理化性质模型的预测不确定度的可靠估计,Journal of Chemical Theory and Computation

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理化性质模型的预测不确定度的可靠估计
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2017-06-22 00:00:00 , DOI: 10.1021/acs.jctc.7b00235
Jonny Proppe ₁ , Markus Reiher ₁

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计算科学的主要挑战之一是确定虚拟测量的不确定性，即基于计算的可观察性的预测。由于对于大多数物理系统而言，高精度的第一性原理计算通常是不可行的，因此通常会求助于可观测参数的参数模型，该模型需要通过合并参考数据来进行校准。所得的预测及其不确定性对系统错误敏感，例如参考数据不一致，参数模型假设或计算方法不足。在这里，我们根据引导程序讨论属性模型的校准，引导程序是一种可用于识别系统误差和可靠地估计预测不确定性的采样方法。对于一组44种分子铁化合物，⁵⁷ FeMössbauer异构体转移到铁核上的接触电子密度。使用雅各布阶梯上的12个密度泛函（PWLDA，BP86，BLYP，PW91，PBE，M06-L，TPSS，B3LYP，B3PW91，PBE0，M06，TPSSh）计算接触电子密度。我们为异构体位移预测提供系统错误诊断和可靠的，本地解决的不确定性。纯和混合密度函数产生的平均预测不确定度分别为0.06-0.08 mm s ^-1和0.04-0.05 mm s ^-1，后者接近0.02 mm s ^–1的平均实验不确定度。。此外，我们表明模型参数和预测不确定性都很大程度上取决于参考数据点的组成和数量。因此，我们建议不应从单个数据集推断基于性能指标（例如，相关系数的平方r ²或均方根误差RMSE）的密度泛函的排名。这项研究为理论Mössbauer光谱学提供了第一个统计上严格的校准分析，该分析对理化性质模型具有普遍适用性，而不仅限于异构体位移预测。我们提供了具有统计意义的参考数据集MIS39和基于PBE0功能的异构体位移的新校准。

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Reliable Estimation of Prediction Uncertainty for Physicochemical Property Models

One of the major challenges in computational science is to determine the uncertainty of a virtual measurement, that is the prediction of an observable based on calculations. As highly accurate first-principles calculations are in general unfeasible for most physical systems, one usually resorts to parameteric property models of observables, which require calibration by incorporating reference data. The resulting predictions and their uncertainties are sensitive to systematic errors such as inconsistent reference data, parametric model assumptions, or inadequate computational methods. Here, we discuss the calibration of property models in the light of bootstrapping, a sampling method that can be employed for identifying systematic errors and for reliable estimation of the prediction uncertainty. We apply bootstrapping to assess a linear property model linking the ⁵⁷Fe Mössbauer isomer shift to the contact electron density at the iron nucleus for a diverse set of 44 molecular iron compounds. The contact electron density is calculated with 12 density functionals across Jacob’s ladder (PWLDA, BP86, BLYP, PW91, PBE, M06-L, TPSS, B3LYP, B3PW91, PBE0, M06, TPSSh). We provide systematic-error diagnostics and reliable, locally resolved uncertainties for isomer-shift predictions. Pure and hybrid density functionals yield average prediction uncertainties of 0.06–0.08 mm s^–1 and 0.04–0.05 mm s^–1, respectively, the latter being close to the average experimental uncertainty of 0.02 mm s^–1. Furthermore, we show that both model parameters and prediction uncertainty depend significantly on the composition and number of reference data points. Accordingly, we suggest that rankings of density functionals based on performance measures (e.g., the squared coefficient of correlation, r², or the root-mean-square error, RMSE) should not be inferred from a single data set. This study presents the first statistically rigorous calibration analysis for theoretical Mössbauer spectroscopy, which is of general applicability for physicochemical property models and not restricted to isomer-shift predictions. We provide the statistically meaningful reference data set MIS39 and a new calibration of the isomer shift based on the PBE0 functional.

更新日期：2017-06-28

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