The Human Resources Strategy for Researchers
Marie Skłodowska-Curie Actions

PhD position 07 – MSCA COFUND, AI4theSciences (PSL, France) - “Physics-Informed Machine Learning in the context of seismic imaging”

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    Université PSL
    First Stage Researcher (R1)
    26/02/2021 23:00 - Europe/Brussels
    France › Fontainebleau
    H2020 / Marie Skłodowska-Curie Actions COFUND


“Artificial intelligence for the Sciences” (AI4theSciences) is an innovative, interdisciplinary and intersectoral PhD programme, led by Université Paris Sciences et Lettres (PSL) and co-funded by the European Commission. Supported by the European innovation and research programme Horizon 2020- Marie Sklodowska-Curie Actions, AI4theSciences is uniquely shaped to train a new generation of researchers at the highest academic level in their main discipline (Physics, Engineering, Biology, Human and Social Sciences) and master the latest technologies in Artificial Intelligence and Machine Learning which apply in their own field.

26 doctoral students will join the PSL university's doctoral schools in 2 academic cohorts to carry out work on subjects suggested and defined by PSL's scientific community. The 2020 call will offer up to 15 PhD positions on 24 PhD research projects. The candidates will be recruited through HR processes of high standard, based on transparency, equal opportunities and excellence.


Description of the PhD subject: “Physics-Informed Machine Learning in the context of seismic imaging”


Context - Motivation

Within the MINDS project (Mines Initiative for Numerics and Data Science) developed at Mines Paris - PSL, the objective is to fill the gap between Machine Learning and Physics-based approaches. Machine Learning is growing very rapidly. After a possible learning step, the objective is to let the data speak. These approaches tend to forget the more traditional physics-based approaches. The objective of the work is to develop, in the context of seismic imaging, an intermediate approach to preserve the physics [1]. Currently, the main contributions of Machine Learning to seismic processing are related to pre-processing steps (de-noising, picking, ...) but not really yet to the imaging part (determining the Earth's properties from surface measurements, a highly non-linear problem). The explicit introduction of physics within Machine Learning should fill this gap.If successful, the project will have a large impact in the way industrial companies handle seismic data.

In 2019, Raissi et al., demonstrated how it is possible to combine Machine Learning approaches with more traditional physics approaches (Physics-Informed Neural Networks, PINN) [3]. The applications are related to the resolution of partial differential equations (i.e. direct problems) as well as to the resolution of inverse problems (determining the main parameters controlling the physical phenomena, for example the wave propagation, from a set of observations). The later approach will be developed here.

On the one hand, deep neural networks are able in theory to describe any functions. Learning is usually a complex task and in physics-related problems, observations are rare and expensive to acquire. On the other hand, Machine Learning does not usually consider physics-based equations, a very useful source of information. As proposed in [3], a modified loss function in the neural networks contains several terms to ensure that the data predict the observations and that the laws of physics are fulfilled. This second term can be seen as a regularisation term, essential in practice to avoid any over-fitting in the case of noisy data. The auto-differentiation (back-propagation of the errors) within the neural networks provides a way to estimate the optimal parameters.This approach is very attractive and will be extended and modified to be applicable in the context of seismic imaging. Seismic acquisition consists of activating a seismic source and of recording acoustic / elastic waves. The objective is to determine seismic velocity wave fields and any other parameters controlling the wave propagation within the sub-surface. In comparison with the first PINN applications, seismic imaging offers some particular aspects to be properly considered:

  • Seismic wave are mainly propagative waves, meaning that the wave field is not smooth. In order to check that the wave field obeys the wave equation, the number of controlling points is a priori much larger than for a diffusive problem with a more regular solution;
  • The traditional loss function in seismic imaging contains a large number of local minima. How does the PINN approach behave? How is it possible to take advantage of the frequency content of the data? In the classical approaches, the model estimation first relies on the low frequencies and then enlarges the frequency spectrum, in order to avoid local minima. How could the neural network benefit from this approach (e.g. a proxi for the modelling part)?
  • Finally, the number of unknowns (number of parameters to be estimated) is potentially very large (thousands or much more, as the parameters depend on the spatial coordinates). In the first articles, only a few values were determined. How to play with the neural network to address this issue? The Generative Adversarial Networks (GAN) could be very useful to determine the optimal parameterisation [2].

Main references:

[1] Chauris, H. (2019). Full Waveform Inversion, inSeismic 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

[2] Goodfellow, I., J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville and Y. Bengio (2014). Generative Adversarial Networks.Proceedings of the International Conference on Neural Information,arXiv:1406.2661

[3] 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


Scientific Objectives, Methodology & Expected results

The objective of the PhD thesis is thus to develop a novel Physics-informed Machine Learning approach in the context of seismic imaging. The validations will be performed on synthetic and real data sets, provided by the industrial company. The company will also co-supervise the work (under a person with “HDR” degree) and propose internship for the application to real data, such that the company can really benefit from the work. As the identified company is international, the real data may come from abroad, with collaboration with local teams. The main academic supervisor has a long experience in seismic imaging and inverse problems. He supervised more than15 PhD students.


International mobility

The candidate is expected to spend around 6 months to work within the company for the application to real data and for the transfer of technology. Summer schools in industrial companies will be highly supported.


Thesis supervision

Hervé Chauris and Elie Hachem



Created in 2012, Université PSL is aiming at developing interdisciplinary training programmes and science projects of excellence within its members. Its 140 laboratories and 2,900 researchers carry out high-level disciplinary research, both fundamental and applied, fostering a strong interdisciplinary approach. The scope of Université PSL covers all areas of knowledge and creation (Sciences, Humanities and Social Science, Engineering, the Arts). Its eleven component schools gather 17,000 students and have won more than 200 ERC. PSL has been ranked 36th in the 2020 Shanghai ranking (ARWU).

More Information


  • Opportunity to conduct academic research in a top 100 university in the world.
  • High-quality doctoral training rewarded by a PhD degree, prepared within Mines Paris - PSL and delivered by PSL.
  • Access to cutting-edge infrastructures for research & innovation.
  • Appointment for a period of 36 months (job contract delivered by the involved component school of PSL) based on a salary of 3100 € gross employer (including employer tax) per month or approximately a 2228 € gross salary per month.
  • Job contract under the French labour legislation in force, respecting health and safety, and social security: 35 hours per week contract, 25 days of annual leave per year (“congés annuels”). Eventual complementary activities may be accepted or proposed by the co-supervisors (maximum of 64h/year for teaching, 32 day/year for specific missions).
  • Short stay(s) or secondment in France or abroad are expected.
  • An international environment supported by the adherence to the European Charter & Code.
  • Access to AI training package, with a strong interdisciplinary focus, together with a Career development Plan.

Eligibility criteria

  • Applicants must have a Master’s degree (or be in the process of obtaining one) or have a University degree equivalent to a European Master’s (5-year duration) to be eligible at the time of the deadline of the relative call.
  • There is no nationality or age criteria, but applicants must not have resided or carried out their main activity (work, studies, etc.) in France for more than 12 months in the 3 years immediately before the deadline of the call (MSCA Mobility rule).
  • Applicants must declare to be available to start the programme on schedule.

For submitting your online application, go to: https://www.psl.eu/recherche/grands-projets-de-recherche/projets-europee...


The online application should contain the following documents:

  • English translated transcripts from the Master’s degree (or equivalent 5-year degree). A copy of the Master’s degree or a certificate of achievement will be required later on for the final registration.
  • International curriculum vitae and a cover letter explaining the reasons that lead him/her to prepare a PhD, why he/she applies to this offer and his/her professional project (guidelines will be given to the applicants in order to help him/her in the writing of his/her letter).
  • Two academic reference letters.
  • A statement duly signed on the mobility rules, availability, and conflicts of interest.


The applicants can only apply to one PhD project among the available ones. Multiple applications of one candidate will automatically make all his/her applications ineligible.

Selection process

The applications will be analysed by the Management Team for eligibility and completeness. Afterwards, the applications will be reviewed by the Selection Committee. In the pre-selection round (March-April 2021), applicants will be rated using a scoring system based on 3 criteria (academic excellence, experience, motivation, and qualities). A shortlist of qualified applicants will be interviewed during the selection round (June 2021) to further assess their qualifications and skills according to the predefined selection criteria.

All information regarding the applications (criteria, composition of the Selection Committee, requirements) can be found on the website of the programme, in greater detail.


The selection and recruitment processes of the PhD student will be in accordance with the European Charter for Researchers and Code of Conduct of the Recruitment of Researchers. The recruitment process will be open, transparent, impartial, equitable, and merit based. There will be no discrimination based on race, gender, sexual orientation, religion of belief, disability, or age.

Additional comments

Centre de Géosciences (Mines Paris - PSL): Located in Fontainebleau, the Geosciences and Geoengineering Department focuses on research and education in the field of Earth and Environmental Science. Research is conducted along three main lines: (1) supply of mineral ressources; (2) underground energy storage and (3) impact of climate changes.This project is in collaboration with the CEMEF (Centre for Materials Processing); a joint unit with CNRS (UMR 7635) and center of Mines Paris - PSL, in particular with the CFL research group working on the coupling of computational mechanics and machine learning.


Mines Paris - PSL is a graduate school (Grande Ecole) in Science, Engineering and Economics under the tutelage of the Ministry of Industry. It provides multidisciplinary education (relying upon around 230 academics) to train high level engineers (150/year in “Master’s degree in science and executive education” track and 200 Advanced Master’s degrees/year) expected to fulfil high responsibilities in government bodies and in the industry in France and abroad. This mission is connected to a very strong research activity closely linked to the industry, that has proved its ability to innovate, anticipate and contribute to the evolutions of the socio-economic world in the fields of risk management, public policies, economics et sustainable development among others.

This long-standing link with the industry has lead Mines Paris - PSL to set up several major collaborations (Research and Education Chairs, Framework agreements…) with leading industrial partners such as SAFRAN, EDF, ArcelorMittal or Total to name a few.


On the academic side, it is a full member of Université PSL and as such participates to a wide number of structuring education and research (both applied and more fundamental) projects, especially with two other Grandes Ecoles (Chimie Paris - PSL and ESPCI - PSL). Mines Paris - PSL is also leader or acting member of several major international academic research programs and projects on its own.

Web site for additional job details

Required Research Experiences

    1 - 4

Offer Requirements

    Geosciences: Master Degree or equivalent
    ENGLISH: Excellent


  • Strong background in Maths and Physics.
  • Clear interest for Machine Learning and for geophysical applications, in particular in the context of seismic imaging.
  • Strong experience in scientific programming.
  • Fluent in English (speaking and writing).

Specific Requirements

  • It is appreciated if the applicant also has some knowledge on high performance computing (HPC).

Work location(s)
1 position(s) available at
Centre de Géosciences, Mines Paris - PSL
35, rue Saint-Honoré

EURAXESS offer ID: 578976


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