Density diversity in training data governs thermodynamic transferability of machine learning interatomic potentials
Machine learning interatomic potentials (MLIPs) offer first-principles accuracy with reduced computational cost, but their transferability across different thermodynamic states remains questionable, particularly for fluid systems where molecules experience local environments far from crystalline equilibrium. Here, we demonstrate that diversifying the density of training configurations, rather than temperature, is the most effective strategy for building thermodynamically transferable MLIPs within a fixed computational budget. We first show that foundation MLIPs trained on solid-state databases accurately describe liquid-like densities but fail at gas-like conditions, while molecular-database-trained models exhibit the opposite behavior. Controlled from-scratch training and distillation experiments confirm that density-diverse datasets resolve both failure modes, whereas temperature-diverse datasets cannot compensate for missing density regimes. Coordination number analysis reveals the physical origin of this behavior: local coordination topology is more susceptible to density than temperature, leading to further structural diversity. These results establish density diversity as a design principle for thermodynamically transferable MLIPs and provide a validation framework for assessing the thermodynamic coverage of both foundation and from-scratch models, enabling reliable atomistic simulation of fluid-phase processes across diverse operating conditions.