arXiv：cs.LG· Yubo Cao, Xi Deng, Mengqi Xia, Vignesh Gopakumar, Ander Gray, Anima Anandkumar·· 5 小时前AI 评分38
PTNO：用含噪蒙特卡洛估计训练神经算子求解粒子输运问题
PTNO: Training Neural Operators with Noisy Monte Carlo Estimates for Particle Transport Problems
AI 导读
研究者提出粒子输运神经算子（PTNO），可直接从含噪、低成本的蒙特卡洛（MC）标签中学习粒子输运代理模型，无需依赖高成本收敛的 MC 解。PTNO 用 softplus 输出层保持物理空间正值，并采用逐点相对 L2 损失（PRelL2）应对高动态范围。在中子输运任务上，PTNO 比同 CPU 上收敛 MC 快 10^4-10^5 倍，在同等精度下比 MC 便宜 10^3-10^5 倍。
正文
Abstract: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.
| Comments: | 41 pages, 15 figures, 35 tables. v2: Yubo Cao and Xi Deng are co-first authors with equal contribution; corrected the author footnote |
| Subjects: | Artificial Intelligence (cs.AI); Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.40090 [cs.AI] |
| (or arXiv:2609.40090v2 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2609.40090 arXiv-issued DOI via DataCite |
Submission history
From: Yubo Cao [view email]
[v1]
Wed, 30 Sep 2026 16:31:40 UTC (1,608 KB)
[v2]
Thu, 1 Oct 2026 19:32:26 UTC (1,608 KB)
来源：arXiv：cs.LG · arxiv.org