Active-learning construction of hyperspherical-harmonics spaces for A = 3
Abstract
The hyperspherical-harmonics (HH) expansion does not require uniform resolution: different components of the wave function converge at very different hyperangular and hyperradial scales. We use active learning to exploit this structure, allowing the calculation to distribute resolution instead of prescribing it. The HH space is decomposed into physically identifiable classes whose hyperangular and hyperradial cutoffs evolve independently; a Gaussian-process surrogate learns the marginal variational gain of each admissible extension, and a cost-aware acquisition selects the next one. The surrogate never replaces the many-body solver: every accepted extension is followed by an explicit solution in the enlarged space, so each reported energy is variational in an explicitly constructed basis. We test the construction on 3H and 3He with the Argonne v18 two-nucleon interaction, without and with the Urbana IX three-nucleon interaction, against uniform HH ladders extended to K=60 that reproduce established benchmarks within $1$~keV. Asked for $5$~keV, the adaptive runs reproduce the energy of the uniform K=60 space within $4$~keV in every case and certify it, leaving more than $60$\% of that space unbuilt. The reduction grows as the requested accuracy is relaxed, to about $88$\% at $20$~keV and $95$\% at $100$~keV. The selected spaces reproduce the known class hierarchy of the trinucleon, and the one-body radii and magnetic moments are converged at about the 2×10−3 level (relative error) in the energy-selected space. A run started from the resolution reached by the mirror nucleus, or by the same nucleus with the two-nucleon interaction alone, certifies a smaller space with a third of the exact solves.
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BibTeX
@misc{filandri2026activelearning,
title = {{Active-learning construction of hyperspherical-harmonics spaces for A = 3}},
author = {Elena Filandri and Andrea Di Luca and Laura Elisa Marcucci and Michele Viviani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11933},
eprint = {2610.11933},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11933},
}
RIS
TY - UNPB
TI - Active-learning construction of hyperspherical-harmonics spaces for A = 3
AU - Elena Filandri
AU - Andrea Di Luca
AU - Laura Elisa Marcucci
AU - Michele Viviani
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11933
UR - https://arxiv.org/abs/2610.11933
AB - The hyperspherical-harmonics (HH) expansion does not require uniform resolution: different components of the wave function converge at very different hyperangular and hyperradial scales. We use active learning to exploit this structure, allowing the calculation to distribute resolution instead of prescribing it. The HH space is decomposed into physically identifiable classes whose hyperangular and hyperradial cutoffs evolve independently; a Gaussian-process surrogate learns the marginal variational gain of each admissible extension, and a cost-aware acquisition selects the next one. The surrogate never replaces the many-body solver: every accepted extension is followed by an explicit solution in the enlarged space, so each reported energy is variational in an explicitly constructed basis. We test the construction on ^3H and ^3He with the Argonne v_18 two-nucleon interaction, without and with the Urbana IX three-nucleon interaction, against uniform HH ladders extended to K=60 that reproduce established benchmarks within $1$~keV. Asked for $5$~keV, the adaptive runs reproduce the energy of the uniform K=60 space within $4$~keV in every case and certify it, leaving more than $60$\% of that space unbuilt. The reduction grows as the requested accuracy is relaxed, to about $88$\% at $20$~keV and $95$\% at $100$~keV. The selected spaces reproduce the known class hierarchy of the trinucleon, and the one-body radii and magnetic moments are converged at about the 2×10^−3 level (relative error) in the energy-selected space. A run started from the resolution reached by the mirror nucleus, or by the same nucleus with the two-nucleon interaction alone, certifies a smaller space with a third of the exact solves.
ER -