arXiv:2512.13965physics.comp-phcs.LG2025-12被引 1

用生成模型替代传统蒙特卡洛,实现粒子输运恒定成本计算

Generative Monte Carlo Sampling for Constant-Cost Particle Transport

  • 将粒子出射状态生成建模为条件流匹配任务,跳过散射过程模拟
  • 在厚介质中计算成本保持常数,速度提升一个数量级,收敛率仍为1/√N
  • 适合作为核能、高能密度物理的高效仿真工具,兼容现代AI硬件

我们提出生成式蒙特卡洛(GMC),一种将生成式人工智能直接融入线性玻尔兹曼方程随机求解的新范式。通过将单元传输问题重构为条件生成任务,利用条件流匹配训练神经网络,直接采样粒子出射状态(位置、方向、路径长度),无需模拟散射历史。方法采用光学坐标缩放,使单个训练模型可跨任意材料泛化。我们在两个经典基准上验证:一是核电堆芯特征的非均匀晶格问题,二是高能量密度辐射传输代表性的线性空腔几何。结果表明,GMC保持了标准蒙特卡洛的统计保真度,呈现预期的1/√N收敛率,并准确还原标量通量分布。标准蒙特卡洛在漫射极限下计算成本随光学厚度线性增长,而GMC每单元传输保持恒定的O(1)成本,在光学厚区域实现数量级加速。该框架与现代计算架构优化的神经网络推理相契合,使输运代码可借助持续发展的AI硬件与算法进步。

原文摘要 · Abstract (English)

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.

粒子输运生成模型蒙特卡洛加速计算

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