Ultra-Fast Muon Transport via Histogram Sampling on GPUs

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.