Tucker Tensor Train Taylor Series | Paper Citation Record

Observation b2a6859f-c424-4fa8-9dd7-d62641dbb2b3 · outbound

This paper cites Trust-region methods on Riemannian manifolds.Foundations of Computational Mathematics, 7(3):303–330, 2007.

Tucker Tensor Train Taylor Series Trust-region methods on Riemannian manifolds.Foundations of Computational Mathematics, 7(3):303–330, 2007

Reference 1

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This paper cites Princeton University Press, 2008.

Tucker Tensor Train Taylor Series Princeton University Press, 2008

Reference 2

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This paper cites SIAM, 2022.

Tucker Tensor Train Taylor Series SIAM, 2022

Reference 3

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Observation f921bee8-2999-4907-8271-18bbb1fce02f · outbound

This paper cites Randomized algorithms for rounding in the tensor-train format.SIAM Journal on Scientific Computing, 45(1):A74–A95, 2023.

Tucker Tensor Train Taylor Series Randomized algorithms for rounding in the tensor-train format.SIAM Journal on Scientific Computing, 45(1):A74–A95, 2023

Reference 4

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Observation 7a9028fa-e43a-4d7c-b040-b9c2a9d8eb38 · outbound

This paper cites Optimal de- sign of large-scale nonlinear Bayesian inverse problems under model uncertainty.Inverse Problems, 40(9):095001, 2024.

Tucker Tensor Train Taylor Series Optimal de- sign of large-scale nonlinear Bayesian inverse problems under model uncertainty.Inverse Problems, 40(9):095001, 2024

Reference 5

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Tucker Tensor Train Taylor Series Unresolved cited work

Reference 6

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Observation 7849fefa-394c-4710-8706-6e70f0e86d01 · outbound

This paper cites Tensor Train Construction From Tensor Actions, With Application to Compression of Large High Order Derivative Tensors.SIAM J.

Tucker Tensor Train Taylor Series Tensor Train Construction From Tensor Actions, With Application to Compression of Large High Order Derivative Tensors.SIAM J

Reference 7

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Observation 2108de36-d3aa-4d58-80bb-c547e605c944 · outbound

This paper cites Methods of applied mathematics.

Tucker Tensor Train Taylor Series Methods of applied mathematics

Reference 8

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Observation 703fc381-6da4-4bb9-87ac-deaf205707ff · outbound

This paper cites A stochastic collocation method for elliptic partial differential equations with random input data.SIAM Journal on Numerical Analysis, 45(3):1005–1034, 2007.

Tucker Tensor Train Taylor Series A stochastic collocation method for elliptic partial differential equations with random input data.SIAM Journal on Numerical Analysis, 45(3):1005–1034, 2007

Reference 9

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Observation 5b2bbb28-3f55-4e84-b3fa-fdac0c994059 · outbound

This paper cites Low-rank tensor methods for partial differential equations.Acta Numerica, 32:1–121, 2023.

Tucker Tensor Train Taylor Series Low-rank tensor methods for partial differential equations.Acta Numerica, 32:1–121, 2023

Reference 10

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Observation 78fceea0-4bac-4f2e-9823-118d4964e7d7 · outbound

This paper cites Springer, 1989.

Tucker Tensor Train Taylor Series Springer, 1989

Reference 11

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Observation ff56ba04-7492-487c-95dc-9ed9d05e3521 · outbound

This paper cites Gradient-based data and parameter dimension reduction for Bayesian models: an information theoretic perspective.

Tucker Tensor Train Taylor Series Gradient-based data and parameter dimension reduction for Bayesian models: an information theoretic perspective

Reference 12

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Observation 92f999d9-9dce-44ee-9112-df660ad9bf9a · outbound

This paper cites Hessian-based model reduction for large-scale systems with initial-condition inputs.International Journal for Numerical Methods in Engineering, 73(6):844–868, 2008.

Tucker Tensor Train Taylor Series Hessian-based model reduction for large-scale systems with initial-condition inputs.International Journal for Numerical Methods in Engineering, 73(6):844–868, 2008

Reference 13

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Observation 6bf8f522-1ce6-410d-9aee-0dbc51c92398 · outbound

This paper cites Model reduction and neural networks for parametric PDEs.The SMAI Journal of computational mathematics, 7:121–157, 2021.

Tucker Tensor Train Taylor Series Model reduction and neural networks for parametric PDEs.The SMAI Journal of computational mathematics, 7:121–157, 2021

Reference 14

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Observation ecf96a93-c0ae-4b6f-a5ab-72d30898b51f · outbound

This paper cites Bonizzoni, F.

Tucker Tensor Train Taylor Series Bonizzoni, F

Reference 15

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Observation 621de531-cdc3-4aad-9a9e-18459022fcee · outbound

This paper cites Analysis and approximation of moment equations for PDEs with stochastic data.

Tucker Tensor Train Taylor Series Analysis and approximation of moment equations for PDEs with stochastic data

Reference 16

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Observation bd6c6fbf-40c1-44e6-8043-3abb22735826 · outbound

This paper cites Regularity and sparse approxi- mation of the recursive first moment equations for the lognormal darcy problem.Computers & Mathematics with Applications, 80(12):2925– 2947, 2020.

Tucker Tensor Train Taylor Series Regularity and sparse approxi- mation of the recursive first moment equations for the lognormal darcy problem.Computers & Mathematics with Applications, 80(12):2925– 2947, 2020

Reference 17

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Observation 982463fe-bcd2-4563-8c3e-ec1a39eb7763 · outbound

This paper cites Cambridge University Press, 2023.

Tucker Tensor Train Taylor Series Cambridge University Press, 2023

Reference 18

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Observation 016b68c3-958a-4271-81bd-acffbd7e5178 · outbound

This paper cites RTRMC: A Riemannian trust-region method for low-rank matrix completion.Advances in neu- ral information processing systems, 24, 2011.

Tucker Tensor Train Taylor Series RTRMC: A Riemannian trust-region method for low-rank matrix completion.Advances in neu- ral information processing systems, 24, 2011

Reference 19

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Observation 3782d636-19c2-40e4-99bf-e8517b4714ff · outbound

This paper cites A Riemannian trust region method for the canonical tensor rank approximation problem.SIAM Journal on Optimization, 28(3):2435–2465, 2018.

Tucker Tensor Train Taylor Series A Riemannian trust region method for the canonical tensor rank approximation problem.SIAM Journal on Optimization, 28(3):2435–2465, 2018

Reference 20

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Observation be2eb782-6cb7-455a-84a0-dc9d51c688bc · outbound

This paper cites Greedy inference with structure-exploiting lazy maps.Advances in Neural Information Processing Systems, 33:8330– 8342, 2020.

Tucker Tensor Train Taylor Series Greedy inference with structure-exploiting lazy maps.Advances in Neural Information Processing Systems, 33:8330– 8342, 2020

Reference 21

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Observation 38e80e22-d57d-491d-9dd2-1db9ca916205 · outbound

This paper cites Hand-waving and in- terpretive dance: an introductory course on tensor networks.Journal of physics A: Mathematical and theoretical, 50(22):223001, 2017.

Tucker Tensor Train Taylor Series Hand-waving and in- terpretive dance: an introductory course on tensor networks.Journal of physics A: Mathematical and theoretical, 50(22):223001, 2017

Reference 22

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Observation 11305916-9608-4827-922a-687f1e08b840 · outbound

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Tucker Tensor Train Taylor Series Unresolved cited work

Reference 23

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Observation 4008e3f3-ced3-4681-90c2-9df584a8e3a8 · outbound

This paper cites Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric.

Tucker Tensor Train Taylor Series Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric

Reference 24

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Observation d112bb61-9e21-4e43-ac42-d5d0de50cb16 · outbound

This paper cites Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional bayesian inverse problems.Journal of Machine Learning Research, 26(78):1–68, 2025.

Tucker Tensor Train Taylor Series Derivative-informed neural operator acceleration of geometric MCMC for infinite-dimensional bayesian inverse problems.Journal of Machine Learning Research, 26(78):1–68, 2025

Reference 25

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Observation 0061cd75-91b7-4a5a-9f3c-9b94eaebd916 · outbound

This paper cites Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems.

Tucker Tensor Train Taylor Series Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

Reference 26

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Tucker Tensor Train Taylor Series Unresolved cited work

Reference 27

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Observation c28c5146-a175-4bff-a7ab-fc75279605fc · outbound

This paper cites Hessian-based sampling for high- dimensional model reduction.International Journal for Uncertainty Quantification, 9(2), 2019.

Tucker Tensor Train Taylor Series Hessian-based sampling for high- dimensional model reduction.International Journal for Uncertainty Quantification, 9(2), 2019

Reference 28

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Tucker Tensor Train Taylor Series Unresolved cited work

Reference 29

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Observation 6640fd38-72bf-4f5d-b749-ce01a857e3e7 · outbound

This paper cites Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis.

Tucker Tensor Train Taylor Series Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis

Reference 30

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Observation b51bcf75-9e37-4e2e-b4e5-504de762b4c3 · outbound

This paper cites First order k-th moment finite element analysis of nonlinear operator equations with stochastic data.

Tucker Tensor Train Taylor Series First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

Reference 31

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Tucker Tensor Train Taylor Series Unresolved cited work

Reference 32

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Observation ec7bcccd-9526-484f-974f-71b1a44ffd21 · outbound

This paper cites Approximation of high-dimensional parametric PDEs.Acta Numerica, 24:1–159, 2015.

Tucker Tensor Train Taylor Series Approximation of high-dimensional parametric PDEs.Acta Numerica, 24:1–159, 2015

Reference 33

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Observation 66006bd7-8b4e-46dc-a027-309246af07be · outbound

This paper cites SIAM, 2015.

Tucker Tensor Train Taylor Series SIAM, 2015

Reference 34

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Observation ad66cecb-18c7-4c57-a95f-1398bf73f353 · outbound

This paper cites Dimension- independent likelihood-informed MCMC.Journal of Computational Physics, 304:109–137, 2016.

Tucker Tensor Train Taylor Series Dimension- independent likelihood-informed MCMC.Journal of Computational Physics, 304:109–137, 2016

Reference 35

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Observation 7ed8a8f5-c22c-46ce-9a40-1d5e3b3d0093 · outbound

This paper cites Likelihood-informed dimension reduction for nonlin- ear inverse problems.Inverse Problems, 30(11):114015, 2014.

Tucker Tensor Train Taylor Series Likelihood-informed dimension reduction for nonlin- ear inverse problems.Inverse Problems, 30(11):114015, 2014

Reference 36

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Observation 0a961523-74db-4800-a3ac-108505691af9 · outbound

This paper cites Mitigating the Influence of the Boundary on PDE-based Covariance Operators.

Tucker Tensor Train Taylor Series Mitigating the Influence of the Boundary on PDE-based Covariance Operators

Reference 37

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Observation 9b1550fc-8b11-4379-8252-4c5fee3c57c5 · outbound

This paper cites A multi- linear singular value decomposition.SIAM journal on Matrix Analysis and Applications, 21(4):1253–1278, 2000.

Tucker Tensor Train Taylor Series A multi- linear singular value decomposition.SIAM journal on Matrix Analysis and Applications, 21(4):1253–1278, 2000

Reference 38

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Observation f32eb6e9-f9d9-4cbe-a44b-eecf805fdd2e · outbound

This paper cites Rank-adaptive ten- sor methods for high-dimensional nonlinear PDEs.Journal of Scientific Computing, 88(2):36, 2021.

Tucker Tensor Train Taylor Series Rank-adaptive ten- sor methods for high-dimensional nonlinear PDEs.Journal of Scientific Computing, 88(2):36, 2021

Reference 39

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Observation 90ee3009-7305-429d-afb3-0125e14041c6 · outbound

This paper cites Model-based geostatistics.Journal of the Royal Statistical Society Series C: Applied Statistics, 47(3), 1998.

Tucker Tensor Train Taylor Series Model-based geostatistics.Journal of the Royal Statistical Society Series C: Applied Statistics, 47(3), 1998

Reference 40

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Observation e5a88878-4adc-4f2c-93fe-13a2ed04d920 · outbound

This paper cites Learning op- timal aerodynamic designs through multi-fidelity reduced-dimensional neural networks.

Tucker Tensor Train Taylor Series Learning op- timal aerodynamic designs through multi-fidelity reduced-dimensional neural networks

Reference 41

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Observation 90fc67d9-8478-46fd-90e0-29eb67df9411 · outbound

This paper cites Springer, 2016.

Tucker Tensor Train Taylor Series Springer, 2016

Reference 42

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Observation 996e3490-932e-4119-ba91-5a1fe74fb924 · outbound

This paper cites Finitely correlated states on quantum spin chains.Communications in mathe- matical physics, 144(3):443–490, 1992.

Tucker Tensor Train Taylor Series Finitely correlated states on quantum spin chains.Communications in mathe- matical physics, 144(3):443–490, 1992

Reference 43

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Tucker Tensor Train Taylor Series Unresolved cited work

Reference 44

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Observation fa2b68b6-41f2-4cfc-8304-95482d0a677b · outbound

This paper cites Dissertation, 2017.

Tucker Tensor Train Taylor Series Dissertation, 2017

Reference 45

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Observation 8449b588-f9b8-43b7-91fb-378916613b3e · outbound

This paper cites Shape derivative-informed neural oper- ators with application to risk-averse shape optimization.arXiv preprint arXiv:2603.03211, 2026.

Tucker Tensor Train Taylor Series Shape derivative-informed neural oper- ators with application to risk-averse shape optimization.arXiv preprint arXiv:2603.03211, 2026

Reference 46

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Observation b35a6160-2bd7-422c-b9f6-4e9f1a508393 · outbound

This paper cites Gradient-based optimiza- tion for regression in the functional tensor-train format.Journal of Computational Physics, 374:1219–1238, 2018.

Tucker Tensor Train Taylor Series Gradient-based optimiza- tion for regression in the functional tensor-train format.Journal of Computational Physics, 374:1219–1238, 2018

Reference 47

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Observation b540f8a5-2de6-4393-8548-e7301841cc24 · outbound

This paper cites Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning.Journal of Machine Learning Research, 23(143):1– 29, 2022.

Tucker Tensor Train Taylor Series Reverse-mode differentiation in arbitrary tensor network format: with application to supervised learning.Journal of Machine Learning Research, 23(143):1– 29, 2022

Reference 48

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Observation b6ebab45-c0b8-4b87-9e73-5c6335dd9e3f · outbound

This paper cites Variants of alternating least squares tensor completion in the tensor train format.

Tucker Tensor Train Taylor Series Variants of alternating least squares tensor completion in the tensor train format

Reference 49

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Observation ff76ad47-0066-4e9c-b72b-e00cc7bea64f · outbound

This paper cites Stable ALS approximation in the TT-format for rank-adaptive tensor completion.Numerische Mathematik, 143(4):855–904, 2019.

Tucker Tensor Train Taylor Series Stable ALS approximation in the TT-format for rank-adaptive tensor completion.Numerische Mathematik, 143(4):855–904, 2019

Reference 50

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Observation 56b357b3-bb02-47fc-bcf3-92e46ece4756 · outbound

This paper cites SIAM, 2002.

Tucker Tensor Train Taylor Series SIAM, 2002

Reference 51

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Observation 7d24c230-d775-4b99-a5d5-7ba3f8625aa4 · outbound

This paper cites Geometry of matrix product states: Metric, parallel transport, and curvature.Journal of Mathematical Physics, 55(2), 2014.

Tucker Tensor Train Taylor Series Geometry of matrix product states: Metric, parallel transport, and curvature.Journal of Mathematical Physics, 55(2), 2014

Reference 52

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Observation e895961b-d646-46b7-a13f-a41299db5437 · outbound

This paper cites Most tensor problems are NP-hard.Journal of the ACM (JACM), 60(6):1–39, 2013.

Tucker Tensor Train Taylor Series Most tensor problems are NP-hard.Journal of the ACM (JACM), 60(6):1–39, 2013

Reference 53

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Observation 3fb559a3-0d0d-42ac-b4fa-3af2bf98703c · outbound

This paper cites The alternating linear scheme for tensor optimization in the tensor train for- mat.SIAM Journal on Scientific Computing, 34(2):A683–A713, 2012.

Tucker Tensor Train Taylor Series The alternating linear scheme for tensor optimization in the tensor train for- mat.SIAM Journal on Scientific Computing, 34(2):A683–A713, 2012

Reference 54

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Observation 1c0527b5-0687-4261-a55f-f6db6d7d2855 · outbound

This paper cites On manifolds of tensors of fixed tt-rank.Numerische Mathematik, 120(4):701–731, 2012.

Tucker Tensor Train Taylor Series On manifolds of tensors of fixed tt-rank.Numerische Mathematik, 120(4):701–731, 2012

Reference 55

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Tucker Tensor Train Taylor Series Unresolved cited work

Reference 56

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Tucker Tensor Train Taylor Series Unresolved cited work

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This paper cites Scalable symmetric Tucker tensor decomposition.SIAM Journal on Matrix Analysis and Applications, 45(4):1746–1781, 2024.

Tucker Tensor Train Taylor Series Scalable symmetric Tucker tensor decomposition.SIAM Journal on Matrix Analysis and Applications, 45(4):1746–1781, 2024

Reference 58

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Observation 28291ddb-5b0e-478a-843c-5be223971fe8 · outbound

This paper cites Springer- Verlag New York, 2005.

Tucker Tensor Train Taylor Series Springer- Verlag New York, 2005

Reference 59

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Observation 37a78940-2428-426f-8924-d3264c3403a1 · outbound

This paper cites Inexact trust-region algorithms on Riemannian manifolds.Advances in neural information processing systems, 31, 2018.

Tucker Tensor Train Taylor Series Inexact trust-region algorithms on Riemannian manifolds.Advances in neural information processing systems, 31, 2018

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This paper cites Walter de Gruyter GmbH & Co KG, 2018.

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Tucker Tensor Train Taylor Series Adam: A Method for Stochastic Optimization

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Observation b4e584af-f963-4ec8-a102-3a3c2bf70328 · outbound

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Observation 318280fd-da05-45a9-997a-52a515db9061 · outbound

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This paper cites Auto- matic differentiation for Riemannian optimization on low-rank matrix and tensor-train manifolds.SIAM Journal on Scientific Computing, 44(2):A843–A869, 2022.

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Observation 26674461-fbe7-44e9-a7ba-3a9b78a32b5f · outbound

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This paper cites an unresolved cited work.

Tucker Tensor Train Taylor Series Unresolved cited work

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Observation 7396ea05-197b-4b32-a6a8-4f42ca4b2474 · outbound

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Observation 32c97d95-abe9-4138-b32a-4ec2d25d6b61 · outbound

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Observation 82649c3d-ba66-42b1-ba89-d3e12a59eea6 · outbound

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Tucker Tensor Train Taylor Series Unresolved cited work

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Observation 14c83ea1-633b-4faf-a926-9c32a0d1f515 · outbound

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Observation 0715fc04-a36e-4a02-8afe-fcdf8189c977 · outbound

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Observation cd373b10-9a35-4248-9f64-eb7235f1c2e3 · outbound

This paper cites On local convergence of alternating schemes for optimization of convex problems in the tensor train format.SIAM Journal on Numerical Analysis, 51(2):1134–1162, 2013.

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Observation 9006bb7e-763b-4923-8e81-d45d4c4096a0 · outbound

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Observation 104c154a-51cd-4d36-a9d6-1d1ad955c60b · outbound

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Observation 50488c6a-8713-4ffd-82a3-00326c62978e · outbound

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This paper cites Riemannian optimization for high-dimensional tensor completion.SIAM Journal on Scientific Computing, 38(5):S461– S484, 2016.

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