• Accepted Paper

Constraint-aware functional cloning for stable and transferable machine-learned density functional theory

Sara Navarro-Rodríguez, Alec Wills, Kimberly J. Daas, María Camarasa-Gómez, and Marivi Fernández-Serra

PRX Intelligence - Accepted 28 October, 2026

DOI: https://doi.org/10.1103/ykrf-jmm8

Abstract

Machine-learned exchange–correlation (XC) functionals must be accurate not only as pointwise maps on sampled density descriptors, but also as self-consistent components of the Kohn–Sham equations. To evaluate whether neural XC models meet this requirement, we introduce , a controlled framework in which a neural XC functional is trained to reproduce an established analytic functional and then evaluated in self-consistent calculations. Because the target functional is known exactly, cloning directly diagnoses whether a neural architecture, descriptor choice, and training protocol preserve the behavior of the functional once densities, potentials, and energies are coupled through the self-consistent-field cycle. We apply this framework to physically constrained and unconstrained generalized-gradient-approximation (GGA) models trained to clone PBE. Tests cover molecular energies, crystalline equations of state, and transfer between codes using different numerical grids and all-electron or pseudopotential descriptions. Constrained models outperform unconstrained ones both in cloning PBE and in subsequent optimization against correlated molecular energies. Clones trained only on molecular densities also transfer to diverse periodic solids, reproducing PBE lattice constants and bulk moduli. Even before cloning, randomly initialized constraint-aware models provide a reasonable solid-state baseline, suggesting that the imposed constraints capture a substantial part of the relevant physics at the GGA level. These results establish functional cloning as a controlled and interpretable intermediate step in the development of neural XC functionals, separating failures of representation and self-consistent stability from the harder problem of improving on the reference functional.

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