Building robust machine learning models for small chemical science data: the case of shear viscosity of fluids

Shear viscosity, though being a fundamental property of all fluids, is computationally expensive to calculate from equilibrium molecular dynamics simulations. Recently, machine learning (ML) methods have been used to augment molecular simulations in many contexts, thus showing promise to estimate viscosity too in a relatively inexpensive manner. However, ML methods face significant challenges—such as overfitting, when the size of the data set is small, as is the case with viscosity. In this work, we train seven ML models to predict the shear viscosity of a Lennard–Jones fluid, with particular emphasis on addressing issues arising from a small data set. Specifically, the issues related to model selection, performance estimation and uncertainty quantification were investigated. First, we show that the widely used performance estimation procedure of using a single unseen data set shows a wide variability—in estimating the errors on—small data sets. In this context, the common practice of using cross validation (CV) to select the hyperparameters (model selection) can be adapted to estimate the generalization error (performance estimation) as well. We compare two simple CV procedures for their ability to do both model selection and performance estimation, and find that k-fold CV based procedure shows a lower variance of error estimates. Also, these CV procedures naturally lead to an ensemble of trained ML models. We discuss the role of performance metrics in training and evaluation and propose a method to rank the ML models based on multiple metrics. Finally, two methods for uncertainty quantification—Gaussian process regression (GPR) and ensemble method—were used to estimate the uncertainty on individual predictions. The uncertainty estimates from GPR were also used to construct an applicability domain using which the ML models provided even more reliable predictions on an independent viscosity data set generated in this work. Overall, the procedures prescribed in this work, together, lead to robust ML models for small data sets.