This Project has received funding from the EU’s Horizon Europe research and innovation programme under the Marie Sklodowska-Curie GA No 101119556.

Ph.D. position at the AGH University of Krakow (AGH, Poland)
for the IN-DEEP European Doctoral Network

Real-time inversion using self-explainable Deep Learning driven by expert knowledge


Reference number: DC8

PhD research topic:  Fast certified graph neural networks for parametric PDEs modelling flow-simulation in porous-fractured geological formations.

Host institution: AGH University of Krakow (AGH), Krakow, Poland

PhD Enrolment: AGH University of Krakow (AGH), Krakow, Poland

Main Supervisor: Maciej Paszynski, AGH University of Krakow,

Co-supervisor: Sergio Gil López, Tecnalia, Bilbao, Spain,

Scientific tasks:

  1. Design fast numerical methods to generate reliable synthetic datasets for training Deep parametric PDE solvers.
  2. Develop explainable Graph Neural Networks architectures for parametric problems arising in flow simulation in porous fractured structures for geothermal applications.
  3. Apply the proposed method to identify the geological structures in a potential basin for underground H2 or CO2


For more information on the IN-DEEP Doctoral Network, please visit


Expected outcomes:

  1. A novel explainable Graph Neural Network method for parametric PDEs.
  2. Model flow simulation in porous fractured structures.
  3. Solve a benchmark problem to identify a subsurface region adequate for underground gas storage.
  4. 2+ peer-reviewed publications
  5. 2+ participation in relevant international conferences


Eligibility Criteria:

  • Mobility: At the time of recruitment, the researcher must not have resided or carried out his/her main activity (work, studies, etc.) in Poland for more than 12 months in the 36 months immediately before the recruitment date. Time spent as part of a procedure for obtaining refugee status under the Geneva Convention or compulsory national service are not taken into account.
  • The candidate must be at the date of recruitment a doctoral candidate (e. not already in possession of doctoral degree). Researchers who have successfully defended their doctoral thesis but who have not yet formally been awarded the doctoral degree will not be considered eligible.
  • The candidate must agree to work exclusively for the action.

Specific requirements:

  • Master degree in Science, Engineering, or any other related fields
  • Studies that grant access to a Ph.D. Program by September 1st, 2024.
  • Programming skills: Previous experience programming in scientific computing.
  • Language: Excellent command of English, together with good academic writing and presentation skills.

Preferred skills:

  • Familiar with neural networks and deep learning algorithms
  • Experience with numerical methods for partial differential equations
  • Able to work independently and flexibly, taking initiative where required
  • Able to communicate and collaborate effectively in a team setting

Contract: Full-time contract

Duration: 36 months, including 2 secondments at other consortium members’ premises

Estimated starting date: September 1st, 2024 at the latest


Terms and conditions of employment and pay according to the current Law with doctoral network measures under the Program HORIZON-MSCA-2022-DN-01. The gross salary amounts to €28,764 (estimated with all costs) per year. The candidate will also receive a mobility allowance of €600 euro per month, and, where applicable, a family allowance of €495 per month and a special needs allowance.

Evaluation criteria:

  • Step 1: Verification of fulfillment of formal - mandatory criteria specified in the MSCA program
  • Step 2:
    • Academic performance during the undergraduate studies - 20 points
    • Research experience in the area of the call, including publications, projects, and internships - 10 points
    • Awards, honors, other significant roles and achievements as a student - 5 points
    • Additional coursework, certifications, training programs, continuous learning - 5 points
    • Letters of recommendation – 10 points
  • Step 2: Only for those scoring 35 or above in step 1:
    • Interview to assess scientific requirements, the communication skills, initiative, critical thinking, and motivation to pursue a PhD on the topic of the call - 50 points.

In case of candidates achieving equal scores, priority will be given to female applicants.

Deadline: April 20th, 2024

Application: Please send an email to with:
- application, CV, personal questionnaire (to be obtained from AGH at your request),
- document confirming the knowledge of the language at the level of at least B-2, in case of lack of documented knowledge of English it will be necessary to take an exam confirming the required level in the Foreign Language Department of AGH.
- a copy of diplomas or other certificates confirming qualifications held
- a letter of motivation containing a brief summary of scientific results achieved so far and motivation to work in the IN-DEEP project
- addresses of two persons who, at the request of AGH, agree to send letters of recommendation.

Women are encouraged to apply!

One person, one value.




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