Dataset-aware entropy-maximized active learning for machine-learned interatomic potentials

Abstract: We present an active learning framework for efficiently generating training data for machine-learned interatomic potentials (MLIPs). The method combines local entropy-driven molecular dynamics with global dataset-aware filtering: a per-configuration entropy term biases MD trajectories toward structurally diverse snapshots, while a global entropy measure, the log-determinant of the fingerprint covariance matrix of the entire dataset, selects only those configurations that provide genuinely new information. We employ dual covariance modes (per-atom for disordered structures and per-config for ordered phases) to achieve broad coverage of configuration space. Combined with a pre-trained foundation model (Allegro-OAM-L) and analytical fingerprint gradients from Gaussian overlap matrix eigenvalues, the framework produces high-quality domain-specific potentials with near- or sub-meV/atom accuracy on test data drawn from the same distribution at training-set sizes of order $10<sup>{2}$ to $10<sup>{3}$ entropy-selected DFT-labeled structures. We demonstrate the method on three systems spanning diverse bonding types and pressure-driven phase transitions: carbon (covalent), silicon (covalent/metallic), and NaCl (ionic). In learning curve comparisons against random molecular dynamics sampling at matched training set sizes ($N = 100$ to $800$), evaluated over three independent training-set draws per condition, entropy-driven sampling achieves a factor of approximately $3$ to $10$ lower energy MAE at $N = 800$ on in-distribution holdouts across the three systems, with the magnitude of the gain depending on the bonding type and the size at which the random-MD baseline saturates.