Ultra-Fast Muon Transport via Histogram Sampling on GPUs

TL;DR

This work tackles the computational bottleneck of Monte Carlo muon transport by introducing a GPU-accelerated framework that replaces detailed event-by-event physics with histogram-based sampling of momentum loss and scattering. It combines an offline histogram-building phase (informed by Geant4 data) with a high-throughput online CUDA transport stage that processes many muons in parallel while integrating motion in a magnetic field via RK4. The key contributions include log-scaled, material- and momentum-bin histograms, constant-time sampling with the Alias method, and a GPU kernel that achieves multi-order-of-magnitude speedups while maintaining fidelity in representative geometries. The results demonstrate strong agreement with Geant4 and substantial practical impact for large-scale studies, with potential extensions to additional processes and differentiable simulation approaches.

Abstract

We present a GPU-accelerated method for muon transport based on histogram sampling that delivers orders of magnitude faster performance than CPU-based Geant4 simulation. Our method employs precomputed histograms of momentum loss and scattering, derived from detailed Geant4 simulations, to statistically reproduce all the non-decaying physics processes during muon traversal through matter. Implemented as a CUDA kernel, the parallel algorithm enables the concurrent simulation of tens of thousands of particles on a single GPU whilst taking into account a complex geometry and a magnetic field force integrated using a fourth-order Runge-Kutta method. Validation against Geant4 in both simple and realistic detector geometries shows that the approach preserves key physical features while achieving speedups of several orders of magnitude, even compared to CPU-based simulations on a large CPU farm with over a thousand cores. This work highlights the significant potential of GPU-based implementations for particle transport, with applicability extending to neutrino propagation and future implementations including discrete processes such as particle decay.

Figures (8)

• Figure 1: Schematic comparison between traditional Geant4 sequential transport (left) and our GPU-parallelized histogram sampling method (right).
• Figure 2: Histograms of momentum loss (left) and scattering (right) for different momentum bins.
• Figure 3: 2D histogram of momentum loss vs scattering for muons with momentum between 118.47 and 128.48 GeV traveling through iron for a distance of 2 cm.
• Figure 4: Plot of average energy loss for muons in iron as a function of momentum, along with two different binning strategies: uniform and logarithmic. Shaded region indicates the standard deviation of the sampled energy loss. Top plots show a zoomed-in view in different momentum ranges.
• Figure 5: Validation of our method against Geant4 for muons for a transport distance of 10m.