The authors introduce Projected Hessian Learning (PHL), which supervises second-order curvature in machine-learning interatomic potentials (MLIPs) through stochastic Hutchinson-trace-based Hessian-vector product (HVP) projections instead of explicit Hessian construction; on a ωB97XD/6-31G(d) dataset of reactants, products, transition states, IRC and normal-mode-sampled geometries they compare four schemes (E-F, E-F-HVP with one-column or Hutchinson probes, and E-F-H), finding that with probe vectors resampled each minibatch both HVP methods are statistically indistinguishable from full-Hessian training in energy, force and Hessian accuracy while giving more than 24x speedup per epoch, and that under the more realistic fixed-vector regime with one HVP per molecule Hutchinson projections con
The authors introduce Projected Hessian Learning (PHL), which supervises second-order curvature in machine-learning interatomic potentials (MLIPs) through stochastic Hutchinson-trace-based Hessian-vector product (HVP) projections instead of explicit Hessian construction; on a ωB97XD/6-31G(d) dataset of reactants, products, transition states, IRC and normal-mode-sampled geometries they compare four schemes (E-F, E-F-HVP with one-column or Hutchinson probes, and E-F-H), finding that with probe vectors resampled each minibatch both HVP methods are statistically indistinguishable from full-Hessian training in energy, force and Hessian accuracy while giving more than 24x speedup per epoch, and that under the more realistic fixed-vector regime with one HVP per molecule Hutchinson projections con