Machine Learning Hamiltonians are Accurate Energy-Force Predictors
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911456782450688 |
|---|---|
| author | Kim, Seongsu Lee, Chanhui Kim, Yoonho Yun, Seongjun Kim, Honghui Kim, Nayoung Park, Changyoung Han, Sehui Lim, Sungbin Ahn, Sungsoo |
| author_facet | Kim, Seongsu Lee, Chanhui Kim, Yoonho Yun, Seongjun Kim, Honghui Kim, Nayoung Park, Changyoung Han, Sehui Lim, Sungbin Ahn, Sungsoo |
| contents | Recently, machine learning Hamiltonian (MLH) models have gained traction as fast approximations of electronic structures such as orbitals and electron densities, while also enabling direct evaluation of energies and forces from their predictions. However, despite their physical grounding, existing Hamiltonian models are evaluated mainly by reconstruction metrics, leaving it unclear how well they perform as energy-force predictors. We address this gap with a benchmark that computes energies and forces directly from predicted Hamiltonians. Within this framework, we propose QHFlow2, a state-of-the-art Hamiltonian model with an SO(2)-equivariant backbone and a two-stage edge update. QHFlow2 achieves $40\%$ lower Hamiltonian error than the previous best model with fewer parameters. Under direct evaluation on MD17/rMD17, it is the first Hamiltonian model to reach NequIP-level force accuracy while achieving up to $20\times$ lower energy MAE. On QH9, QHFlow2 reduces energy error by up to $20\times$ compared to MACE. Finally, we demonstrate that QHFlow2 exhibits consistent scaling behavior with respect to model capacity and data, and that improvements in Hamiltonian accuracy effectively translate into more accurate energy and force computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16897 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Machine Learning Hamiltonians are Accurate Energy-Force Predictors Kim, Seongsu Lee, Chanhui Kim, Yoonho Yun, Seongjun Kim, Honghui Kim, Nayoung Park, Changyoung Han, Sehui Lim, Sungbin Ahn, Sungsoo Computational Physics Materials Science Recently, machine learning Hamiltonian (MLH) models have gained traction as fast approximations of electronic structures such as orbitals and electron densities, while also enabling direct evaluation of energies and forces from their predictions. However, despite their physical grounding, existing Hamiltonian models are evaluated mainly by reconstruction metrics, leaving it unclear how well they perform as energy-force predictors. We address this gap with a benchmark that computes energies and forces directly from predicted Hamiltonians. Within this framework, we propose QHFlow2, a state-of-the-art Hamiltonian model with an SO(2)-equivariant backbone and a two-stage edge update. QHFlow2 achieves $40\%$ lower Hamiltonian error than the previous best model with fewer parameters. Under direct evaluation on MD17/rMD17, it is the first Hamiltonian model to reach NequIP-level force accuracy while achieving up to $20\times$ lower energy MAE. On QH9, QHFlow2 reduces energy error by up to $20\times$ compared to MACE. Finally, we demonstrate that QHFlow2 exhibits consistent scaling behavior with respect to model capacity and data, and that improvements in Hamiltonian accuracy effectively translate into more accurate energy and force computations. |
| title | Machine Learning Hamiltonians are Accurate Energy-Force Predictors |
| topic | Computational Physics Materials Science |
| url | https://arxiv.org/abs/2602.16897 |