Li-Si体系第一性原理计算Phase Diagram的不确定性量化
Uncertainty Quantification of First Principles Computational Phase Diagram Predictions of Li-Si System Via Bayesian Sampling
摘要：
在这项工作中，评估的CALPHAD方法只训练密度泛函理论（DFT）的数据进行锂硅二元系统，作为一个案例研究。使用基于贝叶斯误差估计函数（BEEF-vdW）交换相关势的参数采样方法。通过使用BEEF-vdW的泛函的内置系综，得到吉布斯自由能拟合参数的不确定性，并可以传播到所得的相图。为了找到CALPHAD模型的最佳拟合形式，我们使用贝叶斯信息准则（BIC）实现了模型选择步骤。将从DFT计算中选择的最佳CALPHAD模型应用于其他采样的BEEF泛函，生成CALPHAD模型的集合，从而产生相图预测的集合。然后将所得的相图编译成表示预测的最可能的相以及预测的置信度的定量度量的单相图。这种对DFT产生的不确定度的处理提供了一种严格的方法，以确保DFT的相关误差在不确定度的估计中得到考虑。从相图中，我们已经确定了锂化硅的嵌入电压。结合起来，我们可以更好地理解相变和电压曲线，为实验和电池内Si阳极的性能做出更有分析依据的预测。
英文摘要：
In this work, an assessment of the CALPHAD method trained on only density functional theory (DFT) data is performed for the Li-Si binary system, as a case study. Using a parameter sampling approach based on the Bayesian Error Estimation Functional (BEEF-vdW) exchange-correlation potential. By using built-in ensemble of functionals from BEEF-vdW, the uncertainties of the Gibbs Free Energy fitting parameters are obtained and can be propagated to the resulting phase diagram. To find the best fitting form of the CALPHAD model, we implement a model selection step using the Bayesian information criterion (BIC). Applying the best selected CALPHAD model from the DFT calculation, to other sampled BEEF functionals, an ensemble of CALPHAD models is generated leading to an ensemble of phase diagram predictions. The resulting phase diagrams are then compiled into a single-phase diagram representing the most probable phase predicted as well as a quantitative metric of confidence for the prediction. This treatment of uncertainty resulting from DFT provides a rigorous way to ensure the correlated errors of DFT is accounted for in the estimation of uncertainty. From the phase diagram, we have determined intercalation voltages for lithiated silicon. In combination, we can generate a better understanding of the phase transitions and voltage profile to make a more analysis-informed prediction for experiments and the performance of Si-anodes within batteries.
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