Digital data and the factory of the future

The scientific industrial sectors linked to chemistry, physics and biology require skills in the optimization, dimensioning and control of manufacturing processes and production systems. The computing power available today enables us to develop applications for processing increasingly large and interesting quantities of data. But processing these data requires the use of specific numerical tools. In this module, we propose to introduce some of the most widely used tools, both in the academic world and in industry, such as the digital technologies currently used by GAFAM.
This module is therefore aimed at students wishing to learn about advanced digital data processing methods.

Notion of matrix, eigenvalues and eigenvectors (students will be reminded of this point)

• General: extracts from the FIDLE-CNRS online training course(https://www.youtube.com/c/CNRSFormationFIDLE) 
• M. Azaiez: Data reduction, 9h
  Many problems in science and engineering are still intractable, despite progress in modeling, numerical tools, algorithms and computational science, on the one hand, and in computing power, which has increased steadily in recent years, on the other. In this context, the reduction of data and models (ROM) is bringing about a paradigm shift, with reductions in computation times of several orders of magnitude. These models are making it possible to solve optimization and control problems of great complexity, which would be out of reach of conventional methods in the next quarter century. The following sections will be covered:
  - Two-parameter data: Singular Value Decomposition (SVD), Proper Orthogonal Decomposition (POD), Proper Generalized Decomposition (PGD), Dynamic Mode Decomposition (DMD)
  - Multi-parameter data: High Singular Value Decomposition (HSVD), High Proper Orthogonal Decomposition (HPOD), Recursive Proper Orthogonal Decomposition (RPOD) and PGD
  - Data interpolation: Empirical Interpolation Methods (EIM) and its discrete version (DEIM), Non-Uniform Rational B-Splines (NURBS)
  - The course will be supplemented by practice exercises on a library developed in Python.
  
  - N. Regnier: Machine learning, 8h
  Optimization and control problems in industry and academia are becoming increasingly complex. This is due to the very rapid growth in the amount of data available, its heterogeneous nature (widespread instrumentation, connectivity, publication or archiving of information), and the growing need to automate analyses and decision-making processes that the existence of such data makes possible.
  The resolution of such problems benefits from the increase in computing power and the development of data reduction techniques, but also from the use of numerical methods adapted to complex and/or uncertain systems. These include neural networks and genetic algorithms, which form part of machine learning techniques and, more generally, the field of artificial intelligence. The following sections will be covered:
  - Principles of machine learning, examples, description of some methods (neural networks, genetic algorithms, CM, 2h)
  - Project n°1 / neural networks: pattern recognition (image processing), word recognition (speech processing), etc... (project, 3h)
  - Project n°2 / genetic algorithms: workshop scheduling, agenda optimization, travelling salesman problem, PID controller tuning, mastermind game, etc... (project, 3h)
  - Tools used: Matlab or Python