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The Jean Lamour Institute and the Elie Cartan Institute of the University of Lorraine in Nancy, France invite applications for a 24-month post-doctoral fellowship on the Numerical approximation of phase-field models in metallurgy using Physics Informed Neural Networks (PINNs).

Phase transformations occur, for example, during the additive manufacturing (3D printing) of a metal part. First, the molten liquid metal transforms to a crystalline solid structure and then further phase transformation occur in solid state. The properties of the part depend on the final phases, their size and shape.

Phase-field models that describe phase transformations in materials are formulated by reaction- diffusion partial differential equations (PDEs). In liquid-solid phase transformations they are also coupled to diffusive and convective nonlinear equations that describe the transport of heat and/or chemical species.

Today, PDEs are generally solved with classical discretization methods. Recently emerged artificial intelligence methods for the approximation of solutions of PDEs promise to be faster and could therefore trigger a paradigm shift in modeling of phase transformations. PINNs (Karniadakis et al., Nature Reviews Physics 3 (2021), 422) are one of the most promising methods.

A first objective of the project is to establish PINNs for the approximation of metallurgical phase transformation models. A second objective is to combine the PINNs with the observer theory. Observers allow us to approximate the full state of the system from a partial observation. Thus they could enable PINN training on partial training data. The numerical implementation will be complemented by a theoretical analysis of the underlying observer theory.
The funding is open to excellent researchers from applied mathematics, control engineering, materials science, heat & mass transfer or other disciplines.


  • PhD in a relevant discipline.
  • Expertise in the field of partial differential equations (PDEs).
  • A strong background in numerical approximations of PDEs or control theory will be an asset.
  • Good computer programming skills.
  • Excellent capacity for teamwork and ability to work in a multidisciplinary environment.
  • Proficiency in English.


This two-year LUE (Lorraine University of Excellence) fellowship will be based at the Institut Élie Cartan and the Institut Jean Lamour. The duration cannot exceed 24 months.
The target start date for the position is October 1st, 2023, with some flexibility on the exact start date.


Nancy, Lorraine, France


Candidates should submit the following documents.

  • Full CV and list of publications
  • Cover letter
  • Statement of research
  • Contact information for two references

The position is open until filled. Eligible applicants will be interviewed by an ad hoc committee after receipt of the application.

Applications are only accepted through email. All documents must be sent to:
Ludovick Gagnon,
Miha Založnik,
Benoît Appolaire,