ORGANISATION/COMPANYUniversité Clermont Auvergne
RESEARCH FIELDComputer scienceMathematics
RESEARCHER PROFILEFirst Stage Researcher (R1)
APPLICATION DEADLINE28/06/2020 00:00 - Europe/Brussels
LOCATIONFrance › AUBIERE
TYPE OF CONTRACTTemporary
HOURS PER WEEK35 H
OFFER STARTING DATE01/10/2020
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
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.
- Kim P., MATLAB Deep Learning: With Machine Learning, Neural Networks and Artificial Intelligence, 162p, APress, 2017.
- Skansi S., Introduction to Deep Learning, 196p, Springer, 2018.
- Sirignano J. and Spiliopoulos K.,DGM: A deep learning algorithm for solving PDEs, J. Computational Physics 375, 1339-1364, 2018.
- Han J., Jentzen A. and Weinan E., Solving high-dimensional PDEs using deep learning, P. Nat. Acad. Sci. USA 115, 8505-8510, 2018.
- Fukushima Y. Cayol V. and Durand P., Finding realistic dyke model from interferometric synthetic aperture radar data, J. Geophysical Research 110(B3), 2005.
- 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?
EURAXESS offer ID: 528437
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