Beyond Numerical Hessians: Higher-Order Derivatives for Machine Learning Interatomic Potentials via Automatic Differentiation

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.