发表机构
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Fondazione Bruno Kessler; Data Science for Industry and Physics (DSIP), Fondazione Bruno Kessler; Dipartimento di Fisica “E. Fermi”, Università di Pisa; INFN-Sezione di Pisa（欧洲核物理及相关领域理论研究中心 (ECT*)，布鲁诺·克勒斯勒基金会; 工业与物理学数据科学 (DSIP)，布鲁诺·克勒斯勒基金会; 比萨大学“E. 费米”物理系; 意大利国家核物理研究所比萨分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对A=3的核系统，利用主动学习构建超球谐空间，通过高斯过程代理模型与成本感知获取函数，在保证能量精度的同时大幅减少计算量，重现三核子相关物理量。
AI 中文摘要
超球谐（HH）展开不需要均匀分辨率：波函数的不同分量在截然不同的超角和超径向尺度上收敛。我们利用主动学习来挖掘这种结构，使计算能够自主分配分辨率，而非预先设定。HH空间被分解为可物理识别的类别，其超角和超径向截止值独立演化；高斯过程代理模型学习每个可允许扩展的边际变分增益，成本感知的获取函数选择下一个扩展项。代理模型永远不会替代多体求解器：每一次被接受的扩展之后，都会在扩大的空间中进行显式求解，因此每个报告的能量在显式构建的基矢中都是变分的。我们在³H和³He上测试该构建，采用Argonne v₁₀两核子相互作用，以及结合Urbana IX三核子相互作用的情况，与扩展到K=60的均匀HH阶梯（其在1 keV内重现已确立的基准）进行对比。当要求精度为5 keV时，自适应运行在所有情况下都能将均匀K=60空间的能量重现到4 keV以内，并对其进行验证，同时留下超过60%的该空间未构建。随着要求的精度放宽，这种减少幅度会增大：在20 keV时约为88%，在100 keV时为95%。所选空间重现了三核子的已知类别层级，且在能量选择的空间中，单体质半径和磁矩的收敛度约为2×10⁻³（相对误差）。从镜像核或仅采用两核子相互作用的同一核达到的分辨率开始运行，可验证出一个更小的空间，其显式求解仅为精确求解的三分之一。
英文摘要
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 $^3$H and $^3$He 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 $2\times10^{-3}$ 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.
