Merrill James H, Han Yixuan, Roth Connie B
Department of Physics, Emory University, Atlanta, Georgia 30322, United States.
Macromolecules. 2024 Nov 22;57(23):11055-11074. doi: 10.1021/acs.macromol.4c01867. eCollection 2024 Dec 10.
We present a Bayesian inference-based nonlinear least-squares fitting approach developed to reliably fit challenging, noisy data in an automated and robust manner. The advantages of using Bayesian inference for nonlinear fitting are demonstrated by applying this approach to a set of temperature-dependent film thickness () data collected by ellipsometry for thin films of polystyrene (PS) and poly(2-vinylpyridine) (P2VP). The glass transition experimentally presents as a continuous transition in thickness characterized by a change in slope that in thin films with broadened transitions can become particularly subtle and challenging to fit. This Bayesian fitting approach is implemented using existing open-source Python libraries that make these powerful methods accessible with desktop computers. We show how this Bayesian approach is more versatile and robust than existing methods by comparing it to common fitting methods currently used in the polymer science literature for identifying . As Bayesian inference allows for fitting to more complex models than existing methods in the literature do, our discussion includes an in-depth evaluation of the best functional form for capturing the behavior of () data with temperature-dependent changes in thermal expansivity. This Bayesian fitting approach is easily automated, capable of reliably fitting noisy and challenging data in an unsupervised manner, and ideal for machine learning approaches to materials development.
我们提出了一种基于贝叶斯推理的非线性最小二乘拟合方法，该方法旨在以自动化且稳健的方式可靠地拟合具有挑战性的噪声数据。通过将此方法应用于一组通过椭偏仪收集的聚苯乙烯（PS）和聚（2-乙烯基吡啶）（P2VP）薄膜的随温度变化的膜厚（）数据，证明了使用贝叶斯推理进行非线性拟合的优势。实验中玻璃化转变表现为厚度的连续转变，其特征是斜率变化，在具有加宽转变的薄膜中，这种变化可能会变得特别细微且难以拟合。这种贝叶斯拟合方法是使用现有的开源Python库实现的，这些库使这些强大的方法可以在台式计算机上使用。通过将这种贝叶斯方法与聚合物科学文献中当前用于识别的常用拟合方法进行比较，我们展示了它比现有方法更具通用性和稳健性。由于贝叶斯推理允许拟合比文献中现有方法更复杂的模型，我们的讨论包括对用于捕捉随温度变化的热膨胀系数的（）数据行为的最佳函数形式的深入评估。这种贝叶斯拟合方法易于自动化，能够以无监督的方式可靠地拟合噪声大且具有挑战性的数据，并且非常适合用于材料开发的机器学习方法。
