Understanding Defects in Amorphous Silicon with Million-Atom Simulations and Machine Learning.

The structure of amorphous silicon (a-Si) is widely thought of as a fourfold-connected random network, and yet it is defective atoms, with fewer or more than four bonds, that make it particularly interesting. Despite many attempts to explain such "dangling-bond" and "floating-bond" defects, respectively, a unified understanding is still missing. Here, we use advanced computational chemistry methods to reveal the complex structural and energetic landscape of defects in a-Si. We study an ultra-large-scale, quantum-accurate structural model containing a million atoms, and thousands of individual defects, allowing reliable defect-related statistics to be obtained. We combine structural descriptors and machine-learned atomic energies to develop a classification of the different types of defects in a-Si. The results suggest a revision of the established floating-bond model by showing that fivefold-bonded atoms in a-Si exhibit a wide range of local environments-analogous to fivefold centers in coordination chemistry. Furthermore, it is shown that fivefold (but not threefold) coordination defects tend to cluster together. Our study provides new insights into one of the most widely studied amorphous solids, and has general implications for understanding defects in disordered materials beyond silicon alone.

Robustness of Local Predictions in Atomistic Machine Learning Models.

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost and also allows for the identification and posthoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though practical justifications exist for the local decomposition, only the global quantity is rigorously defined. Thus, when the atom-centered contributions are used, their sensitivity to the training strategy or the model architecture should be carefully considered. To this end, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of the LPR on the aspects of model training, particularly the composition of training data set, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models.

Machine-learned acceleration for molecular dynamics in CASTEP.

Machine learning (ML) methods are of rapidly growing interest for materials modeling, and yet, the use of ML interatomic potentials for new systems is often more demanding than that of established density-functional theory (DFT) packages. Here, we describe computational methodology to combine the CASTEP first-principles simulation software with the on-the-fly fitting and evaluation of ML interatomic potential models. Our approach is based on regular checking against DFT reference data, which provides a direct measure of the accuracy of the evolving ML model. We discuss the general framework and the specific solutions implemented, and we present an example application to high-temperature molecular-dynamics simulations of carbon nanostructures. The code is freely available for academic research.

How to validate machine-learned interatomic potentials.

Machine learning (ML) approaches enable large-scale atomistic simulations with near-quantum-mechanical accuracy. With the growing availability of these methods, there arises a need for careful validation, particularly for physically agnostic models-that is, for potentials that extract the nature of atomic interactions from reference data. Here, we review the basic principles behind ML potentials and their validation for atomic-scale material modeling. We discuss the best practice in defining error metrics based on numerical performance, as well as physically guided validation. We give specific recommendations that we hope will be useful for the wider community, including those researchers who intend to use ML potentials for materials "off the shelf."

Indirect learning and physically guided validation of interatomic potential models.

Machine learning (ML) based interatomic potentials are emerging tools for material simulations, but require a trade-off between accuracy and speed. Here, we show how one can use one ML potential model to train another: we use an accurate, but more computationally expensive model to generate reference data (locations and labels) for a series of much faster potentials. Without the need for quantum-mechanical reference computations at the secondary stage, extensive reference datasets can be easily generated, and we find that this improves the quality of fast potentials with less flexible functional forms. We apply the technique to disordered silicon, including a simulation of vitrification and polycrystalline grain formation under pressure with a system size of a million atoms. Our work provides conceptual insight into the ML of interatomic potential models and suggests a route toward accelerated simulations of condensed-phase systems.