12/03/2021

PhD proposal -- Uncertainties in Physics-Informed Machine Learning

This job offer has expired


  • ORGANISATION/COMPANY
    Ecole Nationale Supérieure des Mines de Paris (MINES ParisTech)
  • RESEARCH FIELD
    PhysicsComputational physics
  • RESEARCHER PROFILE
    First Stage Researcher (R1)
  • APPLICATION DEADLINE
    31/05/2021 00:00 - Europe/Brussels
  • LOCATION
    France › Fontainebleau
  • TYPE OF CONTRACT
    Temporary
  • JOB STATUS
    Full-time
  • HOURS PER WEEK
    37
  • OFFER STARTING DATE
    01/10/2021
  • EU RESEARCH FRAMEWORK PROGRAMME
    H2020
  • REFERENCE NUMBER
    2021-0312

OFFER DESCRIPTION

Proposal description

Recently, Physics-informed Neural Networks (PINN) have been proposed to explicitly introduce the Physics inside Machine Learning. On one side, Machine Learning is able to extract hidden information out of the data. On the other side, the conclusions are not always consistent with the physics. This is a strong limitation, but it offers the possibility to extend the capabilities of Machine Learning. The objective of the of PINN approaches is to update the weights of the neural network to fit the observed data as well as to obey the physics laws (Raissi et al., 2019).

The objective of the PhD work is to quantify the PINN uncertainties. From a starting initial solution, the network learning leads currently towards a deterministic solution. The stochastic gradient is more general, but a unique solution is determined, without uncertainties. Here, we propose to recast the PINN in a Bayesian context to derive a posterior probability.

The applications are related to seismic imaging. The traditional approach (without Machine Learning) is Full Waveform Inversion (Chauris, 2019). The Bayesian approach is here pertinent, as Full Waveform Inversion may easily converge towards a local minimum with the deterministic approaches. The objective is to demonstrate on synthetic and real data sets how the PINN strategy could avoid these local minima and to obtain the posterior probability density functions for different parameters (velocity, density) influencing the wave propagation.

References

Chauris, H. (2019). Full Waveform Inversion, in Seismic Imaging, a practical approach, J-L. Mari and M. Mendes (Eds.), EDP Sciences, chapter 5, 23 p., ISBN (ebook): 978-2-7598-2351-2, doi:10.1051/978-2-7598-2351-2.c007

Raissi, M., P. Perdikaris, G.E. Karniadakis (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707

Contact and location

Pr. Hervé Chauris

Email: herve.chauris@mines-paristech.fr

Tel.: +33 (0)1 64 69 49 13

MINES ParisTech - PSL Research University

Centre de Géosciences

35 rue Saint-Honoré

77305 Fontainebleau Cedex, France

More Information

Benefits

Experience in Machine Learning, with geophysical applications. Coupling between Machine Learning and physics-based approaches.

Eligibility criteria

The project is co-funded by AI4Sciences (Artificial Intelligence for the Sciences, https://psl.eu/en/recherche/grands-projets-de-recherche/projets-europeen...). There are no requirements based on nationality or age, but applicants should not have lived or carried out their main activity (work, studies, etc.) in France for more than 12 months in the last 3 years

Selection process

How to apply?

 

Please send the following documents for the 31st of May, 2021, to herve.chauris@mines-paristech.fr

• Resume

• Motivation letter

• Reference letters or the names of 1 or 2 referees

• If possible, a copy of a research report (e.g. Master report)

Offer Requirements

Skills/Qualifications

Requirements for applicants

The PhD student should have a strong background in maths and physics, as well as good capabilities in scientific programming. He/she should be interested in geophysical applications.

Specific Requirements

The project is co-funded by AI4Sciences (Artificial Intelligence for the Sciences, https://psl.eu/en/recherche/grands-projets-de-recherche/projets-europeen...). There are no requirements based on nationality or age, but applicants should not have lived or carried out their main activity (work, studies, etc.) in France for more than 12 months in the last 3 years

Work location(s)
1 position(s) available at
Ecole Nationale Supérieure des Mines de Paris (MINES ParisTech)
France
Fontainebleau
77300
35, rue Saint-Honore

EURAXESS offer ID: 615472

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