Giulio Imbalzano

Giulio Imbalzano, Yongbin Zhuang, Venkat Kapil et al.

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 the training of the model. 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 provides an indication for the 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 although 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 the 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.

Alexander Goscinski, Guillaume Fraux, Giulio Imbalzano et al.

Eficient, physically-inspired descriptors of the structure and composition of molecules and materials play a key role in the application of machine-learning techniques to atomistic simulations. The proliferation of approaches, as well as the fact that each choice of features can lead to very different behavior depending on how they are used, e.g. by introducing non-linear kernels and non-Euclidean metrics to manipulate them, makes it difficult to objectively compare different methods, and to address fundamental questions on how one feature space is related to another. In this work we introduce a framework to compare different sets of descriptors, and different ways of transforming them by means of metrics and kernels, in terms of the structure of the feature space that they induce. We define diagnostic tools to determine whether alternative feature spaces contain equivalent amounts of information, and whether the common information is substantially distorted when going from one feature space to another. We compare, in particular, representations that are built in terms of n-body correlations of the atom density, quantitatively assessing the information loss associated with the use of low-order features. We also investigate the impact of different choices of basis functions and hyperparameters of the widely used SOAP and Behler-Parrinello features, and investigate how the use of non-linear kernels, and of a Wasserstein-type metric, change the structure of the feature space in comparison to a simpler linear feature space.