Enhancing Machine Learning Interatomic Potentials with Multi-Fidelity Training

Machine learning interatomic potentials (MLIPs) leverage machine learning techniques to approximate energy, force, and stress values obtained from <i>ab initio</i> calculations. The MLIPs are particularly valued for their ability to provide quantum mechanical precision at significantly lower computational costs. As a data-driven approach, the fidelity of MLIPs is dictated by the choice of the exchange-correlation functional used in building the <i>ab initio</i> training set. While the semilocal functional such as GGA is favored for its high speed and decent accuracy in many physical properties, some applications require higher-fidelity functionals for predictive simulations. For example, in studies of ion conductivity in solid-state electrolytes, meta-GGA is preferred because conventional GGA functionals overestimate lattice parameters, resulting in exaggerated ion conductivities. However, constructing a high-fidelity dataset for an MLIP is challenging due to the high computational costs.<br/><br/>A viable strategy to address this is to utilize abundant low-fidelity data, benefiting from the high correlations in data between different exchange-correlation functionals. In this presentation, we introduce an MLIP framework capable of training on multi-fidelity databases simultaneously, which allows for learning high-fidelity potential energy surfaces (PES) using only a small set of high-fidelity data. We implement the multi-fidelity framework into SevenNet [1] an equivariant graph neural network. Specifically, it employs shared parameters to capture the general trends of PES that exist across datasets, alongside fidelity-specific weights that capture finer details in PES variations between the functionals.<br/><br/>We demonstrate the multi-fidelity training with examples of the In<i>_x</i>Ga_1-<i>x</i>N alloy and the argyrodite Li₆PS₅Cl systems. We generate a low-fidelity database from configurations of strained crystals and <i>ab initio</i> molecular dynamics (MD) simulations using the PBE functional. Then, we select a small portion of structures in the low-fidelity database and perform one-shot calculations employing the r²SCAN functional. We find that chemical environments not directly sampled in the high-fidelity database can be effectively inferred from the low-fidelity data. For example, in the In<i>_x</i>Ga_1-<i>x</i>N system, the interactions between In and Ga captured in the low-fidelity dataset can be transferred to enhance the high-fidelity MLIP, resulting in accurate predictions for the ternary alloy even when using only binary crystals for the high-fidelity database. In the Li₆PS₅Cl system, the incorporation of high-force configurations from the low-fidelity data significantly improved the MD stability and lithium-ion conductivity predicted by the high-fidelity MLIP.<br/><br/>Furthermore, we develop a multi-fidelity universal MLIP, utilizing both PBE and r²SCAN databases in the Materials Project. Our approach significantly enhances the accuracy of the MLIP for the high-fidelity channel, enabling accurate predictions of properties such as polymorph energy ordering, equilibrium volumes, and bulk moduli of crystal systems. However, the multi-fidelity MLIP has shown a tendency to underestimate forces, leading to softer phonon spectra. This is attributed to the narrow range of forces around zero in the high-fidelity dataset. We believe that the present methodology holds promise for efficiently creating highly accurate, universal MLIPs by effectively expanding the high-fidelity dataset.<br/><br/>References<br/>[1] Y. Park, J. Kim, S. Hwang, and S. Han, J. Chem. Theory Comput. 20, 4857−4868 (2024)