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| CMS-MLG-24-001 ; CERN-EP-2024-269 | ||
| Reweighting simulated events using machine-learning techniques in the CMS experiment | ||
| CMS Collaboration | ||
| 5 November 2024 | ||
| Submitted to Computing and Software for Big Science | ||
| 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 model parameters to samples with different parameters or samples obtained from entirely different models. 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. | ||
| Links: e-print arXiv:2411.03023 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The normalized differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production in pp collisions at 13 TeV as a function of the $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) of the $ \mathrm{t} \overline{\mathrm{t}} $ system obtained with the POWHEG program. The standard setting of $ h_{\text{damp}}=$ 1.379 $m_{\mathrm{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 lower panels. The vertical bars, in the ratio panels, represent the statistical uncertainties in the MC samples. |
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Figure 1-a:
The normalized differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production in pp collisions at 13 TeV as a function of the $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) of the $ \mathrm{t} \overline{\mathrm{t}} $ system obtained with the POWHEG program. The standard setting of $ h_{\text{damp}}=$ 1.379 $m_{\mathrm{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 lower panels. The vertical bars, in the ratio panels, represent the statistical uncertainties in the MC samples. |
png pdf |
Figure 1-b:
The normalized differential cross section of $ \mathrm{t} \overline{\mathrm{t}} $ production in pp collisions at 13 TeV as a function of the $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) of the $ \mathrm{t} \overline{\mathrm{t}} $ system obtained with the POWHEG program. The standard setting of $ h_{\text{damp}}=$ 1.379 $m_{\mathrm{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 lower panels. The vertical bars, in the ratio panels, represent the statistical uncertainties in the MC samples. |
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Figure 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}} $. |
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Figure 2-a:
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}} $. |
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Figure 2-b:
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}} $. |
png pdf |
Figure 3:
The normalized differential cross section as a function of the $ p_{\mathrm{T}} $ (upper) and $ \eta $ (lower) of the $ \mathrm{t} \overline{\mathrm{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). |
png pdf |
Figure 3-a:
The normalized differential cross section as a function of the $ p_{\mathrm{T}} $ (upper) and $ \eta $ (lower) of the $ \mathrm{t} \overline{\mathrm{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). |
png pdf |
Figure 3-b:
The normalized differential cross section as a function of the $ p_{\mathrm{T}} $ (upper) and $ \eta $ (lower) of the $ \mathrm{t} \overline{\mathrm{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). |
png pdf |
Figure 3-c:
The normalized differential cross section as a function of the $ p_{\mathrm{T}} $ (upper) and $ \eta $ (lower) of the $ \mathrm{t} \overline{\mathrm{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). |
png pdf |
Figure 3-d:
The normalized differential cross section as a function of the $ p_{\mathrm{T}} $ (upper) and $ \eta $ (lower) of the $ \mathrm{t} \overline{\mathrm{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). |
png pdf |
Figure 4:
The normalized differential cross section as a function of $ N_{\text{jet}} $ (left) and $ H_{\mathrm{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. |
png pdf |
Figure 4-a:
The normalized differential cross section as a function of $ N_{\text{jet}} $ (left) and $ H_{\mathrm{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. |
png pdf |
Figure 4-b:
The normalized differential cross section as a function of $ N_{\text{jet}} $ (left) and $ H_{\mathrm{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. |
png pdf |
Figure 5:
Ratios between the $ h_{\text{damp}} $ target distributions in $ p_{\mathrm{T}}({\mathrm{t}\overline{\mathrm{t}}} ) $ (left) and $ \eta({\mathrm{t}\overline{\mathrm{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. |
png pdf |
Figure 5-a:
Ratios between the $ h_{\text{damp}} $ target distributions in $ p_{\mathrm{T}}({\mathrm{t}\overline{\mathrm{t}}} ) $ (left) and $ \eta({\mathrm{t}\overline{\mathrm{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. |
png pdf |
Figure 5-b:
Ratios between the $ h_{\text{damp}} $ target distributions in $ p_{\mathrm{T}}({\mathrm{t}\overline{\mathrm{t}}} ) $ (left) and $ \eta({\mathrm{t}\overline{\mathrm{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. |
png pdf |
Figure 6:
Distributions in $ x_{\mathrm{b}} $ (upper) and $ p_{\mathrm{T}}^{{\mathrm{B}}} $ (lower) from $ \mathrm{t} \overline{\mathrm{t}} $ simulations with PYTHIA8 with value $ r_{\mathrm{b}}= $ 0.855 (dashed blue line) and a second value of $ r_{\mathrm{b}} $ (solid black line). The nominal sample reweighted to $ r_{\mathrm{b}}= $ 1.056 (left) and $ r_{\mathrm{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. |
png pdf |
Figure 6-a:
Distributions in $ x_{\mathrm{b}} $ (upper) and $ p_{\mathrm{T}}^{{\mathrm{B}}} $ (lower) from $ \mathrm{t} \overline{\mathrm{t}} $ simulations with PYTHIA8 with value $ r_{\mathrm{b}}= $ 0.855 (dashed blue line) and a second value of $ r_{\mathrm{b}} $ (solid black line). The nominal sample reweighted to $ r_{\mathrm{b}}= $ 1.056 (left) and $ r_{\mathrm{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. |
png pdf |
Figure 6-b:
Distributions in $ x_{\mathrm{b}} $ (upper) and $ p_{\mathrm{T}}^{{\mathrm{B}}} $ (lower) from $ \mathrm{t} \overline{\mathrm{t}} $ simulations with PYTHIA8 with value $ r_{\mathrm{b}}= $ 0.855 (dashed blue line) and a second value of $ r_{\mathrm{b}} $ (solid black line). The nominal sample reweighted to $ r_{\mathrm{b}}= $ 1.056 (left) and $ r_{\mathrm{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. |
png pdf |
Figure 6-c:
Distributions in $ x_{\mathrm{b}} $ (upper) and $ p_{\mathrm{T}}^{{\mathrm{B}}} $ (lower) from $ \mathrm{t} \overline{\mathrm{t}} $ simulations with PYTHIA8 with value $ r_{\mathrm{b}}= $ 0.855 (dashed blue line) and a second value of $ r_{\mathrm{b}} $ (solid black line). The nominal sample reweighted to $ r_{\mathrm{b}}= $ 1.056 (left) and $ r_{\mathrm{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. |
png pdf |
Figure 6-d:
Distributions in $ x_{\mathrm{b}} $ (upper) and $ p_{\mathrm{T}}^{{\mathrm{B}}} $ (lower) from $ \mathrm{t} \overline{\mathrm{t}} $ simulations with PYTHIA8 with value $ r_{\mathrm{b}}= $ 0.855 (dashed blue line) and a second value of $ r_{\mathrm{b}} $ (solid black line). The nominal sample reweighted to $ r_{\mathrm{b}}= $ 1.056 (left) and $ r_{\mathrm{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. |
png pdf |
Figure 7:
Values of $ \chi^2/\text{NDF} $ obtained for distributions in $ x_{\mathrm{b}} $ (circles) and $ p_{\mathrm{T}}^{{\mathrm{B}}} $ (squares), where target distributions for events with different $ r_{\mathrm{b}} $ values are compared to a distribution with the nominal value of $ r_{\mathrm{b}}= $ 0.855 before the reweighting (blue dashed line) and after the reweighting to the target value of $ r_{\mathrm{b}} $ (red solid line). The lines connecting the markers are shown for illustration purposes only. |
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Figure 8:
Ratios between the $ r_{\mathrm{b}} $ target distributions in $ x_{\mathrm{b}} $ (left) and $ p_{\mathrm{T}}^{{\mathrm{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. |
png pdf |
Figure 8-a:
Ratios between the $ r_{\mathrm{b}} $ target distributions in $ x_{\mathrm{b}} $ (left) and $ p_{\mathrm{T}}^{{\mathrm{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. |
png pdf |
Figure 8-b:
Ratios between the $ r_{\mathrm{b}} $ target distributions in $ x_{\mathrm{b}} $ (left) and $ p_{\mathrm{T}}^{{\mathrm{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. |
png pdf |
Figure 9:
Distributions in top quark $ p_{\mathrm{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 lower panels, where the vertical bars correspond to the statistical uncertainties. |
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Figure 9-a:
Distributions in top quark $ p_{\mathrm{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 lower panels, where the vertical bars correspond to the statistical uncertainties. |
png pdf |
Figure 9-b:
Distributions in top quark $ p_{\mathrm{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 lower panels, where the vertical bars correspond to the statistical uncertainties. |
png pdf |
Figure 10:
Distributions in $ p_{\mathrm{T}} $ (upper left), $ \eta $ (upper right), $ \Delta\phi $ (lower left), and mass (lower right) of the $ \mathrm{t} \overline{\mathrm{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. |
png pdf |
Figure 10-a:
Distributions in $ p_{\mathrm{T}} $ (upper left), $ \eta $ (upper right), $ \Delta\phi $ (lower left), and mass (lower right) of the $ \mathrm{t} \overline{\mathrm{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. |
png pdf |
Figure 10-b:
Distributions in $ p_{\mathrm{T}} $ (upper left), $ \eta $ (upper right), $ \Delta\phi $ (lower left), and mass (lower right) of the $ \mathrm{t} \overline{\mathrm{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. |
png pdf |
Figure 10-c:
Distributions in $ p_{\mathrm{T}} $ (upper left), $ \eta $ (upper right), $ \Delta\phi $ (lower left), and mass (lower right) of the $ \mathrm{t} \overline{\mathrm{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. |
png pdf |
Figure 10-d:
Distributions in $ p_{\mathrm{T}} $ (upper left), $ \eta $ (upper right), $ \Delta\phi $ (lower left), and mass (lower right) of the $ \mathrm{t} \overline{\mathrm{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. |
png pdf |
Figure 11:
Distributions in $ p_{\mathrm{T}} $ of the $ \mathrm{t} \overline{\mathrm{t}} $ system (left) and $ p_{\mathrm{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_{\mathrm{T}} $ of the $ \mathrm{t} \overline{\mathrm{t}} $ system and of the t (violet dash-dotted line). The ratio to the NNLO predictions is shown in the lower panels, where the vertical bars correspond to the statistical uncertainties. |
png pdf |
Figure 11-a:
Distributions in $ p_{\mathrm{T}} $ of the $ \mathrm{t} \overline{\mathrm{t}} $ system (left) and $ p_{\mathrm{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_{\mathrm{T}} $ of the $ \mathrm{t} \overline{\mathrm{t}} $ system and of the t (violet dash-dotted line). The ratio to the NNLO predictions is shown in the lower panels, where the vertical bars correspond to the statistical uncertainties. |
png pdf |
Figure 11-b:
Distributions in $ p_{\mathrm{T}} $ of the $ \mathrm{t} \overline{\mathrm{t}} $ system (left) and $ p_{\mathrm{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_{\mathrm{T}} $ of the $ \mathrm{t} \overline{\mathrm{t}} $ system and of the t (violet dash-dotted line). The ratio to the NNLO predictions is shown in the lower panels, where the vertical bars correspond to the statistical uncertainties. |
| Summary |
| Particle physics relies on the simulation of events using Monte Carlo (MC) event generators for data-to-theory comparisons. Data analyses require the production of several samples simulating the same physical process to estimate systematic uncertainties or the impact of higher-order calculations. To provide statistically significant predictions, these samples have to be very large with billions of events generated and simulated at a high computational cost. Nevertheless, the statistical precision from the finite size of these samples can become a limiting factor in precision analyses. The production of sufficiently large MC samples, such that the statistical precision of these samples is better than the statistical precision of the data, will become increasingly prohibitive at the High-Luminosity LHC (HL-LHC) with the expected computing resources.In this article, the method ``deep neural network using classification for tuning and reweighting (DCTR)'' has been introduced to reweight MC samples used in CMS analyses. The weights calculated with the DCTR model enable the modification of one nominal sample to resemble other samples obtained with different parameters or different simulation programs. This methodology avoids the need for simulating the detector response for multiple samples by incorporating the relevant variations in a single sample. While dedicated samples have to be generated for the training and validation of the model, these do not need the full detector simulation and reconstruction, saving up to 75% of the typical CPU resources needed for the production of MC samples in CMS. In addition, after the training of the DCTR model, the training samples can be deleted saving storage space for several billions of events.The DCTR method has been shown to work reliably for two important sources of modelling uncertainties in the simulation of top quark pair ($ \mathrm{t} \overline{\mathrm{t}} $) production. Currently, the systematic uncertainty connected to the matching of radiation from matrix elements and the parton shower has to be estimated with dedicated samples. The reweighting of variations in the b quark fragmentation shows that a continuous reweighting in a model parameter is possible, paving the way for the determination of model parameters directly from collision data. Additionally, the method has been extended to reweight an NLO simulation to an NNLO one for $ \mathrm{t} \overline{\mathrm{t}} $ production, which will allow for a fast evaluation of the impact of higher-order corrections on data analyses. The DCTR reweighting can be seamlessly integrated into CMS analyses and is already in use by the CMS experiment. A robust performance across a range of scenarios was demonstrated, making the method promising for future applications in other areas as well. For example, it can be extended to other systematic variations or applied to different physics fields beyond top quark studies. It provides an elegant solution to address the computational challenges posed by the production of large MC samples, particularly for the HL-LHC. |
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