Uncertainty estimation for molecular dynamics and sampling

Abstract

Machine-learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale, and complexity. Given the interpolative nature of these models, the reliability of predictions depends on the position in phase space, and it is crucial to obtain an estimate of the error that derives from the finite number of reference structures included during model training. When using a machine-learning potential to sample a finite-temperature ensemble, the uncertainty on individual configurations translates into an error on thermodynamic averages and leads to a loss of accuracy when the simulation enters a previously unexplored region. Here, we discuss how uncertainty quantification can be used, together with a baseline energy model, or a more robust but less accurate interatomic potential, to obtain more resilient simulations and to support active-learning strategies. Furthermore, we introduce an on-the-fly reweighing scheme that makes it possible to estimate the uncertainty in thermodynamic averages extracted from long trajectories. We present examples covering different types of structural and thermodynamic properties and systems as diverse as water and liquid gallium.

Gaussian Process Regression for Materials and Molecules

“…In particular, there is a bias of the variance estimator for small n c . This bias can be reduced by introducing a scaling factor α, that can be computed by maximizing the log-likelihood of the model over a test set, { A }, which yields 204 The corrected ensemble variance is then obtained by redefining σ 2 ← α 2 σ 2 . Furthermore, one can define “calibrated” committee models whose predictions are ŷ j ← + α ( j – ), which have the same mean as the initial committee, and an appropriately scaled variance.…”

“… Applications of committee models for GPR predictions. Two examples are shown: (a) the prediction of the Raman spectrum of paracetamol form I; 203 (b) the prediction of the melting point of water 204 by determining the difference in chemical potential, μ, of hexagonal ice (“Ih”) and the liquid phase (“L”), and defining the zero intersect as corresponding to the melting temperature. Panel a is adapted from ref ( 203 ), where the original figure is published under the CC BY 3.0 license ( ); panel b is adapted from ref ( 204 ).…”

Differentiable sampling of molecular geometries with uncertainty-based adversarial attacks

“…Conventional strategies to increase the stability of NN potentials include performing active learning loops by retraining the networks on MD-sampled data (Supplementary Fig. 21a) 20,25,36,37 . However, sampling new host-guest geometries to diversify the training of NN potentials and stabilize their predictions is computationally inefficient due to the large number of atoms in these systems.…”

“…Strategies such as Bayesian NNs 30 , Monte Carlo dropout 31 , or NN committees [32][33][34] allow estimating the model uncertainty by building a set of related models and comparing their predictions for a given input. In particular, NN committee force fields have been used to control simulations 35 , to inform sampling strategies 36 and to calibrate error bars for computed properties 37 .…”

Uncertainty Estimation for Machine Learning Models in Multiphase Flow Applications

“…Focusing on the uncertainty estimation, the literature concerning the application of these methodologies to real-life problems is quite vast; it ranges from chemistry [11,12] to material science [13], localization [14], geology [15], and, of course, medical science [16], where the majority of the work employed techniques based on bootstrapping, Bayesian approaches, and dropouts.…”