arXiv Machine Learning By Joseph A. Farmer, Aidan Murray, Johannes Krotz, Ryan G. McClarren

Generative Monte Carlo Sampling for Constant-Cost Particle Transport

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Generative Monte Carlo (GMC) is a new particle transport simulation method that embeds generative AI into solving the linear Boltzmann equation. By treating cell transmission as a conditional generation task, neural networks trained with conditional flow matching produce particle exit states—position, direction, and path length—without simulating scattering histories. GMC generalizes across materials using optical coordinate scaling, matches standard Monte Carlo’s statistical accuracy and convergence, and achieves constant‑cost per cell transmission, offering significant speedups in optically thick regimes.

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