[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-956202","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Calcul tensoriel\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          2.5\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semestre 1\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E10.5\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ETravaux pratiques :\u003C\/span\u003E\n                                      \u003Cspan\u003E10.5\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                                          \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003ELinear Algebra (vector spaces, matrix-vector calculus, matrix decompositions - QR, SVD, Cholesky, LU)\u003C\/li\u003E\n\u003Cli\u003EBasic programming in Python\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThis course explores the theory and applications of tensor computations, ranging from the basic operations on tensors to the numerical algorithms for the formation and manipulation of tensor decompositions and networks. After providing all theoretical fundamentals for the tensor algebra, the course focuses on the state-of-the-art research work that leverages tensor decompositions and networks in the domains of quantum computing, high performance computing, and AI\/data analysis.\u003C\/p\u003E\n\u003Cp\u003ETopics covered:\u003C\/p\u003E\n\u003Cp\u003EIntroduction to Tensor Algebra\u003Cbr\u003E\n\u2022 Definition and notation\u003Cbr\u003E\n\u2022 Scalars, vectors, matrices, and generalization to tensors\u003Cbr\u003E\n\u2022 Basic tensor operations: addition, multiplication, contraction\u003Cbr\u003E\n\u2022 Tensor products and outer products\u003Cbr\u003E\n\u2022 Einstein summation convention and index manipulation\u003C\/p\u003E\n\u003Cp\u003ETensor Decompositions and Networks\u003Cbr\u003E\n\u2022 Refresher on matrix decompositions (QR, SVD, Cholesky, LU, low-rank decompositions)\u003Cbr\u003E\n\u2022 Introduction to tensor decompositions and networks\u003Cbr\u003E\n\u2022 Canonical polyadic decomposition (CPD)\u003Cbr\u003E\n\u2022 Tucker and Hierarchical Tucker decompositions\u003Cbr\u003E\n\u2022 Tensor-train decomposition (TT), Matrix product states (MPS) and Projected entangled-pair states (PEPS) networks\u003C\/p\u003E\n\u003Cp\u003ENumerical Methods for Tensor Computations\u003Cbr\u003E\n\u2022 Algorithms for computing tensor decompositions (Tensor SVD)\u003Cbr\u003E\n\u2022 Low-rank tensor arithmetic\u003Cbr\u003E\n\u2022 Tensor cross-approximation\u003Cbr\u003E\n\u2022 Optimization algorithms on tensor manifolds (ALS, AMEN)\u003Cbr\u003E\n\u2022 Tensor completion and recovery\u003C\/p\u003E\n\u003Cp\u003EApplications in Quantum Computing, High Performance Computing, and AI\u003Cbr\u003E\n\u2022 Computational challenges in tensor algorithms\u003Cbr\u003E\n\u2022 Tensor networks in quantum chemistry and physics, quantum simulation, etc\u003Cbr\u003E\n\u2022 Tensor decompositions in multivariate data analysis, neural networks, recommender systems, etc\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003ELearn the mathematical foundation of tensors and tensor operations.\u003C\/li\u003E\n\u003Cli\u003EUnderstand the philosophy of low-rank computations using tensor decompositions\/networks.\u003C\/li\u003E\n\u003Cli\u003EImplement tensor network computations using Python libraries such as NumPy or TT-toolbox.\u003C\/li\u003E\n\u003Cli\u003EExplore the applications of tensor computations in in quantum computing, high performance computing, and AI\/data science.\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cul\u003E\n\u003Cli\u003ETensor Decompositions and Applications by Tamara G. Kolda and Brett W. Bader.\u003C\/li\u003E\n\u003Cli\u003ETensor Ranks for the Pedestrian for Dimension Reduction and Disentangling Interactions by Alain Franc.\u003C\/li\u003E\n\u003Cli\u003ETensor Spaces and Numerical Tensor Calculus by Wolfgang Hackbusch.\u003C\/li\u003E\n\u003Cli\u003EAnd many research papers and articles provided throughout the course.\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]