Hessian-Informed Conformation Augmentation for Potential Energy Surface Curvature in Machine Learning Interatomic Potentials

While machine-learning interatomic potentials (MLIPs) have successfully learned potential energy surfaces (PES) and atomic forces, many practical applications, such as vibrational analysis and transition state search, rely heavily on the PES Hessian. Yet standard MLIPs are trained on energy and forces only, and using the Hessian as an additional training objective requires backpropagation whose memory cost grows quadratically with the number of atoms. To address these limitations, we propose two Hessian-derived data augmentation schemes: isotropic Gaussian displacement (UniAug) and normal mode-weighted displacement (ModeAug). Both methods utilize simple Taylor expansions, generating physically grounded molecular structures with highly accurate energy and force labels. By preserving the underlying MLIP architecture and training procedure, this approach contributes to improving energy and force predictions in various benchmarks. Comprehensive evaluations across non-equilibrium and equilibrium datasets demonstrate that our approach enhances model accuracy where reference forces are large and training data are limited.