Derivative Informed Learning of Exchange-Correlation Functionals

MCML Authors

Stephan Günnemann

Prof. Dr.

Core PI

Data Analytics & Machine Learning

Abstract

Machine-learned (ML) XC functionals aim to replace human-designed density functional approximations by learning directly from reference data, but they still do not consistently outperform traditional O(N4)-scaling hybrid functionals. We therefore study a hybrid-distillation setting, where O(N3)-scaling semilocal ML-XC functionals are trained to reproduce B3LYP/def2-SVP targets. We introduce Derivative Informed XC-Loss (DI-Loss), a loss that incorporates additional information from the reference hybrid functional by supervising first and second derivatives of the energy on the Grassmannian of admissible density matrices. Rather than only matching the self-consistent fixed point, DI-Loss aligns the local first- and second-order response of the learned functional with that of the target functional. Across four evaluated architectures, DI-Loss consistently improves the main energy metrics. Averaged uniformly across architectures, the total-energy MAE decreases by 66% relative to energy and density supervision alone. The density-sensitive meanfield energy metric Eρ improves from 1.2 to 0.8 mEh on average, while dipole and L2 density errors do not improve uniformly. We further show that densities from the distilled functionals reduce hybrid-functional SCF iterations by up to 55%. In downstream TDDFT calculations, Hessian supervision improves excited-state predictions, with XCdiff reducing the mean excitation-energy MAE by 24–35% across molecule sizes on QM40

inproceedings ETA+26

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ICML 2026

43rd International Conference on Machine Learning. Seoul, South Korea, Jul 06-11, 2026. To be published. Preprint available.

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Authors

E. S. Eberhard • L. A. Thiede • A. Aldossary • A. Burger • N. Gao • V. Bhethanabotla • A. Aspuru-Guzik • S. Günnemann

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Links

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Research Area

 A3 | Computational Models