Reproduce “HIP: Hessian Interatomic Potentials without derivatives” on OpenResearch

About this paper

Andreas Burger, Luca Thiede, Nikolaj Rønne, Varinia Bernales, Nandita Vijaykumar, Tejs Vegge, Arghya Bhowmik, Alan Aspuru-Guzik

HIP predicts molecular Hessians directly from equivariant model representations, using a readout designed to preserve rotational behavior and matrix symmetry, rather than differentiating energies or forces. On HORM-T1x, frozen-backbone HIP-EquiformerV2 achieved Hessian MAE 0.030 eV/Ų versus 0.077 for automatic differentiation, and 38.5 versus 562.3 ms per prediction. This comparison uses neutral, closed-shell molecules labeled at ωB97X/6-31G*.

Key insights

• Directly predicting the Hessian with an SE(3)-equivariant architecture leads to significantly higher accuracy for second derivatives compared to deriving them via automatic differentiation from a learned potential.
• Optimizing the Hessian prediction with a subspace loss focusing on the lowest eigenvalues/eigenvectors improves performance in critical downstream applications like transition state searches and ZPE calculations.
• The direct prediction approach offers substantial computational efficiency, achieving O(N) scaling for Hessian inference time and significantly reduced memory usage, overcoming the O(N^2) limitations of AD.

Summary by alphaXiv.