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. In general, ML models employ generic mathematical functions and attempt to learn essential physics and chemistry from large amounts of data. The reliability of predictions, however, is often not guaranteed, particularly for out-of-distribution data, due to the limited physical or chemical principles in the functional form. Therefore, it is critical to quantify the uncertainty in ML predictions and understand its propagation to downstream chemical and materials applications. This review examines existing uncertainty quantification (UQ) and uncertainty propagation (UP) methods for atomistic ML under the framework of probabilistic modeling. We first categorize the UQ methods and explain the similarities and differences among them. Following this, performance metrics for evaluating their accuracy, precision, calibration, and efficiency are presented, along with techniques for recalibration. These metrics are then applied to survey existing UQ benchmark studies that use molecular and materials datasets. Furthermore, we discuss UP methods to propagate uncertainty in widely used materials and chemical simulation techniques, such as molecular dynamics and microkinetic modeling. We conclude with remarks on the challenges and opportunities of UQ and UP in atomistic ML.