MD stability of Hessian-augmented energy models

Determine whether E(3)-equivariant graph neural network interatomic potential models that are trained with additional Hessian matrix data exhibit improved stability in molecular dynamics simulations compared to models trained only on energies and forces, given that local stability is governed by second-derivative Hessians.

Background

Within their phonax framework, the authors show that augmenting training with molecular Hessians improves local force prediction accuracy and shifts learning curves favorably, indicating better local characterization of the energy landscape around training configurations.

They note, however, that whether these improvements translate into enhanced stability during molecular dynamics simulations remains unresolved. Because MD stability is influenced by the curvature of the potential energy surface, which is encoded in the second-derivative Hessians, confirming this effect would establish a practical benefit of Hessian-augmented training for long-time dynamical simulations.