Digitizing materials development requires the accurate prediction of materials properties at lower costs than an equivalent experiment. Our machine learning technology enables this by reducing the cost of accurate quantum mechanics simulations by 10,000x. To make these methods accessible to the materials community, we are developing PHIN-atomic to simplify using machine learning interatomic potentials (MLIPs) in atomic scale simulation workflows. The simple interface allows scientists to focus on testing material properties instead of worrying about the accuracy of their interatomic potential. We find that our MLIPs are more than ten times faster than open source foundation models like MACE while being five times more accurate. Keep reading to learn more about our motivation for creating this interface and how PHIN-atomic can accurately predict materials properties.
Making machine learning learning accessible
Machine learning is revolutionizing computational materials science by making automatic training of high-fidelity models easier than ever. For quantum mechanics simulations, for instance, we can reliably reduce the cost of a simulation by 10,000 times without sacrificing any accuracy. In practice, achieving these benefits is more challenging including months to generate datasets, diverse teams of experts across materials science and machine learning to validate model performance, and access to high performance computational resources. All this is before you even start to think about designing your simulation workflow. To accomplish PHIN’s primary goal of digitizing materials development, we needed to simplify the use of machine learning tools so that materials scientists can directly use them. Enter PHIN-atomic.
PHIN-atomic predicts material properties from user-supplied material structures and simulation protocols. We address all three key barriers to adoption: accuracy, availability, and resources. The software removes the availability of accurate interatomic potentials by using active learning to automatically train MLIPs on density functional theory (DFT) data. The software ensures the accuracy of every simulation that is run through our uncertainty quantification module that predicts the error of each model evaluation. And finally, the software addresses the computational resources needed for using digital tools by providing a web interface for accessing cloud computing resources.
The figure below showcases how PHIN-atomic accomplishes this. Two user inputs are used to specify a specific material and simulation to run which uniquely determines a specific material property that will be output. PHIN-atomic connects the inputs and the outputs by performing uncertainty aware simulations. If there are no uncertain MLIP evaluations, the simulation is accurate and the material properties are returned to the user. However, if any evaluation is uncertain, the MLIP is automatically improved by entering our active learning workflow. As more simulations are run, the MLIP continues to improve by increasing the size and chemical complexity of the DFT dataset it is trained on to accurately simulate any material. In tandem, as the model improves, the active learning is called less frequently and the user begins to benefit from the generalizability of our equivariant graph neural network architecture and its 10,000x lower cost relative to DFT.
Simulating the properties of silicon
To demonstrate the performance of PHIN-atomic we perform benchmark simulations on silicon. Silicon has been a core technological material in the semiconductor industry for nearly a century and is becoming more critical in the energy storage market, making it a technologically relevant benchmark material with established material properties and digital models. Here we simulate both the elastic properties and the melting temperature, using crystalline silicon for the initial structure and a combination of single-point, NVT, and NPT simulations. We compare our model to ground truth quantum mechanics data and experimental quantities as well as two alternative digital models. A Stillinger-Weber classical interatomic potential for silicon and the open-source MLIP MACE. These alternative models provide insight into the relative performance of PHIN-atomic. The decades of development into the functional form of the Stillinger-Weber potential makes it an accurate method for digitally predicting silicon properties while the open-source foundation model is an alternative method for users to measure properties of other novel materials.
Elastic Constants
We encounter the elastic response of materials everyday. Beyond the simple springs you find around your house, elastic properties are critical to understanding how a material will behave. They are used every time an engineer designs a product ranging from buildings to batteries and circuits to wind turbines. Since they are easy to measure, heuristics have also been developed to shed light on more complicated material properties like friction, fracture, wear, and toughness.
Elastic properties are determined by applying small deformations to a material and measuring the corresponding stress the material is under. Linear elastic constants of materials can quickly be defined to describe how a material deforms under an applied load, where the elastic response is the initial deformation characterized by a linear dependence between the stress and strain.
The C11, C12, and C44 elastic constants are plotted in the figure below for each of the different digital models. Since silicon has been the subject of intense research for over half a century, the classical interatomic potentials are quite good and match experimental results well. The agreement between the classical and DFT and classical and experimental measurements are a good baseline for the accuracy a digital model should have to be useful in digital design. The error between PHIN’s model and DFT/experiment for 0K/300K respectively is equal to or lower than the classical interatomic potential error for C11 and C44, while the error for C12 is marginally higher. When we calculate the same elastic constants with the MACE foundation model, we can see that the elastic constants it predicts are systematically lower than PHIN’s. This is in alignment with previous work showing that pretrained foundation models have artificially low elastic constants. However, since the classical potential and PHIN MLIP overestimate C12, the systematic softening of the pre-trained model means that it predicts C12 pretty well by chance.
Melting Temperature
From the elastic properties, we move to the melting temperature. All materials have a single temperature which defines a transition from a solid state to a liquid state. Knowing the melting temperature has implications on a materials thermal stability, strength, and manufacturability. The melting temperature, however, is tricky to measure, both experimentally and digitally. In an experiment, the melting temperature is observed by either heating or cooling a material and watching the temperature change over time. The phase transition requires a certain amount of energy creating a plateau in the temperature versus time plot. However, to change phases a material often needs to be superheated or supercooled to overcome an activation energy needed to create the nuclei of the new phase. This is observed as a temperature overshooting the melting temperature before settling into the melting temperature. The activation barrier means that we cannot use the same procedure to digitally predict the melting temperature using an atomic scale simulation because of the time it would take to overcome the activation barrier. Instead, clever methods have been devised to sidestep the activation barrier and enable the accurate estimation of melting temperatures from atomic scale simulations. Here we use the SLUSCHI method, which takes a supercell that is half solid and half melted. During an NPT simulation, the solid-liquid interface can move, enabling the solid or liquid to grow. The heterogeneous nucleation has a much lower activation barrier enabling simulations of 100ps to be used for estimating the melting temperature. The trace of many simulations at different temperatures reveals the phase transition in an enthalpy versus temperature plot.
This method, although developed with density functional theory in mind, is still expensive to run with DFT. Therefore, we only compare the predicted melting temperature of PHIN against the pretrained model and a classical interatomic potential with the DFT prediction coming from the literature.
The PHIN-atomic and classical interatomic potential melting temperatures agree well with DFT, both having roughly 5% error, but the foundation model has more than a 25% error. The significant error of the open-source pre-trained model is due to the dataset being biased towards low-temperature data. While the model can be used to simulate this property, the hallucinations in the force, energy, and stress predictions mean that its predictions are inaccurate. These models therefore need to be retrained with additional data. Even worse, there is no indication from the model that it is inaccurate. The combination of the quiet failing and expert knowledge required to retrain these models make them inaccessible to large numbers of materials scientists.
Conclusion
Machine learning models will digitize materials development once they are accessible, accurate, and cost effective. PHIN-atomic addresses each of these concerns through the use of uncertainty quantification, active learning, and cloud simulations. As compared to open-source foundation models that errors of 25%, PHIN-atomic has lower than 5% error while being 10x lower cost. The PHIN-atomic interface allows scientists to quickly include it into their materials development workflows without having to worry about training a machine learning model or the accuracy of the interatomic potential they use. The active learning of the PHIN-atomic backend ensures that every simulation is accurate to the underlying DFT data so that scientists can use the predicted material properties in materials development.