[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-952841","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  [M2 DiPaC] Calcul tensoriel\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          3\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          Semester 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\u003Cp\u003E\u003Cstrong\u003EPrerequisites:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EBasic programming in Python\u003C\/li\u003E\n\u003Cli\u003ELinear algebra (vector spaces, matrix-vector calculus, matrix decompositions - QR, SVD, Cholesky, LU)\u003C\/li\u003E\n\u003Cli\u003E(Recommended) Basics in continuous optimization (gradient descent, newton\u0027s method) and scientific computing\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\u003E\u003Cstrong\u003ECourse program, plan, content:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003ETotal duration:\u003C\/strong\u003E\u0026nbsp;21 hours (7 sessions \u00d7 3 hours)\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003ETopics covered:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003E\u003Cem\u003E\u003Cstrong\u003EIntroduction to tensor algebra\u003C\/strong\u003E\u003C\/em\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EDefinition and notation\u003C\/li\u003E\n\u003Cli\u003EScalars, vectors, matrices, and generalization to tensors\u003C\/li\u003E\n\u003Cli\u003EBasic tensor operations: addition, multiplication, contraction\u003C\/li\u003E\n\u003Cli\u003ETensor products and outer products\u003C\/li\u003E\n\u003Cli\u003EEinstein summation convention and index manipulation\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cem\u003E\u003Cstrong\u003ETensor decompositions and networks\u003C\/strong\u003E\u003C\/em\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003ERefresher on matrix decompositions (QR, SVD, Cholesky, LU, low-rank decompositions)\u003C\/li\u003E\n\u003Cli\u003EIntroduction to tensor decompositions and networks\u003C\/li\u003E\n\u003Cli\u003ECanonical polyadic decomposition (CPD)\u003C\/li\u003E\n\u003Cli\u003ETucker and Hierarchical Tucker decompositions\u003C\/li\u003E\n\u003Cli\u003ETensor-train decomposition (TT), Matrix product states (MPS) and Projected entangled-pair states (PEPS) networks\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cem\u003E\u003Cstrong\u003ENumerical methods for tensor computations\u003C\/strong\u003E\u003C\/em\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EAlgorithms for computing tensor decompositions (Tensor SVD)\u003C\/li\u003E\n\u003Cli\u003ELow-rank tensor arithmetic\u003C\/li\u003E\n\u003Cli\u003ETensor cross-approximation\u003C\/li\u003E\n\u003Cli\u003EOptimization algorithms on tensor manifolds (ALS, AMEN)\u003C\/li\u003E\n\u003Cli\u003ETensor completion and recovery\u003C\/li\u003E\n\u003C\/ul\u003E\n\u003Cp\u003E\u003Cem\u003E\u003Cstrong\u003EApplications in Quantum Computing, High Performance Computing, and AI\u003C\/strong\u003E\u003C\/em\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EComputational challenges in tensor algorithms\u003C\/li\u003E\n\u003Cli\u003ETensor networks in quantum chemistry and physics, quantum simulation, ...\u003C\/li\u003E\n\u003Cli\u003ETensor decompositions in multivariate data analysis, neural networks, recommender systems, ...\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\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E\u003Cstrong\u003ELearning objectives:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003EAt the end of this course, students will be able to:\u003C\/p\u003E\n\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\u003EOrganisation g\u00e9n\u00e9rale et modalit\u00e9s p\u00e9dagogiques\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E\u003Cstrong\u003EGeneral course organization and teaching modalities:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EThe course combines\u0026nbsp;\u003Cstrong\u003Electures\u003C\/strong\u003E\u0026nbsp;introducing theoretical concepts with\u0026nbsp;\u003Cstrong\u003Ehands-on programming labs\u003C\/strong\u003E\u0026nbsp;that allow students to apply and test these concepts in practice.\u003C\/li\u003E\n\u003Cli\u003EEvaluation is\u0026nbsp;\u003Cstrong\u003Econtinuous\u003C\/strong\u003E, based on\u0026nbsp;\u003Cstrong\u003Emultiple written and programming assignments\u003C\/strong\u003E\u0026nbsp;distributed 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\u003EComp\u00e9tences\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E\u003Cstrong\u003ECompetencies gained in the course:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cp\u003EUpon successful completion, students will have acquired the following competencies:\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003E\u003Cstrong\u003ETechnical competence:\u003C\/strong\u003E\u0026nbsp;Ability to design and implement numerical methods using tensor networks.\u003C\/li\u003E\n\u003Cli\u003E\u003Cstrong\u003EAnalytical competence:\u003C\/strong\u003E Mastering the mathematical foundations of low-rank tensor decompositions and networks and numerical algorithms leveraging them.\u003C\/li\u003E\n\u003Cli\u003E\u003Cstrong\u003EPractical competence:\u003C\/strong\u003E\u0026nbsp;Using tensor network toolboxes in Python for rapidly developing tensor network applications.\u003C\/li\u003E\n\u003Cli\u003E\u003Cstrong\u003EProblem-solving competence:\u003C\/strong\u003E\u0026nbsp;Understand when and where low-rank tensor computations can be applied to accelerate computations through effective numerical compression.\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\u003Cp\u003E\u003Cstrong\u003EBibliography:\u003C\/strong\u003E\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EGrey Ballard, Tamara Kolda. \u003Cem\u003ETensor Decompositions for Data Science\u003C\/em\u003E. 2025.\u003C\/li\u003E\n\u003Cli\u003EAlain Franc. \u003Cem\u003ETensor Ranks for the Pedestrian for Dimension Reduction and Disentangling Interactions,\u003C\/em\u003E 2002.\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}]