Ex post estimates

This course is a continuation of the optimization course from the second semester of the third year of mathematics and the course on optimization and machine learning from the first year of the MANU master's program. The course builds on the content covered in other modules of the MANU master's program in PDE analysis and numerical simulation.

After reviewing the results and numerical methods for numerical simulation of PDEs on adaptive meshes, a posteriori error estimation results, and supervised learning methods from the M1, the course focuses on the generation of high-quality databases and their completion and certification through certified numerical simulation using error control.

This question is fundamental to the certified use of machine learning in industry. Indeed, the accuracy of mathematical learning during inference is heavily dependent on the quality of the database.

The course includes a significant amount of ongoing IT projects. All sessions take place in a computerized environment and allow for immediate implementation of theoretical concepts.

The course focuses in particular on transfer learning for industrial regression problems with multiple outputs. These issues are illustrated using direct and inverse engineering problems.

Fundamentals of analysis, numerical solutions of ordinary differential equations and partial differential equations, numerical linear algebra, experience in programming in interpreted and compiled languages.

Recommended prerequisites: L3 semester 2 optimization course. M1 Master MANU optimization and machine learning course. Python, Fortran, C/C++ programming.

Continuous assessment throughout the course.

-Main results of posterior error estimation

-Adaptation of unstructured meshes by Riemannian metric control

-Algorithm for adapting meshes in steady and unsteady conditions

-Impact of a posteriori error control in optimization in the presence of a state equation

-Adaptive simulation for generating certified databases for mathematical learning

-Incremental learning

Hourly volumes:

            CM: 21

            TD: 0

            TP: 0

            Land: 0