About the Center or Functional Department
Inria is the French National Institute for Research in Digital Science, of which the Inria Côte d'Azur University Center is a part. With strong expertise in computer science and applied mathematics, the research projects of the Inria Côte d'Azur University Center cover all aspects of digital science and technology and generate innovation. Based mainly in Sophia Antipolis, but also in Nice and Montpellier, it brings together 47 research teams and nine support services. It is active in the fields of artificial intelligence, data science, IT system security, robotics, network engineering, natural risk prevention, ecological transition, digital biology, computational neuroscience, health data, and more. The Inria Center at Université Côte d'Azur is a major player in terms of scientific excellence, thanks to the results it has achieved and its collaborations at both European and international level.
Context and Advantages of the Position
Every year Inria International Relations Department has a few postdoctoral positions in order to support Inria international collaborations.
This postdoctoral position is opening within the framework of the associate team GEM3 between the IPES research team (http://ipes.lncc.br/) at LNCC/Brazil and the Galets Project Team at the Inria Center at Université Côte d'Azur.
The team is focused on the development and analysis of multiscale numerical methods for elliptic and parabolic partial differential equations (PDEs) arising in surface and subsurface geophysics, and ranging, in terms of applications, from modeling floods in realistic urban environments to subsurface CO2 storage and induced seismicity modeling. Those applications are characterized by their geometrical complexity and strong nonlinear couplings. This motivates our focus on multiscale discretization methods, with a particular emphasis on the treatment of nonlinear problems.
The postdoctoral contract will have a duration of 12 months, and could be extended up to 24 months. The default start date is November 1st, 2026 and not later than January, 1st 2027. The postdoctoral fellow will be recruted by the Inria center at Université Côte d'Azur France but will be jointly supervised by French and Brazilian members of GEM3 team and will be expected to carry out multiple research visits to Brazil.
Mission Assigned
Unlike the traditional finite element method, which relies on an explicitly given approximation space (typically piecewise polynomial), in multiscale numerical methods the approximation space is driven numerically by the PDE model, incorporating fine-scale details of the domain geometry and coefficient distribution. The multiscale methods developed by the associate team can be interpreted as approximate substructuring techniques, where the interiors of macro-cells are eliminated through a low-dimensional parametrization of either Neumann data (as in MHM [1,3]) or Dirichlet data (as in Trefftz methods [2]). Since the computation of the approximation basis is local to the coarse cells, multiscale numerical methods are highly parallelizable, which allows them to benefit from increasing computational facilities while keeping communications very low. Alternatively, multiscale basis functions can be “learned” using machine learning techniques, which makes multiscale methods even more accessible.
The research program of this postdoctoral position will focus on error analysis of multiscale numerical discretization methods for nonlinear problems, and their integration with domain decomposition and scientific machine learning approaches. In terms of applications, the research program aims to go beyond simplified academic examples and address problems such as subsurface multiphase flow and contact mechanics.
- Araya, R., Harder, C., Paredes, D., & Valentin, F. (2013). Multiscale hybrid-mixed method. SIAM Journal on Numerical Analysis, 51(6), 3505-3531.
- Boutilier, M., Brenner, K., & Dolean, V. (2024). Robust methods for multiscale coarse approximations of diffusion models in perforated domains. Applied Numerical Mathematics, 201, 561-578.
- Gomes, A. T. A., Pereira, W. S., & Valentin, F. (2023). The MHM method for linear elasticity on polytopal meshes. IMA Journal of Numerical Analysis, 43(4), 2265-2298.
Main Activities
- Conduct bibliographical reviews.
- Perform theoretical analysis of multiscale and domain decomposition methods.
- Implement multiscale and domain decomposition methods within an existing parallel framework.
- Design novel techniques combining scientific machine learning and multiscale numerical methods.
- Write and publish research articles.
Benefits
- Subsidized meals
- Partial reimbursement of public transport costs
- Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
- Possibility of teleworking and flexible organization of working hours
- Professional equipment available (videoconferencing, loan of computer equipment, etc.)
- Social, cultural and sports events and activities
- Access to vocational training
- Contribution to mutual insurance (subject to conditions)
Compensation
- Contract duration: 12 months, could be extended to 24 months
- Remuneration: 2 927 gross/month
Application process
Apply before June 7th 2026 on https://jobs.inria.fr/public/classic/fr/offres/2026-10033
Submit the following documents:
- Detailed CV with a description of the PhD and a complete list of publications with the two most significant ones highlighted
- Motivation letter
- 2 letters of recommendation
