Post-hoc estimates

This course is a continuation of the optimization course offered in the second semester of the L3 Mathematics program and the course on optimization and machine learning in the M1 MANU program. The course builds on the concepts covered in other modules of the MANU master’s program in PDE analysis and numerical simulation.

Following a review of the results and numerical methods for the numerical simulation of PDEs on adaptive meshes, results on a posteriori error estimation, and supervised learning methods covered in the M1 program, the course focuses on the generation of high-quality databases and their completion and certification through certified numerical simulation based on error control.

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

The course includes a significant number of ongoing computer projects. All sessions take place in a computer-based environment and allow students to immediately apply the theoretical concepts they have learned.

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

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

Recommended prerequisites: L3, second-semester course in optimization. M1 course in the MANU Master’s program on optimization and machine learning. Programming in Python, Fortran, and C/C++.

Assessment based entirely on continuous evaluation.

-Key Results of Posterior Error Estimation

-Adaptation of unstructured meshes using Riemannian metric control

-Algorithm for mesh adaptation in steady-state and unsteady-state conditions

-The Impact of Post-Processing Error Control in Optimization in the Presence of a State Equation

-Adaptive simulation for generating certified databases for mathematics learning

-Incremental learning

Hourly volumes:

            CM: 21

            TD: 0

            TP: 0

            Land: 0