Tim Mueller

Alberto Hernandez, Tim Mueller

In recent years there has been great progress in the use of machine learning algorithms to develop interatomic potential models. Machine-learned potential models are typically orders of magnitude faster than density functional theory but also orders of magnitude slower than physics-derived models such as the embedded atom method. In our previous work, we used symbolic regression to develop fast, accurate and transferrable interatomic potential models for copper with novel functional forms that resemble those of the embedded atom method. To determine the extent to which the success of these forms was specific to copper, here we explore the generalizability of these models to other face-centered cubic transition metals and analyze their out-of-sample performance on several material properties. We found that these forms work particularly well on elements that are chemically similar to copper. When compared to optimized Sutton-Chen models, which have similar complexity, the functional forms discovered using symbolic regression perform better across all elements considered except gold where they have a similar performance. They perform similarly to a moderately more complex embedded atom form on properties on which they were trained, and they are more accurate on average on other properties. We attribute this improved generalized accuracy to the relative simplicity of the models discovered using symbolic regression. The genetic programming models are found to outperform other models from the literature about 50% of the time in a variety of property predictions, with about 1/10th the model complexity on average. We discuss the implications of these results to the broader application of symbolic regression to the development of new potentials and highlight how models discovered for one element can be used to seed new searches for different elements.

Xiangyun Lei, Weike Ye, Joseph Montoya et al.

This paper introduces the Chemical Environment Modeling Theory (CEMT), a novel, generalized framework designed to overcome the limitations inherent in traditional atom-centered Machine Learning Force Field (MLFF) models, widely used in atomistic simulations of chemical systems. CEMT demonstrated enhanced flexibility and adaptability by allowing reference points to exist anywhere within the modeled domain and thus, enabling the study of various model architectures. Utilizing Gaussian Multipole (GMP) featurization functions, several models with different reference point sets, including finite difference grid-centered and bond-centered models, were tested to analyze the variance in capabilities intrinsic to models built on distinct reference points. The results underscore the potential of non-atom-centered reference points in force training, revealing variations in prediction accuracy, inference speed and learning efficiency. Finally, a unique connection between CEMT and real-space orbital-free finite element Density Functional Theory (FE-DFT) is established, and the implications include the enhancement of data efficiency and robustness. It allows the leveraging of spatially-resolved energy densities and charge densities from FE-DFT calculations, as well as serving as a pivotal step towards integrating known quantum-mechanical laws into the architecture of ML models.

Alberto Hernandez, Adarsh Balasubramanian, Fenglin Yuan et al.

The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient manybody potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton Chen embedded atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed.