PTNO：用于粒子输运问题的带噪声蒙特卡洛估计训练神经算子
PTNO: Training Neural Operators with Noisy Monte Carlo Estimates for Particle Transport Problems
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中文总结 AI 辅助
PTNO是一种直接从噪声蒙特卡洛标签训练神经算子的方法，用于粒子输运问题，通过预算分配和相对损失应对高方差与高动态范围，在聚变和辐射传输任务上大幅加速并降低成本。
中文摘要 AI 辅助
多次散射下的粒子输运是辐射传输和等离子体物理的核心问题，然而高保真蒙特卡洛（MC）模拟必须追踪数量极其庞大的粒子。基于学习的替代模型可以分摊这一成本，但通常需要昂贵的、收敛良好的MC解作为训练数据。我们提出粒子输运神经算子（PTNO），一种直接从噪声大、成本低的MC标签中学习粒子输运替代模型的神经算子。此类标签带来两个挑战：（1）高方差，这会破坏标准监督学习；（2）跨越多个数量级的高动态范围（HDR）。针对第一个挑战，我们从许多配置的噪声标签中学习解算子，分摊MC成本并泛化到未见过的配置。由于MC标签是无偏的，我们证明在其上的平方损失与在收敛解上的损失共享最小化器，并且我们对训练场景数$M$、每个渲染的MC样本数$N$以及每个场景的独立渲染数$K$的预算分配研究表明，许多噪声场景优于少数收敛场景。针对第二个挑战，诸如对数之类的非线性变换会使噪声监督产生偏差。相反，PTNO将标签保持在物理空间中，并通过softplus输出层强制正性，从而有效表示小值。我们进一步使用逐点相对$L_2$损失（PRelL2）进行训练，这是HDR去噪和神经渲染的停止梯度相对损失，它通过停止梯度预测而非噪声标签来归一化每个残差。我们在聚变反应堆中的中子输运和参与介质中的辐射传输上展示了PTNO。在两个中子学任务上，PTNO在相同CPU上比收敛MC快$10^4$-$10^5$倍，在匹配精度下比MC便宜$10^3$-$10^5$倍；在两个辐射传输任务上，匹配精度下的MC成本是PTNO的$0.8$-$11$倍。
英文摘要
Particle transport under multiple scattering is central to radiative transfer and plasma physics, yet high-fidelity Monte Carlo (MC) simulations must trace prohibitively many particles. Learning-based surrogates can amortize this cost, but typically train on expensive, well-converged MC solutions. We propose the Particle Transport Neural Operator (PTNO), a neural operator that learns particle transport surrogates directly from noisy, low-cost MC labels. Such labels pose two challenges: (1) high variance, which destabilizes standard supervised learning, and (2) a high dynamic range (HDR) spanning many orders of magnitude. For the first, we learn the solution operator from noisy labels of many configurations, amortizing MC cost and generalizing to unseen configurations. Because MC labels are unbiased, we show that the squared loss on them shares its minimizer with the loss on converged solutions, and our budget-allocation study over training scenes $M$, MC samples per render $N$, and independent renders per scene $K$ shows that many noisy scenes beat fewer converged ones. For the second, a nonlinear transform such as the logarithm biases noisy supervision. Instead, PTNO keeps labels in physical space and enforces positivity with a softplus output layer that represents small values effectively. We further train with a pointwise relative $L_2$ loss (PRelL2), the stop-gradient relative loss of HDR denoising and neural rendering, which normalizes each residual by the stop-gradient prediction instead of the noisy label. We demonstrate PTNO on neutron transport in fusion reactors and radiative transfer in participating media. On the two neutronics tasks, PTNO is $10^4$-$10^5\times$ faster than converged MC on the same CPU and $10^3$-$10^5\times$ cheaper than MC at matched accuracy; on the two radiative-transfer tasks, MC at matched accuracy costs $0.8$-$11\times$ as much as PTNO.
发表机构
- California Institute of Technology（加州理工学院）
- Yale University（耶鲁大学）
- UK Atomic Energy Authority（英国原子能管理局）
- LIX, CNRS, École polytechnique（LIX，法国国家科学研究中心，巴黎综合理工学院）
机构由 AI 辅助整理，请以论文原文为准。
