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.