具有约束性的功能克隆用于稳定且可迁移的机器学习密度泛函理论
Constraint-aware functional cloning for stable and transferable machine-learned density functional theory
AI总结：
本文研究了神经交换-相关功能的简单但有用的测试方法：神经模型能否在自洽情况下复现已知的交换-相关功能？通过比较约束和非约束架构，发现约束模型在分子自洽计算中更准确，且能提供更好的初始参数。
摘要：
我们研究了一种简单但有用的神经交换-相关（XC）功能的测试方法：神经模型能否在自洽情况下复现已知的XC功能？我们称之为功能克隆。模型在GGA级别训练，以复现已知的半局部功能，使用约束或非约束架构。动机是XC功能并非固定输入。在Kohn-Sham自洽场计算中，它贡献于势能，而得到的密度是同一计算的结果。因此，仅对采样密度描述符进行点状拟合并不足够。由于目标功能已知，误差可直接测量。我们比较了克隆模型在采样描述符、分子总能量、能量差异、PySCF与SIESTA之间的转移以及晶体固体的方程状态。约束模型在分子自洽计算中更准确地复现参考功能。它们还为后续优化提供更好的初始参数。此外，约束架构在克隆前已能提供合理的固态基线。仅在分子密度上训练的克隆模型能良好地迁移到固体，复现参考晶格常数和体积模量。跨代码测试显示，能量差异相对稳健，而总能量强烈依赖于克隆描述符来自全电子密度还是赝势密度。这些结果使功能克隆成为在完整自洽训练神经XC功能之前有用的诊断工具。
英文摘要：
We study a simple but useful test for neural exchange-correlation (XC) functionals: can a neural model reproduce an established XC functional when it is used self-consistently? We call this test functional cloning. The model is trained at the GGA level to reproduce a known semilocal functional, using either a constrained or an unconstrained architecture. The motivation is that an XC functional is not used on a fixed input. In a Kohn-Sham self-consistent-field calculation it contributes to the potential, and the resulting density is part of the outcome of the same calculation. A good pointwise fit to sampled density descriptors is therefore not by itself enough. Because the target functional is known, the error can be measured directly. We compare the clones on sampled descriptors, molecular total energies, energy differences, transfer between PySCF and SIESTA, and equations of state for crystalline solids. The constrained models reproduce the reference functional more accurately in molecular self-consistent calculations. They also give better initial parameters for later optimization against correlated molecular energies. An additional observation is that the constrained architecture already gives a reasonable solid-state baseline before cloning, as seen from randomly initialized constrained models. Clones trained only on molecular densities transfer well to solids, reproducing reference lattice constants and bulk moduli across metallic, covalent, ionic, oxide, and layered systems. Cross-code tests show that energy differences are relatively robust, while total energies depend strongly on whether the cloning descriptors come from all-electron or pseudopotential densities. These results make functional cloning a useful diagnostic before full self-consistent training of neural XC functionals.
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