Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation Functionals
We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies.
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Key points
- Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities.
- Penalizing it requires no self-consistent-field solution during training.
- Trained on 6 energies and 11 CCSD densities, a neural meta-GGA surpasses SCAN in both atomization energies and densities of unseen molecules.
Sources (1)
- [1]Stationarity Constraints Improve Both Energies and Densities of Machine-Learned Exchange-Correlation FunctionalsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 21, 04:49 PM
We show that the Brillouin residual of a trained functional on the Kohn-Sham orbitals of an accurate density controls, to first order, both the self-consistent density shift and the gap between fitted and self-consistent energies.
Empirical exchange-correlation functionals are fitted on fixed orbitals but used self-consistently, so better energies often come with worse densities.
Extractive summary: sentences quoted from the sources.