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Where the Error Lives: Spectral Representations of Learned Kohn-Sham Hamiltonians — arXiv:2610.37843

Source

arXiv (en)

Original

https://arxiv.org/abs/2610.37843

License (as archived)

CC0-1.0

Archived

2026-10-31T06:11:06.690Z

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4d5f5104867ed213ea78cc29811529e245484df243a6beb16a663476be3cc64a

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Where the Error Lives: Spectral Representations of Learned Kohn-Sham Hamiltonians — arXiv:2610.37843 — arXiv (en), https://arxiv.org/abs/2610.37843 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ecfc458fc2e8 (Metraipolis archive dc_ecfc458fc2e8, sha256 4d5f5104867ed213ea78cc29811529e245484df243a6beb16a663476be3cc64a)

@misc{dcecfc458fc2e8,
  title = {Where the Error Lives: Spectral Representations of Learned Kohn-Sham Hamiltonians — arXiv:2610.37843},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.37843},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ecfc458fc2e8; sha256 4d5f5104867ed213ea78cc29811529e245484df243a6beb16a663476be3cc64a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.37843. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Kohn-Sham density functional theory (DFT) is the standard method for computing the electronic structure of molecules and materials, but its self-consistent-field (SCF) iterations make it expensive for large systems and high-throughput screening. Machine-learned Hamiltonian models offer a shortcut: an equivariant network predicts the Kohn-Sham Hamiltonian matrix in one forward pass, and diagonalizing the prediction yields orbital energies, the HOMO-LUMO gap, molecular orbitals and the electron density. These models are trained to match the reference matrix entry by entry, yet a small entry-wise error does not guarantee accurate eigenvalues or eigenvectors. Two physics-informed alternatives go partway: a recently proposed wavefunction-alignment loss adds a spectral penalty without diagonalizing the prediction, and matching the electron density of the diagonalized prediction supervises it directly. Neither is complete: by representing the prediction error in the eigenbasis of the reference Hamiltonian, we show that each sees only part of the error, and that shifting the predicted orbital energies leaves the electron density exactly unchanged. The same analysis identifies a complete training signal: the cumulative local density of states (cumulative LDOS), the number of electrons at each point in space with energy below a given threshold. The cumulative LDOS is a single physical observable that contains the electron density as a special case, responds to every component of the error, determines the Hamiltonian uniquely, and yields gradients that do not vanish for large orbitalenergy errors. Fine-tuning three Hamiltonian networks on QH9 in this way, which we call FermiScope, reduces the HOMO-LUMO gap error without increasing the element-wise error. The gains carry over to out-of-distribution and molecular-dynamics splits, where the wavefunction-alignment loss helps less.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.AI, nuovi lavori del giorno).
Categorie arXiv: Chemical Physics (physics.chem-ph) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2610.37843 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-31T06:07:08.599Z dalla pagina https://arxiv.org/list/cs.AI/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).