  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 lack of 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 and categorize existing uncertainty quantification (UQ)
methods for atomistic ML under a united framework of probabilistic modeling
with the aim of elucidating the similarities and differences between them. We
also discuss performance metrics to evaluate the calibration, precision,
accuracy, and efficiency of the UQ methods and techniques for model
recalibration. In addition, we discuss uncertainty propagation (UP) in widely
used simulation techniques in chemical and materials science, such as molecular
dynamics and microkinetic modeling. We also provide remarks on the challenges
and future opportunities of UQ and UP in atomistic ML.
