Uncertainty Quantification and Propagation in Atomistic Machine Learning

Machine learning (ML) offers promising new approaches to tackle complex problems and has been increasingly adopted in chemical and materials sciences. Broadly speaking, ML models employ generic mathematical functions and attempt to learn essential physics and chemistry from a large amount of data. Consequently, because of the limited physical or chemical principles in the functional form, the reliability of the predictions is oftentimes not guaranteed, particularly for data far out of distribution. It is critical to quantify the uncertainty in model predictions and understand how the uncertainty propagates to downstream chemical and materials applications. Herein, we review existing uncertainty quantification (UQ) and uncertainty propagation (UP) methods for atomistic ML under a united framework of probabilistic modeling. We first categorize the UQ methods, with the aim to elucidate the similarities and differences between them. We also discuss performance metrics to evaluate the accuracy, precision, calibration, and efficiency of the UQ methods and techniques for model recalibration. With these metrics, we survey existing benchmark studies of the UQ methods using molecular and materials datasets. Furthermore, we discuss UP methods to propagate the uncertainty obtained from ML models in widely used materials and chemical simulation techniques, such as molecular dynamics and microkinetic modeling. We also provide remarks on the challenges and future opportunities of UQ and UP in atomistic ML.