02/06/2020
The Human Resources Strategy for Researchers

PhD contract in the field of Computer science and mathematics financed during 3 years by the University Clermont Auvergne

This job offer has expired


  • ORGANISATION/COMPANY
    Université Clermont Auvergne
  • RESEARCH FIELD
    Computer science
    Mathematics
  • RESEARCHER PROFILE
    First Stage Researcher (R1)
  • APPLICATION DEADLINE
    28/06/2020 00:00 - Europe/Brussels
  • LOCATION
    France › AUBIERE
  • TYPE OF CONTRACT
    Temporary
  • JOB STATUS
    Full-time
  • HOURS PER WEEK
    35 H
  • OFFER STARTING DATE
    01/10/2020
  • REFERENCE NUMBER
    UCA/ANR/010
  • IS THE JOB RELATED TO STAFF POSITION WITHIN A RESEARCH INFRASTRUCTURE?
    Yes

Subject: Deep Learning approach for an inverse problem in volcanos

Supervisor: Jonas KOKO

Laboratory: LIMOS

Email and phone: Jonas.Koko@uca.fr (06 81 19 34 45)

Co-advisor(s): Valérie CAYOL, LMV

Abstract (up to 10 lines): The inversion of the volcanic surface deformation makes it possible to determine the characteristics (location, pressure) of the fracture within the structure. Solving this inverse problem with classical tools lead to a large scale problem. We propose to study a deep learning approach in which the loss function is the difference between observed and computed deformations. The direct problem (the mechanical equilibrium equations) are solved by classical tools (finite element method). Training will use sampled fracture configurations. The main advantage of the proposed approach is that the computational cost will be transferred to the training phase.

 

Skills: Applied Mathematics with skills in Scientific Computing, Partial Differential Equations, Numerical Optimization. Knowledge of Deep Learning would be a plus.

Keywords: Scientific Computing, inverse problems, numerical optimization, deep learning.

Description (up to 1 page):

The computational cost is a key issue for recovering information on fracture for several problems in Geophysics and Engineering: magma filled cracks, seismogenic fault, enhancing the recovery of hydrocarbon by creating permeable pathways, etc. The inverse problem consists of determining the fracture characteristics from ground surface observations. It leads to a large scale constrained optimization problem for which the cost function is the differences between the observed and the computed deformations. The constraints are the mechanical equilibrium equations for a given fracture. The geophysics scientific community has been addressing this type of problem for a long time with classical methods (e.g. Monte Carlo ref.4) or domain decompositions methods(e.g. ref. 5).

Recently, deep learning (e.g. ref.1-2) emerges as a powerful technique in many applications: image and signal processing, classification, etc. In the numerical approximation of partial differential equations, the topic is rather new and there are few literature (e.g. Ref.3-4). In this project we propose to use a deep learning method for the inversion of the volcanic surface deformation. Firstly, only the loss function (difference between observed and computed deformations) will be used as output by the neural network. The mechanical equilibrium equations will be solved by the finite element method. There are two main advantages for our approach:

  • The computational cost will be transferred to training.
  • The final code will be used as a black-box that will provide a solution faster than a standard code.

Firstly, the location of the fracture and the pressure inside will be the characteristics taken into account. The propagation of the fracture will be considered later.

Our project will be based on the Optimization/Scientific Computing/Deep Learning skills from LIMOS, and the Geophysics/Scientific Computing/Mechanics from LMV.

References :

  1. Kim P., MATLAB Deep Learning: With Machine Learning, Neural Networks and Artificial Intelligence, 162p, APress, 2017.
  2. Skansi S., Introduction to Deep Learning, 196p, Springer, 2018.
  3. Sirignano J. and Spiliopoulos K.,DGM: A deep learning algorithm for solving PDEs, J. Computational Physics 375, 1339-1364, 2018.
  4. Han J., Jentzen A. and Weinan E., Solving high-dimensional PDEs using deep learning, P. Nat. Acad. Sci. USA 115, 8505-8510, 2018.
  5. Fukushima Y. Cayol V. and Durand P., Finding realistic dyke model from interferometric synthetic aperture radar data, J. Geophysical Research 110(B3), 2005.
  6. Bodart O. et al., XFEM-based fictitious domain method for linear elasticity with crack, SIAM J. Sci. Comput. 38(2), B219-B246, 2016.

How to candidate?

Contact the supervisors: Jonas.koko@uca.fr or Valerie.Cayol@opgc.fr

Benefits

 

 
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Offer Requirements

  • REQUIRED EDUCATION LEVEL
    Other: Master Degree or equivalent

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Work location(s)
1 position(s) available at
Laboratory of Informatics, Modeling and Optimization of Systems (LIMOS)
France
Région Auvergne Rhône-Alpes
AUBIERE
63178
Campus Universitaire des Cézeaux TSA 60125 - CS 60026 1, Rue de la Chebarde

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EURAXESS offer ID: 528437

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