机器学习多群截面可靠不确定性估计（无需重训练）
Reliable Uncertainty Estimation for Machine-Learned Multigroup Cross Sections Without Retraining
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中文总结 AI 辅助
本研究提出一种无需重训练即可为机器学习多群截面模型提供可靠不确定性估计的方法，通过连接不确定性预测网络与预训练模型，并利用共形预测实现逐样本自适应区间，显著降低区间宽度和超界预测。
中文摘要 AI 辅助
机器学习模型中的不确定性量化对于核能应用至关重要。虽然机器学习模型能够同时进行不确定性预测和点预测，但这些模型通常比仅进行点预测的模型更难联合训练。分裂共形预测是一类方法，通过在校准数据集中计算与目标分位数对应的非一致性分数，来生成无分布假设的预测区间。尽管共形预测仅保证边际覆盖率，但通过归一化非一致性分数，可以逐样本计算预测区间宽度，从而提供对条件覆盖率的近似。在本工作中，我们将不确定性预测神经网络与预训练的、用于估计多群中子截面中屏蔽因子的网络相连接。我们在预训练模型所使用的同一OpenMC数据上训练不确定性模型，而预训练模型的权重和偏置保持固定。不确定性模型的输出是残差的标准差，并分为模型不确定性和计数不确定性两部分贡献。它们对应的方差通过平方和开方合并，为共形预测提供归一化因子，从而提供逐样本自适应的区间宽度。我们使用Mondrian共形预测以及将真实OpenMC不确定性作为共形框架中的归一化因子来建立比较基线。我们以预测的不确定性区间宽度以及预测超出区间宽度的严重程度为基础，将我们的归一化因子与基线进行比较。我们发现，我们的方法显著减少了区间宽度以及预测超出这些宽度的程度。
英文摘要
Uncertainty quantification in machine learning models is essential for nuclear energy applications. While machine learning models can make both uncertainty and point predictions, these models are often significantly more difficult to train jointly than models that make point predictions alone. Split conformal prediction is a family of methods for computing distribution-free prediction intervals by calculating nonconformity scores corresponding to a target quantile in a calibration dataset. Although conformal prediction only guarantees marginal coverage, normalizing nonconformity scores enables predictive interval widths to be calculated on a per-sample basis, providing an approximation to conditional coverage. In this work, we connect uncertainty predicting neural networks to pre-trained networks that estimate shielding factors in multigroup neutron cross sections. We train the uncertainty models on the same OpenMC data used by the pre-trained models, whose weights and biases remain fixed. The outputs of the uncertainty models are the standard deviations of the residual, separated into contributions from the model and tally uncertainty. Their corresponding variances are combined in quadrature to provide a normalizing factor for conformal prediction, providing interval widths that are adaptive on a per-sample basis. Baselines for comparison are established using Mondrian conformal prediction, and by using the ground truth OpenMC uncertainties as normalizers in the conformal framework. We use predicted uncertainty interval widths and the severity of predictions that overshoot the interval widths as bases for comparing our normalizer with the baselines. We find that our method dramatically reduces both interval widths and the degree to which predictions fall outside these widths.
发表机构
- The Colorado School of Mines（科罗拉多矿业学院）
机构由 AI 辅助整理，请以论文原文为准。
