Reweighting simulated events using machine-learning techniques in the CMS experiment

Abstract

Data analyses in particle physics rely on an accurate simulation of particle collisions and a detailed simulation of detector effects to extract physics knowledge from the recorded data. Event generators together with a geant-based simulation of the detectors are used to produce large samples of simulated events for analysis by the LHC experiments. These simulations come at a high computational cost, where the detector simulation and reconstruction algorithms have the largest CPU demands. This article describes how machine-learning (ML) techniques are used to reweight simulated samples obtained with a given set of parameters to samples with different parameters or samples obtained from entirely different simulation programs. The ML reweighting method avoids the need for simulating the detector response multiple times by incorporating the relevant information in a single sample through event weights. Results are presented for reweighting to model variations and higher-order calculations in simulated top quark pair production at the LHC. This ML-based reweighting is an important element of the future computing model of the CMS experiment and will facilitate precision measurements at the High-Luminosity LHC.

Fig. 1

The normalized differential cross section of $\text{t}\overline{\text{t}}$ production in pp collisions at 13$\text{Te}\text{V}$ as a function of the $p_{\text{T}}$ (left) and $\eta$ (right) of the $\text{t}\overline{\text{t}}$ system obtained with the powheg program. The standard setting of $h_{\text{damp}}=1.379m_{\text{t}}$ (black solid lines) is compared to down (orange dashed lines) and up (violet dotted lines) variations in $h_{\text{damp}}$. The ratios of the predictions with the $h_{\text{damp}}$ variations to the nominal one are shown in the right panels. The vertical bars, in the ratio panels, represent the statistical uncertainties in the MC samples

Fig. 2

The NN histories of the training for the $h_{\text{damp}}$ parameter reweighting. Shown are the loss functions for the training data (blue solid line) and the validation data (orange dash-dotted line) for the down (left) and up (right) variations of $h_{\text{damp}}$

Fig. 3

The normalized differential cross section as a function of the $p_{\text{T}}$ (upper) and $\eta$ (lower) of the $\text{t}\overline{\text{t}}$ system. The black solid line shows the predictions from the down (left) and up (right) variations in $h_{\text{damp}}$, and the blue dashed line presents the prediction from the nominal sample. The red dotted line indicates the nominal sample reweighted to the down (left) and up (right) $h_{\text{damp}}$ variations using the DCTR method. The ratios to the samples with the target values of $h_{\text{damp}}$ are displayed in the lower panels, together with their almost negligible statistical uncertainties (vertical error bars)

Fig. 4

The normalized differential cross section as a function of $N_{\text{jet}}$ (left) and $H_{\text{T}}$ (right). The black solid line shows the predictions from the up variation in $h_{\text{damp}}$ and the blue dashed line presents the prediction from the nominal sample. The red dotted line indicates the nominal sample reweighted to the $h_{\text{damp}}$ variation using the DCTR method. The ratios to the target distributions are displayed in the pads below, where the vertical bars represent statistical uncertainties

Fig. 5

Ratios between the $h_{\text{damp}}$ target distributions in $p_{\text{T}}(\text{t}\overline{\text{t}})$ (left) and $\eta (\text{t}\overline{\text{t}})$ (right), and 50 different reweightings (grey solid lines). The ratio to the target before the reweighting is shown as a blue dashed line and the mean of the different reweightings as a red dotted line. The red band represents the statistical uncertainty of the method obtained from the standard deviation of the 50 reweighted samples

Fig. 6

Distributions in $x_{\text{b}}$ (upper) and $p_{\text{T}}^{\text{B}}$ (lower) from $\text{t}\overline{\text{t}}$ simulations with pythia 8 with value $r_{\text{b}}=0.855$ (dashed blue line) and a second value of $r_{\text{b}}$ (solid black line). The nominal sample reweighted to $r_{\text{b}}=1.056$ (left) and $r_{\text{b}}=1.252$ (right) is shown as red dotted lines. Below each distribution, the ratios to the target distribution are displayed, where the vertical bars represent the statistical uncertainties

Fig. 7

Values of ${\chi }^2/\text{NDF}$ obtained for distributions in $x_{\text{b}}$ (circles) and $p_{\text{T}}^{\text{B}}$ (squares), where target distributions for events with different $r_{\text{b}}$ values are compared to a distribution with the nominal value of $r_{\text{b}}=0.855$ before the reweighting (blue dashed line) and after the reweighting to the target value of $r_{\text{b}}$ (red solid line). The lines connecting the markers are shown for illustration purposes only

Fig. 8

Ratios between the $r_{\text{b}}$ target distributions in $x_{\text{b}}$ (left) and $p_{\text{T}}^{\text{B}}$ (right), and 50 different reweightings (grey solid lines). The ratio to the target before the reweighting is shown as a blue dashed line and the mean of the different reweightings as a red dotted line. The red band represents the statistical uncertainty of the method obtained from the standard deviation of the 50 reweighted samples. The vertical bars show the statistical precision of the samples. In particular, the red bars display the average statistical uncertainty of the 50 reweighted samples

Fig. 9

Distributions in top quark $p_{\text{T}}$ (left) and $\eta$ (right) obtained from simulations at NNLO accuracy (black solid lines), NLO accuracy (blue dashed lines), and NLO reweighted to NNLO with the DCTR method (red dotted lines). The ratio to the NNLO predictions is shown in the right panels, where the vertical bars correspond to the statistical uncertainties

Fig. 10

Distributions in $p_{\text{T}}$ (upper left), $\eta$ (upper right), $\Delta \varphi$ (lower left), and mass (lower right) of the $\text{t}\overline{\text{t}}$ system obtained from simulations at NNLO accuracy (black solid lines), NLO accuracy (blue dashed lines), and NLO reweighted to NNLO with the DCTR method (red dotted lines). The ratio to the NNLO predictions is shown in the lower panels, where the vertical bars correspond to the statistical uncertainties

Fig. 11

Distributions in $p_{\text{T}}$ of the $\text{t}\overline{\text{t}}$ system (left) and $p_{\text{T}}$ of the t (right) obtained from simulations at NNLO accuracy (black solid lines), NLO accuracy (blue dashed lines), NLO reweighted to NNLO with the DCTR method (red dotted lines), and NLO reweighted using a two-dimensional reweighting in $p_{\text{T}}$ of the $\text{t}\overline{\text{t}}$ system and of the t (violet dash-dotted line). The ratio to the NNLO predictions is shown in the right panels, where the vertical bars correspond to the statistical uncertainties