Chemical Environment Modeling Theory: Revolutionizing Machine Learning Force Field with Flexible Reference Points

This study introduces the Chemical Environment Modeling Theory (CEMT), a novel and powerful framework that generalizes the theory of machine learning force field (MLFF), which is widely used in atomistic simulations of chemical systems. The flexible and adaptable framework permits reference points to be positioned anywhere within the modeled domain rather than only atom centers, transcending this implicit constraint of traditional MLFFs, and enabling a diverse range of new model architectures. Leveraging 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. It clearly shows that the choice of reference points is an additional dimension of complexity that can be optimized for model performance, on top of environment featurization and model architecture. 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 by allowing the leveraging of intermediate results of DFT calculations. This framework could also serve as a cornerstone towards integrating known quantum-mechanical laws into the architecture of ML models.