Data-efficient multi-fidelity training for high-fidelity machine learning interatomic potentials

Machine learning interatomic potentials (MLIPs) are used to estimate potential energy surfaces (PES) from ab initio calculations, providing near quantum-level accuracy with reduced computational costs. However, the high cost of assembling high-fidelity databases hampers the application of MLIPs to systems that require high chemical accuracy. Utilizing an equivariant graph neural network, we present an MLIP framework that trains on multi-fidelity databases simultaneously. This approach enables the accurate learning of high-fidelity PES with minimal high-fidelity data. We test this framework on the Li$_6$PS$_5$Cl and In$_x$Ga$_{1-x}$N systems. The computational results indicate that geometric and compositional spaces not covered by the high-fidelity meta-gradient generalized approximation (meta-GGA) database can be effectively inferred from low-fidelity GGA data, thus enhancing accuracy and molecular dynamics stability. We also develop a general-purpose MLIP that utilizes both GGA and meta-GGA data from the Materials Project, significantly enhancing MLIP performance for high-accuracy tasks such as predicting energies above hull for crystals in general. Furthermore, we demonstrate that the present multi-fidelity learning is more effective than transfer learning or $\Delta$-learning an d that it can also be applied to learn higher-fidelity up to the coupled-cluster level. We believe this methodology holds promise for creating highly accurate bespoke or universal MLIPs by effectively expanding the high-fidelity dataset.