Physics-Aligned Electronic Ground-State Learning Improves Generalization

Abstract

Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the cost-accuracy Pareto frontier by designing observable-agnostic electronic ground-state descriptor models (GSMs) with computational costs situated between MLIPs and Kohn-Sham density functional theory (KS-DFT). We align the learning objectives and architectures of GSMs with the governing equations of KS-DFT by enforcing physical constraints and removing optimization pressure on unphysical or irrelevant degrees of freedom. In our size-extrapolation experiments from QM9 to QM40, our combined contributions OrthoNormal-Loss (ON-Loss) and Grassmann Restricted Occupied-Orbital Training (GROOT) reach a 79.1% energy and 83.4% force mean absolute error (MAE) reduction over previous state-of-the-art density GSMs. For Hamiltonian GSMs, ON-Loss and Residual Optimal-gauge Conditioning-aware KS-Eq. Training (ROCKET) together reduce the energy and force MAEs of the strongest baseline by 99.8% and 95.9%, respectively. Using a self-consistency rejection criterion, we filter out extrapolation errors on QMugs, rejecting fewer than 0.4% of predictions while reaching an energy MAE of 0.07 mHa. Finally, we demonstrate the efficiency of label-free self-consistency fine-tuning, and transfer GSMs to reactive chemistry in Transition1x, reaching energy errors below chemical accuracy.

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BibTeX RIS

BibTeX

@misc{eberhard2026physicsaligned,
  title = {{Physics-Aligned Electronic Ground-State Learning Improves Generalization}},
  author = {Eike S. Eberhard and Xaver Kainz and Viktor Kotsev and Abdulrahman Aldossary and Stephan Günnemann},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10298},
  eprint = {2610.10298},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10298},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Physics-Aligned Electronic Ground-State Learning Improves Generalization
AU  - Eike S. Eberhard
AU  - Xaver Kainz
AU  - Viktor Kotsev
AU  - Abdulrahman Aldossary
AU  - Stephan Günnemann
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10298
UR  - https://arxiv.org/abs/2610.10298
AB  - Machine-learned interatomic potentials (MLIPs) excel at in-distribution tasks, accelerating drug and material development, yet they struggle to generalize out-of-distribution. We propose to push the cost-accuracy Pareto frontier by designing observable-agnostic electronic ground-state descriptor models (GSMs) with computational costs situated between MLIPs and Kohn-Sham density functional theory (KS-DFT). We align the learning objectives and architectures of GSMs with the governing equations of KS-DFT by enforcing physical constraints and removing optimization pressure on unphysical or irrelevant degrees of freedom. In our size-extrapolation experiments from QM9 to QM40, our combined contributions OrthoNormal-Loss (ON-Loss) and Grassmann Restricted Occupied-Orbital Training (GROOT) reach a 79.1% energy and 83.4% force mean absolute error (MAE) reduction over previous state-of-the-art density GSMs. For Hamiltonian GSMs, ON-Loss and Residual Optimal-gauge Conditioning-aware KS-Eq. Training (ROCKET) together reduce the energy and force MAEs of the strongest baseline by 99.8% and 95.9%, respectively. Using a self-consistency rejection criterion, we filter out extrapolation errors on QMugs, rejecting fewer than 0.4% of predictions while reaching an energy MAE of 0.07 mHa. Finally, we demonstrate the efficiency of label-free self-consistency fine-tuning, and transfer GSMs to reactive chemistry in Transition1x, reaching energy errors below chemical accuracy.
ER  -

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