Lamarr: LHCb ultra-fast simulation based on machine learning models

During the LHC Run 2, the LHCb experiment has spent more than 80% of the pledged CPU time to produce simulated samples. Run 3 CPU resource needs will far exceed the computing resources available to the LHCb Collaboration, that is spending huge efforts in developing faster options for simulation, like the new Lamarr framework.

The new ultra-fast simulation framework for LHCb is named Lamarr¹ and is embedded within the LHCb simulation framework Gauss. Lamarr consists of a pipeline of (ML-based) modular parameterizations designed to replace both the physics simulation and the reconstruction steps.

• Compatibility with LHCb-tuned generators (e.g. Pythia8, Particle Guns);
• Promotion of generator-level particles to successfully reconstructed candidates;
• Possibility of submitting Lamarr jobs through the LHCb distributed computing middleware Dirac;
• Capability of producing datasets with the same persistency format as the LHCb physics analysis framework DaVinci.

¹ The framework name comes from Hedy Lamarr, that was an Austrian-born American film actress and inventor. Read more on Wikipedia.

Efficiencies: Gradient Boosted Decision Trees (GBDT) trained on simulated data to predict the fraction of accepted / reconstructed / selected candidates.

High-level quantities: Conditional Generative Adversarial Networks (GAN) trained on either simulated or calibration data to synthetize the high-level response of LHCb sub-detectors.

Best-performing parameterizations can easily replace specific modules without recompiling the whole pipeline using the deployment tool scikinC.

scikinC translates ML-based models to be dynamically linked to the main application (Gauss). In this way, parameterizations can be developed and released independently.

• Train a model;
• Transpile the model to a C file with scikinC;
• Compile the C file to a shared object;
• Link the shared object to the LHCb simulation software;
• Produce simulated samples.

Lamarr is currently under validation, comparing the distributions of the analysis-level reconstructed quantities parameterized with what obtained from detailed simulation for \(\Lambda_b^0 \to \Lambda_c^+ \mu^- X\) decays with \(\Lambda_c^+ \to p K^- \pi^+\).

• Decay abundantly produced in the LHCb acceptance, widely studied, and also utilized as PID calibration sample;
• It is described by a complex decay model including many feed-down modes;
• It provides examples for muons, pions, kaons and protons in a single decay mode.

The momentum and the point of closest approach to the beams at generator-level get smeared: GAN-based model is used to parameterize multiple scattering and residual detector effects (alignment, calibration).

Track reconstruction uncertainties rely on dedicated GAN-based model. Correct modeling track uncertainties is essential for LHCb analyses: e.g., the impact parameter (IP) is a common discriminator between prompt and displaced vertices.

Output quantities can be used within LHCb offline reconstruction to compute higher-level quantities, like the reconstructed mass.

Smeared track kinematics and detector occupancy are used by two sets of GAN-based models to parameterize the high-level response of the RICH and MUON systems.

Further GAN-based models are trained to reproduce the higher-level PID classifiers typically used in physics analyses, relying only on the input and the output of RICH and MUON parameterizations.

The adopted stacked GAN structure is designed to simulate both single-system detector response (RICH and MUON) and higher-level PID classifiers, enabling analysts to define new higher level classifiers based on the underlying basic quantities.

Overall time needed for producing simulated samples has been analyzed for fully detailed simulation (Geant4-based propagation) and Lamarr. Lamarr timing is dominated by particle generation (Pythia8).

Preliminary studies show that Lamarr ensure a CPU reduction of at least 98% for the physics simulation phase. Further improvement in timing can be achieved tacking the generation, as shown when using Particle Guns (e.g. only generating signal of interest).

Detailed simulation: Pythia8 + Geant4
1M events @ 2.5 kHS06.s/event ≃ 80 HS06.y

Ultra-fast simulation: Pythia8 + Lamarr
1M events @ 0.5 kHS06.s/event ≃ 15 HS06.y

Ultra-fast simulation: Particle Gun + Lamarr
100M events @ 1 HS06.s/event ≃ 4 HS06.y

Great progress has been made on developing a fully parametric simulation of the LHCb experiment, aiming to reduce the pressure on the CPU computing resources.

Model development, tuning and specialization will continue taking full advantage of opportunistic GPU resources made available to the LHCb Collaboration.

• Further speed improvements under study;
• Thread safety for multithreaded Gaudi algorithms under development.

This work is partially supported by ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by European Union – NextGenerationEU.