AI 中文总结
本研究将基于神经网络的变分方法扩展至核密度泛函理论的Kohn–Sham方案，用多层感知器表示单粒子轨道旋量，经多维度验证其精度与适用性，为核理论计算提供新途径。
AI 中文摘要
我们将基于神经网络的变分方法扩展到核密度泛函理论的Kohn–Sham方案中，用多层感知器表示单粒子轨道的复杂旋量分量。我们表明，对给定能量密度泛函进行神经网络优化，结合正交归一化后处理步骤，在数学上等价于投影到由网络参数张成的波函数流形切空间上的变分条件，且训练不仅优化展开系数，还优化基函数本身。我们从三个角度评估该方法：首先，研究结果如何依赖于单元数、层数和算术精度，发现定量精度需要足够的宽度和深度，而单精度算术足以表示核密度分布；其次，多个闭壳核的结合能和电荷半径与传统Skyrme–Hartree–Fock结果一致，开壳核的四极形变与包含对关联的参考计算及实验相符；第三，我们确认神经网络单粒子基可表示基本 pasta 相的三维构型：球、棒和板。该框架为计算核理论提供了新视角，非常适合即将到来的面向GPU和AI的高通量超级计算机。
英文摘要
We extend the neural-network-based variational method for nuclear density functional theory to the Kohn--Sham scheme, representing the complex spinor components of the single-particle orbitals by multi-layer perceptrons. We show that neural-network optimization of a given energy density functional, combined with an orthonormalization post-processing step, is mathematically equivalent to the variational condition projected onto the tangent space of the wave-function manifold spanned by the network parameters, and that the training optimizes not only the expansion coefficients but also the basis functions themselves. We assess the method from three points of view. In the first place, we examine how the results depend on the number of units, the number of layers, and the arithmetic precision, and find that quantitative accuracy requires both a sufficient width and a sufficient depth, while single-precision arithmetic is sufficient to represent the nuclear density distribution. In the second place, the binding energies and charge radii of several closed-shell nuclei agree with conventional Skyrme--Hartree--Fock results, and the quadrupole deformations of open-shell nuclei are consistent with reference calculations that include pairing and with experiment. In the third place, we confirm that a neural-network single-particle basis can represent the three-dimensional configurations of the fundamental pasta phases: spheres, rods, and slabs. The framework offers a new perspective on computational nuclear theory, well suited to the forthcoming generation of GPU- and AI-oriented high-throughput supercomputers.
Comments13 pages, 3 figures, 5 tables
