Bridge the gap between the micro and the macro scale properties of materials with new numerical approaches: elaboration of estimation functions using a database and machine learning.

Stage de Master 2 ou de fin d’étude ingénieurs

Bridge the gap between the micro and the macro scale properties of materials with new numerical approaches: elaboration of estimation functions

using a database and machine learning.

Context

This project will cross three research domains: the modelling of the macroscopic behavior of components in extreme conditions, the modelling of the evolution of crystal defects in irradiated materials and the elaboration of mathematical estimators and machine learning.

The objective is to innovate the numerical models of evolution of the materials properties, necessary to the safety of any industrial power plan. This project is in link with the international project ITER, whose machine is under construction in southern France. ITER will be the first device to produce net energy based on the fusion of hydrogen isotopes, one free-carbon solution to produce electricity.

The properties of materials evolve when they are subjected to extreme conditions.

The modelling approach must be multiscale because of the variety of processes involved which happen at the atomic to macroscopic scales and at the femtosecond to the year time scale.

In this project you will develop an original method to bridge the gap between the well-known macroscopic model based on the Finite Elements in Abaqus code [1] and an atomic scale model called Object Kinetic Monte Carlo in the code LAKIMOCA developed for more than 15 years [2].

Abaqus calculates the temperature gradient and transients in a macroscopic component facing the plasma [3]. LAKIMOCA is used to model the evolution of the microstructure defects under irradiation and different temperature conditions [4]. The approach for software coupling is to store LAKIMOCA’s results in a database, which is used by Abaqus to get the relevant data for the macroscopic computations. As LAKIMOCA is a multiparameter code, which computes a set of variables, the database, multidimensional, will be used based on classical tools developed for big data problems.

Objective

Some tools have already been developed, as the one that allows Abaqus to work with a database. It is needed, however, to improve the way Abaqus gets information from it, and to ensure the quality of the obtained data as well as the efficiency of the process. As a consequence, several aspects will be focused on:

1. Choosing a relevant interpolation method between known points, among the one existing ones, considering its flexibility for adding extra dimensions.

2. For each method, estimate the prediction error (for instance, using the ‘leave-one-out’

method).

3. Depending on the time, expanding the database dimension might be considered.

This work is mainly numerical, focused on data processing and optimization.

The project is carried out in collaboration between two Université Sorbonne Paris Nord labs, LSPM (http://www.lspm.cnrs.fr) and L2TI (https://www-l2ti.univ-paris13.fr).

Student's profile:

- Python programming and environments (jupyter notebooks).

- Data Science or statistics: basic machine learning.

- No previous experience in Physics is required.

K

eywords

Duration

Application must be send to:

Y. Charles, [email protected] E. Viennet, [email protected]

(all team members are able to work in French or English language).

[1] https://www.3ds.com/products-services/simulia/products/abaqus/

[2] C. Domain, C. Becquart, L. Malerba, J. Nucl. Mater, vol. 335 (2004), p. 121

[3] S. Benannoune, Y. Charles, J. Mougenot, M. Gaspérini and G. De Temmerman, Phys. Scr.

T171 (2020) 014011

[4] B. Christiaen, C. Domain, L. Thuinet, A. Ambard, A. Legris, Acta Materialia Volume 195, 15 August 2020, Pages 631-644