论文标题
张量网络的稳健近似：应用于库仑相互作用的无网张量分解
Robust approximation of tensor networks: application to grid-free tensor factorization of the Coulomb interaction
论文作者
论文摘要
通过取消由于选民的近似值而取消前阶误差，可以改善张量网络的近似张量网络（例如，分解一个或多个构成张量）。对于（密度拟合）分解的2粒子库仑相互作用张量的强大规范多核（CP）近似，证明了这种可靠近似的实用性。库仑张量的最终代数（无网格）近似值与伪谱和张量超捕获方法的分解密切相关，是有效而准确的，与天真（不稳定）近似相比，等级显着降低。在耦合群集单打中稳健近似与粒子粒子阶梯期限的应用可将大小的复杂性从$ \ \ \ \ \ m nathcal {o}（n^6）$降低到$ \ nathcal {o}（o}（o}（n^5）$，可确保使用化学上的能量差异均衡，以确保可忽略不相比的尺寸差异均衡。
Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents' approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized 2-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (non-robust) approximation. Application of the robust approximation to the particle-particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from $\mathcal{O}(N^6)$ to $\mathcal{O}(N^5)$ with robustness ensuring negligible errors in chemically-relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.
