Generative Monte Carlo Sampling for Constant-Cost Particle Transport

TL;DR

This paper introduces Generative Monte Carlo (GMC), a neural network-based method for particle transport simulation that achieves constant-cost sampling and maintains statistical accuracy, significantly speeding up computations in thick regimes.

Contribution

GMC integrates generative AI into particle transport simulation, enabling generalization across materials and reducing computational cost to constant time per cell.

Findings

GMC preserves the $1/rac{1}{\sqrt{N}}$ convergence rate of standard Monte Carlo.

GMC achieves order-of-magnitude speedups in optically thick regimes.

GMC generalizes across materials using optical coordinate scaling.

Abstract

We present Generative Monte Carlo (GMC), a novel paradigm for particle transport simulation that integrates generative artificial intelligence directly into the stochastic solution of the linear Boltzmann equation. By reformulating the cell-transmission problem as a conditional generation task, we train neural networks using conditional flow matching to sample particle exit states, including position, direction, and path length, without simulating scattering histories. The method employs optical coordinate scaling, enabling a single trained model to generalize across any material. We validate GMC on two canonical benchmarks, namely a heterogeneous lattice problem characteristic of nuclear reactor cores and a linearized hohlraum geometry representative of high-energy density radiative transfer. Results demonstrate that GMC preserves the statistical fidelity of standard Monte Carlo, exhibiting the expected $1/\sqrt{N}$ convergence rate while maintaining accurate scalar flux profiles. While standard Monte Carlo computational cost scales linearly with optical thickness in the diffusive limit, GMC achieves constant $O(1)$ cost per cell transmission, yielding order-of-magnitude speedups in optically thick regimes. This framework strategically aligns particle transport with modern computing architectures optimized for neural network inference, positioning transport codes to leverage ongoing advances in AI hardware and algorithms.