Target-Distribution-Guided Cross-Functional Fine-Tuning of Machine-Learning Interatomic Potentials

Cross-functional fine-tuning of machine-learning interatomic potentials (MLIPs) is often treated as a relabeling problem, where configurations generated at one density-functional level are relabeled using a higher-fidelity target functional. However, the resulting training data may be drawn from the wrong equilibrium distribution, because the statistical weights of configurations change across exchange–correlation functionals. Here we address this distribution mismatch using a target-distribution-guided workflow based on self-learning hybrid Monte Carlo (SLHMC), in which trial configurations are proposed by a machine-learning potential and accepted or rejected using target-functional density-functional-theory energies. Using rutile TiO${}_2$ as a test system, we fine-tune the MACE-MP-0 foundation potential toward PBE, r${}^2$SCAN, and HSE06 target functionals. The resulting adapted potentials reproduce target-anchored nearest-neighbor Ti–O distributions, radial distribution functions, and the NPT cell metrics examined here more accurately than the foundation-model and off-target relabeling controls considered in this work. In particular, HSE06-guided fine-tuning improves structural and thermodynamic properties that are difficult to access with direct hybrid-functional molecular dynamics because of the computational cost of exact exchange. These results indicate that target-distribution coverage is an essential component of cross-functional MLIP transfer, and that accurate target-level labels alone may be insufficient when the configurational distribution is mismatched.