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

2025/04/25 by Nils Gönnheimer, Karsten Reuter, Johannes T. Margraf · 1 voice · 2 citations
Chemical Engineering · Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #Catalysis and Oxidation Reactions #Machine Learning in Materials Science

paper · pdf · doi:10.1021/acs.jctc.4c01790

openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

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Cited by

• General Learning of the Electric Response of Inorganic Materials
• Algorithmic differentiation for plane-wave DFT: materials design, error control and learning model parameters

Discussions

• #RobSelects paper of the week #JCTC: Implementing computationally efficient and precise second-order derivatives for an equivariant graph neural network architecture for molecules via automatic differ [bsky, 1 points, 0 comments]

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