High-Dimensional Approximation.

Research School on Uncertainty in Scientific Computing (ETICS), Golfe de Lozari (L'Ile Rousse), France, October 2-7, 2022.

• Part 1: Elements of approximation theory
• Part 2: High-dimensional approximation tools
• Part 3: Approximation from samples

High-Dimensional Approximation and Approximation Theory of tensor networks.

Journees du GDR MANU, Le Croisic, October 25-26, 2021.

• Part I: High-Dimensional Approximation
• Part II: Approximation theory of tree tensor networks

Approximation and learning with tree tensor networks.

CEMRACS 2021 on Data Assimilation and Reduced Modeling for High Dimensional Problems, CIRM, Luminy, July 19-23, 2021.

• Part I: Tensors, ranks and tensor networks
• Part II: Approximation theory of tree tensor networks
• Part III: Computational aspects
• Hands-on session: exercises
• Hands-on session: python files

Deep tensor networks.

Workshop Learning and simulation in high dimension, Airbus Group, Paris, June 25-27, 2019.

• Introduction
• Part I: Tensors, ranks and related tensor formats
• Part II: Approximation
• Part III: Supervised learning
• Part IV: Unsupervised learning

Polynomial, sparse and low-rank approximations.

RICAM Special Semester on “Multivariate Algorithms and their Foundations in Number Theory”, Workshop Frontier Technologies for High-Dimensional Problems and Uncertainty Quantification, Linz, 14-21 December, 2018.Linz, 2018.

Slides

Approximation with tree tensor networks.

Model Order Reduction Summer School 2019, Eindhoven, Sep. 23-27, 2019.

Slides

A brief introduction to Randomized Linear Algebra.

Model Order Reduction Summer School 2019, Eindhoven, Sep. 23-27, 2019.

Slides

Low-rank and sparse methods for high-dimensional approximation and model order reduction.

Summer school CEA/EDF/INRIA, 20-24 June, 2016.

• Outline and References
• Lecture 1 : High-dimensional approximation
• Lecture 2: Sparse approximation
• Lecture 3: Tensors - Sparse tensors
• Lecture 4: Low-rank tensors
• Lecture 5: Tensor structure of high-dimensional equations
• Lecture 6: Low-rank methods for tensor-structured equations
• Lecture 7: Higher-order singular value decompositions and related tensor truncation schemes
• Lecture 8: Sampling methods for low-rank tensor approximation: a subspace point of view
• Lecture 9: Geometry of tensor manifolds and applications
• Lecture 10: Quantized tensor formats

Tensor numerical methods for high-dimensional problems.

Journees du GDR AMORE, IHP, Paris, December 2019.

• References
• Part 1: High-dimensional approximation, low-rank tensor formats
• Part 2: Approximation in low-rank formats

Tensor numerical methods for high-dimensional problems.

IHP quarter on Numerical Methods for PDEs, Cargese, September 5-9, 2016.

• Outline and References
• Part 1: High-dimensional approximation
• Part 2: Tensors and low-rank tensor formats
• Part 3: Tensor structure of high-dimensional equations
• Part 4: Low-rank methods for tensor-structured problems

Low-rank tensor methods for parametric and stochastic problems.

Oberwolfach Seminar: Projection Based Model Reduction: Reduced Basis Methods, Proper Orthogonal Decomposition, and Low Rank Tensor Approximations, Oberwolfach, 23 Nov - 29 Nov, 2014.

• Outline and References
• Part 1: Low-rank methods and projection-based model reduction
• Part 2: Sparse and low-rank tensor methods for high-dimensional approximation
• Part 3: Adaptive algorithms for low-rank approximation: subspace point of view and goal-oriented approximation