ECTS
6 credits
Component
Faculty of Science
Description
This course is a continuation of the optimization course of the second semester of L3 Mathematics and the optimization and machine learning course of M1 MANU. The course is based on the ingredients given in the other modules of the MANU master in PDE analysis and numerical simulation.
After a reminder of the results and numerical methods for the numerical simulation of PDEs on adaptive mesh, of the results of a posteriori error estimation, and of the supervised learning methods of the M1, the course focuses on the generation of quality databases and their completion and certification thanks to the numerical simulation certified by an error control.
This question is fundamental for a 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 an important part of computer projects along the way. All the sessions take place in a computerized environment and allow an immediate implementation of the theoretical elements.
Objectives
The course focuses on transfer learning for industrial regression problems with multiple outputs. These issues are illustrated on direct and inverse engineering problems
Necessary pre-requisites
Fundamentals of 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
Evaluation by continuous assessment.
Syllabus
-Main results of a posteriori error estimation
-Adaptation of unstructured meshes by Riemannian metric control
-Mesh adaptation algorithm in stationary and unsteady mode
-Impact of a posteriori error control in optimization in the presence of an equation of state
-Adaptive simulation for generating certified databases for mathematical learning
-Incremental learning
Additional information
Hourly volumes:
CM : 21
TD : 0
TP : 0
Land : 0