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Can machines learn density functionals? Past, present, and future of ML in DFT

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arxiv 2503.01709 v1 pith:CF7S6O6P submitted 2025-03-03 physics.comp-ph cond-mat.mtrl-sciphysics.chem-ph

classification physics.comp-phcond-mat.mtrl-sciphysics.chem-ph
keywords densitydifferentfunctionalfuturemanyappliedapproachesapproximations
verification ladder T0 review T1 audit T2 compute T3 formal
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Density functional theory has become the world's favorite electronic structure method, and is routinely applied to both materials and molecules. Here, we review recent attempts to use modern machine-learning to improve density functional approximations. Many different researchers have tried many different approaches, but some common themes and lessons have emerged. We discuss these trends and where they might bring us in the future.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Accurate and scalable exchange-correlation with deep learning

    physics.chem-ph 2025-06 unverdicted novelty 7.0 of 10

    Skala is a neural XC functional trained on wavefunction data that beats state-of-the-art hybrids on main-group chemistry benchmarks at semi-local computational cost.

  2. Overfitting by design: neural network density functionals for water

    physics.chem-ph 2026-05 unverdicted novelty 6.0 of 10

    A neural network LDA functional overfit to water data achieves 1 kcal/mol errors on ionization and atomization energies and matches PBE/B3LYP on WATER27 binding energies after transfer learning from one datum.

  3. ML and AI for density functional theory: different priorities for Kohn-Sham and orbital-free DFT, for electronic and nuclear DFT

    physics.chem-ph 2026-07 accept novelty 5.0 of 10

    Deep neural nets remain useful for KS DFT XC functionals, but KEFs and nuclear DFT favor lighter models and symbolic regression because of stricter accuracy and cost constraints.

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    cond-mat.stat-mech 2026-05 unverdicted novelty 5.0 of 10

    Extends gauge invariance via operator shifting in quantum statistical mechanics, deriving sum rules and hyperdensity functionals for equilibrium and nonequilibrium cases.

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    cond-mat.stat-mech 2026-05 conditional novelty 5.0 of 10

    Operator shifting, defined by commutation with the local current, is an exact gauge symmetry of quantum statistical mechanics and yields a family of force, hyperforce, product, two-body, and nonequilibrium sum rules.

  6. Future directions in nuclear $\beta$ decay at FRIB and beyond

    nucl-th 2026-07 unverdicted

    A community white paper summarizing the current state and future directions of nuclear beta-decay studies at FRIB, with no new quantitative result.

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