Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction
Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction
复制标题
张量网络的鲁棒逼近：库仑相互作用无网格张量分解的应用
DOI：
10.1021/acs.jctc.0c01310
复制
发表时间：
2021
影响因子：
5.5
通讯作者：
Valeev, Edward F.
中科院分区：
文献类型：
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作者：
Pierce, Karl;Rishi, Varun;Valeev, Edward F.
张量网络的近似通过近似（例如，因式分解）其一个或多个组成张量可以通过消除由于组成近似引起的前阶误差来改进。这种强大的近似的实用程序的（密度拟合）因式分解的两粒子库仑相互作用张量的强大的正则polyadic（CP）近似证明。由此产生的库仑张量的代数（无网格）近似，与伪谱和张量超收缩方法中出现的因式分解密切相关，是有效和准确的，与朴素（非鲁棒）近似相比，秩显著降低。在耦合团簇单粒子和双粒子中应用粒子-粒子阶梯项的鲁棒近似将尺寸复杂性从O（N6）降低到O（N5），鲁棒性确保化学相关能量差中的误差可以忽略不计，使用CP秩近似等于密度拟合基的尺寸。
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 two-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 (nonrobust) approximation. Application of the robust approximation to the particle–particle ladder term in the coupled-cluster singles and doubles reduces the size complexity fromO(N6) toO(N5) with robustness ensuring negligible errors in chemically relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.