Predicting the Young’s Modulus of Silicate Glasses using High-Throughput Molecular Dynamics Simulations and Machine Learning

The application of machine learning to predict materials’ properties usually requires a large number of consistent data for training. However, experimental datasets of high quality are not always available or self-consistent. Here, as an alternative route, we combine machine learning with high-throughput molecular dynamics simulations to predict the Young’s modulus of silicate glasses. We demonstrate that this combined approach offers good and reliable predictions over the entire compositional domain. By comparing the performances of select machine learning algorithms, we discuss the nature of the balance between accuracy, simplicity, and interpretability in machine learning.

Improving the mechanical properties of glasses is crucial to address major challenges in energy, communications, and infrastructure1. In particular, the stiffness of glass (e.g., its Young’s modulus E) plays a critical role in flexible substrates and roll-to-roll processing of displays, optical fibres, architectural glazing, ultra-stiff composites, hard discs and surgery equipment, or lightweight construction materials1,2,3,4. Addressing these challenges requires the discovery of new glass compositions featuring tailored mechanical properties5,6.

Although the discovery of new materials with enhanced properties is always a difficult task, glassy materials present some unique challenges. First, a glass can be made out of virtually all the elements of the periodic table if quenched fast enough from the liquid state7. Second, unlike crystals, glasses are out-of-equilibrium phases and, hence, do not have to obey any fixed stoichiometry8. These two unique properties of glass open limitless possibilities for the development of new compositions with enhanced properties—for instance, the total number of possible glass compositions7 has been estimated to be around 1052! Clearly, only a tiny portion of the compositional envelope accessible to glass has been explored thus far.

The design of new glasses for a targeted application can be formulated as an optimization problem, wherein the composition needs to be optimized to minimize or maximize a cost function (e.g., the Young’s modulus) while satisfying some constraints (e.g., ensuring low cost and processability)9. Although the vast compositional envelop accessible to glass opens limitless possibilities for compositional tuning, optimization problems in such highly-dimensional spaces are notoriously challenging—which is known as the “curse of dimensionality.” Namely, the virtually infinite number of possible glass compositions render largely inefficient traditional discovery methods based on trial-and-error Edisonian approaches10.

To overcome this challenge, the development of predictive models relating the composition of glasses to their engineering properties is required9. Ideally, physics-based models should offer the most robust predictions. In the case of glass stiffness, the Makishima–Mackenzie (MM) model may be the most popular predictive model11,12. This approach is essentially an additive model, wherein stiffness is expressed as a linear function of the oxide concentrations. However, such additive models are intrinsically unable to capture any non-linear compositional dependence, as commonly observed for stiffness1,5,13. On the other hand, molecular dynamics (MD) simulations offer a powerful method to compute the stiffness of a given glass14,15. However, MD is a brute-force method, that is, it requires (at least) one simulation per glass composition—so that the systematic use of MD to explore the large compositional envelop accessible to glass is not a realistic option.

In turn, machine learning (ML) offers an attractive and pragmatic approach to predict glasses’ properties16. In contrast with physics-based models, ML-based models are developed by “learning” from existing databases. Although the fact that glass composition can be tuned in a continuous fashion renders glass an ideal material for ML methods, the application of ML to this material has been rather limited thus far16,17,18,19,20. This partially comes from the fact that ML methods critically relies on the existence of “useful” data. To be useful, data must be (i) available (i.e., easily accessible), (ii) complete (i.e., with a large range of parameters), (iii) consistent (i.e., obtained with the same testing protocol), (iv) accurate (i.e., to avoid “garbage in, garbage out” models), and (v) representative (i.e., the dataset needs to provide enough information to train the models). Although some glass property databases do exist21, some inconsistencies in the ways glasses are produced or tested among various groups may render challenging their direct use as training sets for ML methods—or would require some significant efforts in data cleaning and non-biased outlier detection.

To overcome these challenges, we present here a general method wherein high-throughput molecular dynamics simulations are coupled with machine learning methods to predict the relationship between glass composition and stiffness. Specifically, we take the example of the ternary calcium aluminosilicate (CAS) glass system—which is an archetypical model for alkali-free display glasses22—and focus on the prediction of their Young’s modulus. We show that our method offers good and reliable predictions of the Young’s modulus of CAS glasses over the entire compositional domain. By comparing the performance of select ML algorithms—polynomial regression (PR), LASSO, random forest (RF), and artificial neural network (ANN)—we show that the artificial neural network algorithm offers the highest level of accuracy. Based on these results, we discuss the balance between accuracy, complexity, and interpretability offered by each ML method.