数据驱动模型的诊断：PM7半经验量子化学方法的不确定性量化
Diagnostics of Data-Driven Models: Uncertainty Quantification of PM7 Semi-Empirical Quantum Chemical Method
摘要：
我们报告了一个半经验的量子化学方法PM 7的不确定性量化的角度进行评估。具体来说，我们应用边界到边界数据协作，一个不确定性量化框架，来表征a）与训练数据中的不确定性一致的PM7模型参数值的可变性，以及b）从训练数据到模型预测的不确定性传播。实验热形成的一系列的直链烷烃被用作感兴趣的属性。训练数据在化学上是准确的，即，根据计算化学的标准，它们具有非常低的不确定性。分析没有发现PM7与整个数据集一致的证据，因为没有发现单个参数值集可以捕获所有训练数据的实验不确定性。然而，PM7被发现是一致的训练数据的子集。在这种情况下，如果预测是针对具有可比大小的分子进行的，则从化学准确的训练数据到预测值的不确定性传播将误差保持在化学准确性的范围内。否则，误差随着分子的相对大小线性增长。
英文摘要：
We report an evaluation of a semi-empirical quantum chemical method PM7 from the perspective of uncertainty quantification. Specifically, we apply Bound-to-Bound Data Collaboration, an uncertainty quantification framework, to characterize a) variability of PM7 model parameter values consistent with the uncertainty in the training data, and b) uncertainty propagation from the training data to the model predictions. Experimental heats of formation of a homologous series of linear alkanes are used as the property of interest. The training data are chemically accurate, i.e., they have very low uncertainty by the standards of computational chemistry. The analysis does not find evidence of PM7 consistency with the entire data set considered as no single set of parameter values is found that captures the experimental uncertainties of all training data. Nevertheless, PM7 is found to be consistent for subsets of the training data. In such cases, uncertainty propagation from the chemically accurate training data to the predicted values preserves error within bounds of chemical accuracy if predictions are made for the molecules of comparable size. Otherwise, the error grows linearly with the relative size of the molecules.
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