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

TL;DR

This paper introduces a method called functional cloning to evaluate neural exchange-correlation functionals' ability to reproduce established functionals self-consistently, highlighting the benefits of constrained architectures for transferability and accuracy.

Contribution

The study demonstrates that constrained neural architectures improve the accuracy and transferability of functional cloning in density functional theory, especially for solid-state systems.

Findings

Constrained models better reproduce reference functionals in molecular self-consistent calculations.

Clones trained on molecular densities transfer well to solid-state systems.

Energy differences are robust across codes, but total energies vary with density source.

Abstract

We study a simple but useful test for neural exchange-correlation (XC) functionals: can a neural model reproduce an established XC functional when it is used self-consistently? We call this test functional cloning. The model is trained at the GGA level to reproduce a known semilocal functional, using either a constrained or an unconstrained architecture. The motivation is that an XC functional is not used on a fixed input. In a Kohn-Sham self-consistent-field calculation it contributes to the potential, and the resulting density is part of the outcome of the same calculation. A good pointwise fit to sampled density descriptors is therefore not by itself enough. Because the target functional is known, the error can be measured directly. We compare the clones on sampled descriptors, molecular total energies, energy differences, transfer between PySCF and SIESTA, and equations of state for crystalline solids. The constrained models reproduce the reference functional more accurately in molecular self-consistent calculations. They also give better initial parameters for later optimization against correlated molecular energies. An additional observation is that the constrained architecture already gives a reasonable solid-state baseline before cloning, as seen from randomly initialized constrained models. Clones trained only on molecular densities transfer well to solids, reproducing reference lattice constants and bulk moduli across metallic, covalent, ionic, oxide, and layered systems. Cross-code tests show that energy differences are relatively robust, while total energies depend strongly on whether the cloning descriptors come from all-electron or pseudopotential densities. These results make functional cloning a useful diagnostic before full self-consistent training of neural XC functionals.