Accelerating multijet-merged event generation with neural network matrix element surrogates

TL;DR

The work tackles the heavy computational burden of simulating multijet final states at the HL-LHC by introducing a two-stage rejection-sampling scheme that uses neural-network surrogates to unweight matrix elements. It extends previous surrogate methods to tree-level multijet merging, integrating seamlessly with Sherpa’s phase-space biasing, colour treatments, and Sudakov vetoes, and trains surrogates on a reduced basis of process groups for efficiency. Applied to inclusive $Z+$jets production with up to six final-state partons, the approach yields large CPU-time reductions—approximately a factor of $11$ for $Z+6$ jets and $3.3$ for $Z+5$ jets—without compromising physics, as validated by Rivet. The results demonstrate the practicality of fast, unbiased, high-statistics simulations at HL-LHC, with potential extensions to NLO/one-loop elements and broader processes.

Abstract

The efficient simulation of multijet final states presents a serious computational task for analyses of LHC data and will be even more so at the HL-LHC. We here discuss means to accelerate the generation of unweighted events based on a two-stage rejection-sampling algorithm that employs neural-network surrogates for unweighting the hard-process matrix elements. To this end, we generalise the previously proposed algorithm based on factorisation-aware neural networks to the case of multijet merging at tree-level accuracy. We thereby account for several non-trivial aspects of realistic event-simulation setups, including biased phase-space sampling, partial unweighting, and the mapping of partonic subprocesses. We apply our methods to the production of Z+jets final states at the HL-LHC using the Sherpa event generator, including matrix elements with up to six final-state partons. When using neural-network surrogates for the dominant Z+5 jets and Z+6 jets partonic processes, we find a reduction in the total event-generation time by more than a factor of 10 compared to baseline Sherpa.

Figures (10)

• Figure 1: Comparison of the efficiency of the second unweighting step for the process $g u\to Z g g g g g u$ for two alternative definitions of the correction weight $x$ as described in the text. The efficiencies resulting from the same surrogate model are displayed as a function of the first unweighting maximum reduction, $\epsilon_{s}\xspace$. The blue line uses $\epsilon_{x}$=0.001, while for comparability the orange line has an adjusted $\epsilon_{x}$, so that for each value of $\epsilon_{s}\xspace$ both curves feature the same contribution to the total cross section from overweights.
• Figure 2: Loss function curves for the MSE and gain-factor training for $g u \to e\textsuperscript{+} e\textsuperscript{--} g g g g g u$.
• Figure 3: Accuracy $x$ of the surrogate-model prediction in dependence on the weight $w_{\text{ME}}$ for the channel $g u \to e\textsuperscript{+} e\textsuperscript{--} g g g g g u$. The ratio $\frac{\langle w_\text{ME} \rangle}{\langle s_\text{ME} \rangle}$ that determines the second-unweighting efficiency is shown as dashed red line.
• Figure 4: Total compute time per subprocess for $Z+6$ jets (left) and $Z+5$ jets (right) channels contributing to inclusive $Z+\leq 6$ jets production. For the overhead time we here consider $t_{\text{overhead}}=25\,$HS23s per event. The channels are sorted on the $x$-axis according to their estimated time reduction.
• Figure 5: Contribution per subprocess to the total computation time for $\epsilon_{\text{max}}\xspace=0.001$ of inclusive $Z+\leq 6$-jets with overhead time estimate of 25 HS23s/event in the Sherpa baseline approach, i.e. without surrogates. Labels are shown for processes with more than 2% contribution to the total compute time. Subprocesses for which a surrogate got trained for are moved outwards.