PhD position Mathematics of Neural Networks & Operators for PDEs

Project description The PhD project involves the design and analysis of neural operator surrogates for linear and nonlinear partial differential equations. The PhD candidate will work both on the theoretical aspects and on the implementa- tion of the neural architectures introduced. They will investigate the role of neural net- works and operators for preconditioning, eigenvalue problems, etc. by combining tech- niques from numerical analysis, approximation theory, machine learning, and the analysis of PDEs. Candidate profile We are looking for a highly motivated candidate with: - A Master’s degree in Mathematics or a closely related field. - A strong background in numerical analysis and PDEs - Interest in the mathematics of machine learning - Programming experience; knowledge of python and frameworks such as pytorch/- JAX is a plus How to apply Interested candidates should send the following documents: - CV (including contact details of references) - academic transcripts - a concise statement describing interest and relevant experience Applications and informal inquiries can be sent to꞉ Prof. Carlo Marcati ( a carlo.marcati@univ‐lyon1.fr) Important dates - Starting date: between October and December 2026 - Application deadline: June 15, 2026