NeuralFEM Workshop 2026

The workshop is the first meeting of the NeuralFEM project, a MATH-AmSud collaboration between Uruguay, Colombia, Chile and France. It concerns the certified approximation of partial differential equations by neural networks. It gathers mathematicians working on the following topics:

• Neural network methods for nonlinear and non-smooth problems and hybrid schemes combining them with finite elements. Some expected mathematical applications include variational inequalities from contact and plasticity or fractional operators modelling anomalous diffusion.
• A priori error analysis of the network approximation: what are the best function spaces, how many neurons does a given accuracy cost, how to make the optimization algorithms converge towards a meaningful solution?
• A posteriori error estimation and adaptive strategies: similarly to finite elements, how can we adapt the certify the network approximation, and how can we use the error estimates to drive the optimization of the network?
• Reduced basis methods, as the competing approach against which the networks are measured.
• The applications in biomechanics and biomedicine are expected to include tissue compression, stent–artery interaction, or anomalous diffusion in biological tissue.

The workshop is open to anyone working on these questions. Registration is free but mandatory, before 30 October 2026.

Local organising committee

• Michel Duprez, Inria, MIMESIS team, Strasbourg
• Pablo Alvarez, Inria, MIMESIS team, Strasbourg
• Stéphane Cotin, Inria, MIMESIS team, Strasbourg
• Raphaël Bulle, Inria, MIMESIS team, Strasbourg
• Emmanuel Franck, Inria, MACARON team, IRMA, Strasbourg
• Victor Michel-Dansac, Inria, MACARON team, IRMA, Strasbourg
• Laurent Navoret, IRMA, Université de Strasbourg, and Inria
• Vanessa Lleras, IMAG, Université de Montpellier
• Vincent Vigon, IRMA, Université de Strasbourg, and Inria

Scientific committee

• Michel Duprez, Inria, MIMESIS team, Strasbourg, France (international coordinator)
• Franz Chouly, Universidad de la República, Montevideo, Uruguay
• Manuela Bastidas, Universidad Nacional de Colombia, Medellín, Colombia
• Rodolfo Araya, Universidad de Concepción, Chile
• Virginie Ehrlacher, CERMICS, École nationale des Ponts et Chaussées, France

Contact

If you have questions about the workshop, please send an email to neuralfem-workshop@inria.fr.