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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.13002 |
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| _version_ | 1866917734714966016 |
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| author | Pierce, Karl Rishi, Varun Valeev, Edward F. |
| author_facet | Pierce, Karl Rishi, Varun Valeev, Edward F. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_13002 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Robust approximation of tensor networks: application to grid-free tensor factorization of the Coulomb interaction Pierce, Karl Rishi, Varun Valeev, Edward F. Chemical Physics 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. |
| title | Robust approximation of tensor networks: application to grid-free tensor factorization of the Coulomb interaction |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2012.13002 |