评估预测密度、哈密顿量和密度矩阵作为周期性自洽场初始值
Evaluating Predicted Densities, Hamiltonians, and Density Matrices as Periodic SCF Initializers
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中文总结 AI 辅助
本研究通过构建ρHD-43K数据集和闭环基准，发现直接电荷密度预测作为SCF初始值可加速约91%晶体，节省中位3次迭代，而仅降低离线误差不足以保证更好的初始值，需在求解器循环中评估其效用。
中文摘要 AI 辅助
学习得到的电子态通常通过预测误差来评估，尽管其预期用途是加速密度泛函理论（DFT）的自洽场（SCF）循环。我们探究较低的离线误差是否确实能带来更好的SCF初始值。我们构建了ρHD-43K，一个包含43,851个晶体的DFT语料库，具有对齐的电荷密度、哈密顿量和密度矩阵标签，并扩展求解器工作流程以注入所有三种预测状态。闭环基准测试在冻结的非磁性晶体测试集上，将直接收敛态预测与基于求解器原生参考的残差预测进行比较，使用配对的收敛次数、迭代次数和SCF循环时间测量。将精确收敛的密度矩阵或哈密顿量作为预言机上限注入，可将中位SCF次数从16次降至1次，显示出巨大的加速空间。在学习输入中，直接电荷密度预测（Charge3Net-E3）加速了约91%的配对晶体，节省了中位3次SCF迭代，并实现了1.18倍的SCF循环加速。相比之下，测试的残差密度和矩阵初始值并未持续优于标准的原子密度叠加基线。这些结果表明，仅目标空间精度是不够的：学习得到的初始值还必须与非线性求解器轨迹兼容，其效用必须在循环中进行衡量。
英文摘要
Learned electronic states are usually evaluated by prediction error, even though their intended use is to accelerate the self-consistent-field (SCF) loop of density functional theory (DFT). We ask whether lower offline error actually yields a better SCF initializer. We construct $ρ$HD-43K, a 43,851-crystal DFT corpus with aligned charge-density, Hamiltonian, and density-matrix labels, and extend the solver workflow to inject all three predicted states. The closed-loop benchmark compares direct converged-state prediction against residual prediction from solver-native references on a frozen test set of non-magnetic crystals, using paired convergence, iteration, and SCF-loop timing measurements. Injecting the exact converged density matrix or Hamiltonian as an oracle upper bound cuts the median SCF count from 16 to one, revealing substantial acceleration headroom. Among learned inputs, direct charge-density prediction (Charge3Net-E3) accelerates about 91% of paired crystals, saves a median of three SCF iterations, and yields a $1.18\times$ SCF-loop speedup. In contrast, the tested residual-density and matrix initializers do not consistently improve over the standard superposition-of-atomic-densities baseline. These results establish that target-space accuracy alone is insufficient: a learned initializer must also be compatible with the nonlinear solver trajectory, and its utility must be measured in the loop.
发表机构
- School of Computer Science and Engineering, Sun Yat-sen University（中山大学计算机科学与工程学院）
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