Lamarr: implementing a flash-simulation paradigm at LHCb

Detailed simulation of the interaction between the traversing particles and the LHCb active volumes is the major consumer of CPU resources. During the LHC Run2, the LHCb experiment has spent more than 90% of the pledged CPU time to simulate events of interest. Matching the upcoming and future demand for simulated samples means that the development of faster simulation options is critical.

Lamarr is the novel flash-simulation framework of LHCb, able to offer the fastest option to produce simulated samples. Lamarr consists of a pipeline of (ML-based) modular parameterizations designed to replace both the simulation and reconstruction steps.

The Lamarr pipeline can be split in two chains:

1. a branch treating charged particles relying on tracking and particle identification models;
2. a branch facing the particle-to-particle correlation problem innate in the neutral objects reconstruction.

Assuming the existence of an unambiguous (\(k\)-to-\(k\)) relation between generated particles and reconstructed objects, the high-level detector response can be modeled in terms of efficiency and "resolution" (i.e., analysis-level quantities):

• Efficiency: Deep Neural Networks (DNN) trained to perform classification tasks so that they can be used to parameterize the fraction of "good" candidates (e.g., accepted, reconstructed, or selected).
• Resolution: Conditional Generative Adversarial Networks (GAN) trained on detailed simulated samples to parameterize the high-level response of LHCb detector (e.g., reconstruction errors, differential log-likelihoods, or multivariate classifier output).

Lamarr parameterizes the high-level response of the LHCb tracking system relying on the following models:

• propagation: approximates the trajectory of charged particles through the dipole magnetic field → parametric model;
• geometrical acceptance: predicts which of the generated tracks lay within a sensitive area of the detector → DNN model;
• tracking efficiency: predicts which of the generated tracks in the acceptance are properly reconstructed by the detector → DNN model;
• tracking resolution: parameterizes the errors introduced by the reconstruction algorithms to the track parameters → GAN model;
• covariance matrix: parameterizes the uncertainties assessed by the Kalman filter procedure → GAN model.

Lamarr parameterizes the high-level response of the LHCb PID system relying on the following models:

• RICH PID: parameterizes DLLs resulting from the RICH detectors → GAN model;
• MUON PID: parameterizes likelihoods resulting from the MUON system → GAN model;
• isMuon: parameterizes the response of a FPGA-based criterion for muon loose boolean selection → DNN model;
• Global PID: parameterizes the global high-level response of the PID system, consisting of CombDLLs and ProbNNs → GAN model.

Lamarr provides separated models for muons, pions, kaons, and protons for each PID set of variables.

The flash simulation of the LHCb ECAL detector is not trivial task:

• bremsstrahlung radiation, converted photons, or merged \(\pi^0\) may lead to have \(n\) generated particles responsible for \(m\) reconstructed objects (in general, with \(n \ne m)\);
• the particle-to-particle correlation problem limits the validity of strategies used for modeling the unambiguous \(k\)-to-\(k\) detector response.

To parameterize a generic \(n\)-to-\(m\) response of the ECAL detector, solutions inspired by the natural language translation problem are currently under investigation:

• the aim is to define an event-level description of the ECAL response;
• assuming ordered sequences of photons/clusters, the problem can be modeled with a Transformer model;
• complying with the problem topology, the ECAL response can be modeled with a Graph Neural Network (GNN) model

Lamarr provides the high-level response of the LHCb detector by relying on a pipeline of (subsequent) ML-based modules. To validate the charged particles chain, the distributions of a set of analysis-level reconstructed quantities resulting from Lamarr have been compared with that obtained from detailed simulation for \(\Lambda_b^0 \to \Lambda_c^+ \mu^- X\) decays with \(\Lambda_c^+ \to p K^- \pi^+\).

The deployment of the ML-based models follows a transcompilation approach based on scikinC. The models are translated to C files, compiled as shared objects, and then dynamically linked in the LHCb simulation software (Gauss).

The integration of Lamarr with Gauss enables:

• interface with all the LHCb-tuned physics generators (e.g., Pythia8, EvtGen);
• compatibility with the distributed computing middleware and production environment;
• providing ready-to-use datasets for centralized analysis.

Overall time needed for producing simulated samples has been analyzed for detailed simulation (Geant4-based) and Lamarr. When Lamarr is employed, the generation of particles from collisions (e.g., with Pythia8) becomes the new major CPU consumer.

Lamarr allows to reduce the CPU cost for the simulation phase of (at least) two-order-of-magnitude. Further timing will require speeding up the generators.

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 effort is ongoing to put a fully parametric simulation of the LHCb experiment into production, aiming to reduce the pressure on computing resources.

DNN-based and GAN-based models succeed in describing the high-level response of the LHCb tracking and PID detectors for charged particles. Work is still required to parameterize the response of the ECAL detector due to the particle-to-particle correlation problem.

Future development Lamarr aims to support both integration within the LHCb software stack and its use as a stand-alone package.

The work presented in this contribution is performed in the framework of Spoke 0 and Spoke 2 of the ICSC project - Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by the NextGenerationEU European initiative through the Italian Ministry of University and Research, PNRR Mission 4, Component 2: Investment 1.4, Project code CN00000013 - CUP I53C21000340006.