BibTeX
@ARTICLE{
         Gonnheimer2025BNH,
       author = "G{\"o}nnheimer, Nils and Reuter, Karsten and Margraf, Johannes T.",
       title = "Beyond Numerical {H}essians: Higher-Order Derivatives for Machine Learning Interatomic
         Potentials via Automatic Differentiation",
       journal = "Journal of Chemical Theory and Computation",
       volume = "21",
       number = "9",
       pages = "4742--4752",
       year = "2025",
       doi = "10.1021/acs.jctc.4c01790",
       abstract = "{ The development of machine learning interatomic potentials (MLIPs) has
         revolutionized computational chemistry by enhancing the accuracy of empirical force fields while
         retaining a large computational speed-up compared to first-principles calculations. Despite these
         advancements, the calculation of Hessian matrices for large systems remains challenging, in
         particular because analytical second-order derivatives are often not implemented. This necessitates
         the use of computationally expensive finite-difference methods, which can furthermore display low
         precision in some cases. Automatic differentiation (AD) offers a promising alternative to reduce
         this computational effort and makes the calculation of Hessian matrices more efficient and accurate.
         Here, we present the implementation of AD-based second-order derivatives for the popular MACE
         equivariant graph neural network architecture. The benefits of this method are showcased via a
         high-throughput prediction of heat capacities of porous materials with the MACE-MP-0 foundation
         model. This is essential for precisely describing gas adsorption in these systems and was previously
         possible only with bespoke ML models or expensive first-principles calculations. We find that the
         availability of foundation models and accurate analytical Hessian matrices offers comparable
         accuracy to bespoke ML models in a zero-shot manner and additionally allows for the investigation of
         finite-size and rounding errors in the first-principles data. }",
       ad_area = "Chemistry",
       ad_theotech = "Hessian"
}