用回归法拟合热力学积分数据减少自由能估算的偏差和不确定性
Reducing the Bias and Uncertainty of Free Energy Estimates by Using Regression to Fit Thermodynamic Integration Data
摘要：
这份报告提出了应用多项式回归估计自由能差异使用热力学积分。我们采用线性回归来构建一个多项式，最佳地适合的热力学积分数据，从而减少了由此产生的自由能估计的偏差和不确定性。两个测试系统的分析解决方案被用来验证的方法的准确度和精密度。我们的研究结果表明，与常用的正交技术相比，具有高程度的多项式回归给出了最准确的自由能差估计，但通常具有稍大的方差。高次多项式具有紧密拟合热力学积分数据的灵活性，但通常对数据点的微小变化敏感。为了进一步提高整体精度和减少不确定性，我们还研究了使用切比雪夫节点来指导热力学积分方案的非等距λ值的选择。我们得出结论，多项式回归与非等距λ值提供了最准确和精确的自由能估计热力学积分数据。软件和文档可在http://www.phys.uidaho.edu/ytreberg/software上获得
英文摘要：
This report presents the application of polynomial regression for estimating free energy differences using thermodynamic integration. We employ linear regression to construct a polynomial that optimally fits the thermodynamic integration data, and thus reduces the bias and uncertainty of the resulting free energy estimate. Two test systems with analytical solutions were used to verify the accuracy and precision of the approach. Our results suggest that regression with a high degree of polynomials give the most accurate free energy difference estimates, but often with a slightly larger variance, compared to commonly used quadrature techniques. High degrees of polynomials possess the flexibility to closely fit the thermodynamic integration data but are often sensitive to small changes in data points. To further improve overall accuracy and reduce uncertainty, we also examine the use of Chebyshev nodes to guide the selection of non-equidistant lambda values for the thermodynamic integration scheme. We conclude that polynomial regression with non-equidistant lambda values delivers the most accurate and precise free energy estimates for thermodynamic integration data. Software and documentation is available at http://www.phys.uidaho.edu/ytreberg/software
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