufficient precision for HEP phenomenology?
• RQ2 How much faster can ML-based amplitude evaluation be compared to traditional exact amplitude computation?
• RQ3 What is the optimal trade-off between model size, training time, and prediction accuracy for HEP applications?
• RQ4 Can phase space partitioning improve the performance of ML models on highly peaked amplitudes?
• RQ5 Is it feasible to deploy such ML models in real-world Monte Carlo generators for precision LHC physics?

Key findings

• ML regressors using XGBoost achieve prediction errors below 0.1% on fully differential distributions for the gg → ZZ process.
• Prediction speeds are approximately 1,000 times faster than exact amplitude evaluation using OpenLoops.
• Training time is under 7 minutes on a single CPU core, with model sizes under 30 MB.
• Phase space partitioning into 10 regions improves model performance by reducing amplitude variation per sub-region.
• The method is robust and generalizable, with potential for extension to other loop-induced processes.
• The approach enables a new pathway to accelerate Monte Carlo event generation without compromising accuracy.