ECTS
6 credits
Component
Faculty of Science
Description
This course is a continuation of the optimization course in the second semester of L3 Mathematics and the optimization and machine learning course in M1 MANU. The course builds on the ingredients given in the other MANU master's modules in PDE analysis and numerical simulation.
After a reminder of the results and numerical methods for numerical simulation of PDEs on adaptive meshes, a posteriori error estimation results, and supervised learning methods from M1, the course looks at the generation of quality databases and their completion and certification thanks to numerical simulation certified by error checking.
This question is fundamental to the certified use of machine learning in industry. Indeed, the accuracy of mathematical learning during inference is strongly conditioned by the quality of the database.
The course includes a significant number of ongoing IT projects. All sessions take place in a computerized environment, enabling immediate implementation of theoretical elements.
Objectives
The course focuses on transfer learning for multi-output industrial regression problems. These issues are illustrated on direct and inverse engineering problems.
Necessary prerequisites
Basic analysis, numerical solutions of ordinary differential equations and partial differential equations, numerical linear algebra, programming experience in interpreted and compiled languages.
Recommended prerequisites: L3 semester 2 optimization course. Course M1 Master MANU optimization and machine learning. Python, Fortran, C/C++ programming.
Knowledge control
Assessment by continuous assessment.
Syllabus
-Main results of a posteriori error estimation
-Adaptation of unstructured meshes by Riemannian metric control
-Mesh adaptation algorithm for stationary and unsteady meshes
-Impact of a posteriori error control in optimization in the presence of an equation of state
-Adaptive simulation for generating certified mathematical learning databases
-Incremental learning
Further information
Hourly volumes :
CM: 21
TD : 0
TP: 0
Land: 0