The topic is the analysis of large quantities of data, for example observations at the microscopical scale, in order to understand a physical phenomenon. The example considered consists in the utilization of tomographies and microscopic pictures of a porous material in order to build a permeability model.
We will consider supervised and unsupervised learning methods and show how they are used in modern approaches in computational mechanics. One can mention the following ideas, that will be considered more or less extensively, and that make data and physical laws work together at different extents:
| On completion of the unit, the student will be capable of: | Classification level | Priority |
|---|---|---|
| Overview of AI methods used in mechanics | 1. Knowledge | Useful |
| Associated mathematical methods | 1. Knowledge | Useful |
| Choose the good method for a given problem | 3. Apply | Important |
| Formulate a problem in a mathematical form | 3. Apply | Important |
| Implement the problem's resolution | 3. Apply | Important |
| Analyze the results | 4. Analyse | Essential |
| Percentage ratio of individual assessment | Percentage ratio of group assessment | ||||
|---|---|---|---|---|---|
| Written exam: | 50 | % | Project submission: | % | |
| Individual oral exam: | % | Group presentation: | % | ||
| Individual presentation: | % | Group practical exercise: | % | ||
| Individual practical exercise: | 50 | % | Group report: | % | |
| Individual report: | % | ||||
| Other(s): % | |||||
| Type of teaching activity | Content, sequencing and organisation |
|---|---|
| CM | Course introduction Introductory example to motivate utilization of physical principles in data driven computational mechanics Presentation of the course's main application example |
| CM, TD, TP | Clustering and classification : the goal is to sort a group of individuals in separate ensembles. The most standard algorithms that we will use are based on the distance between individuals. The importance of the choice of the measure of this distance will be discussed, and it will be shown that one can (should) base this choice on mechanical expertise. The practical part will be about effective implementation of these algorithmically very simple methods, and to "watch their behavior" when being used on mechanical data. More recent method in computational mechanics will be mentioned, that use (among others) clustering or classification (constitutive relation-less FE computations or failure prediction). The goal here is to illustrate the course, and the objective is not to make students operational on thos advanced methods. |
| CM, TD, TP | Interpolation and regression : the goal is to build a continuous function that links two vectors x and y from a finite number of duets (x,y) We will show how to take into account known physical laws (via the addition of constraints) and the interest of it in terms of quantity of necessary data, and algorithmic complexity. We will present, as illustrations, results obtained by recent research in this domain (multi-fidelity Kriging, Physics-informed neural networks...) |