张量网络的鲁棒近似：在Coulomb相互作用无网格张量分解中的应用
Robust approximation of tensor networks: application to grid-free tensor factorization of the Coulomb interaction
AI总结：
提出一种消除首阶误差的张量网络鲁棒近似方法，将其应用于Coulomb相互作用张量的无网格CP分解，在保持化学相关能量误差可忽略的同时，成功将耦合簇方法的计算复杂度从$\mathcal{O}(N^6)$降至$\mathcal{O}(N^5)$。
摘要：
通过对张量网络中的一个或多个组成张量进行近似（例如分解）来近似该张量网络，可以通过消除由组成张量近似引起的首阶误差来改进。这种鲁棒近似在2粒子Coulomb相互作用张量的（密度拟合）分解的鲁棒典范多项式（CP）近似中展示了其效用。由此得到的Coulomb张量的代数（无网格）近似与伪谱和张量超收缩方法中出现的分解密切相关，其高效且准确，与朴素（非鲁棒）近似相比秩显著降低。将鲁棒近似应用于耦合簇单双激发中的粒子-粒子阶梯项，将大小复杂度从$\mathcal{O}(N^6)$降低至$\mathcal{O}(N^5)$，其鲁棒性确保在CP秩约等于密度拟合基大小的情况下，化学相关能量差异的误差可忽略不计。
英文摘要：
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.
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