AI 中文总结
研究利用经验插值法加速核密度泛函理论中坐标 - 组态变换，构建DFT模拟器。通过改变模型参数训练测试，考虑多种核模型。该方法能快速准确预测可观测量，相比原始求解器加速显著，有助于提高核特性预测可靠性。
AI 中文摘要
核密度泛函理论（DFT）是预测核基态和裂变特性的合适工具。统计不确定性量化对于使这些预测可靠至关重要，尤其是对于远离稳定态的核。然而，DFT中描述变形核的计算成本使得这种不确定性量化成为一项挑战。许多求解器的主要计算瓶颈是将依赖波函数的算符从坐标空间转换到组态空间。我们探索使用经验插值法（EIM）来加速坐标 - 组态变换，有效地构建用于基态和裂变特性的DFT模拟器。为了训练和测试模拟器，我们在其现实的后验分布中改变模型参数。我们考虑了简化的一维模型以及Hartree - Fock - Boguliubov（HFB）水平下的现实轴向变形核。对于现实计算，我们考虑了从$A = 60$到$A = 254$的整个图表中的样本核以及一个高度变形的裂变异构体。我们为每种情况构建一个模拟器，并研究结合能、四极形变和裂变异构体的激发能。在所有核中，对于所有考虑的可观测量，EIM模拟器与DFT值在原始DFT计算的精度内一致，使用少至100次HFB计算来构建模拟器。对于给定的核基态或异构体，模拟器能够同时预测所有可观测量。模拟器比原始求解器提供了一个数量级的加速，使EIM成为DFT的合适模拟方案，特别是在模型校准和裂变中需要高精度时。因此，EIM有助于使统计不确定性可行，提高未来预测的可靠性。
英文摘要
Nuclear density functional theory (DFT) is a suitable tool for predicting nuclear ground-state and fission properties. Statistical uncertainty quantification is desirable to make those predictions reliable, especially for nuclei far from stability. However, the computational cost associated with describing deformed nuclei in DFT makes such uncertainty quantification a challenge. In many solvers, the main computational bottleneck is the transformation of the wavefunction-dependent operators from coordinate to configuration space. We explore the use of the empirical interpolation method (EIM) to speed up the coordinate-configuration transformations, effectively constructing DFT emulators for ground-state and fission properties. To train and test the emulator we vary the model parameters across their realistic posterior distribution. We consider both a simplified one-dimensional model, and realistic axially-deformed nuclei at the Hartree-Fock-Boguliubov (HFB) level. For realistic calculations, we consider sample nuclei from across the chart, from $A=60$ up to $A=254$, as well as a highly-deformed fission isomer. We construct one emulator for each case, and study the binding energy, quadrupole deformation, and excitation energy of the fission isomer. In all nuclei, for all observables considered, the EIM emulator agrees with the DFT value to the precision of the original DFT calculations, using as few as 100 HFB calculations to build the emulator. For a given nuclear ground state or isomer, the emulator is able to predict all observables simultaneously. The emulator provides an order-of-magnitude speedup over the original solver, making EIM a suitable emulation scheme for DFT, especially when high precision is desired as in model calibration and fission. Thus, the EIM helps make statistical uncertainty feasible, improving the reliability of future predictions.
Comments10 pages, 7 figures
