Beyond Numerical Hessians: Higher-Order Derivatives for Machine Learning Interatomic Potentials via Automatic Differentiation
Year: 2025
Type: article
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.
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,500
Funder: Max-Planck-Gesellschaft
OpenAlex ID: W4409759917