NeuralFEM: Optimal and certified NEURAL network predictions thanks to tools coming from Finite Element Methods

Programa AmSud
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AmSud_Abril-2026-14

Math AmSud

Starting year: 2026

Ending year: 2027

Leading institutions:

Project Summary

This project aims at developing new optimized and certified Neural Network (NN) based numerical schemes to model non-smooth biomecanical problems. By integrating classical Finite Element Methods (FEM) techniques into the design and study of NNs, the project seeks to enhance approximation and control error capabilities while preserving key properties such as versatility and rapidity. A central objective is to establish certified optimal approaches-grounded in rigorous a priori and a posteriori error analysis that ensure the reliability and interpretability of the NNs. The research will address both theoretical foundations and practical implementations, targeting benchmark problems where traditional methods struggle, particularly in the presence of high gradients, singularities, or discontinuities.

Team

In France: 

  • Pablo Alvarez, researcher, MIMESIS project-team, Inria Branch‌​‌ at the University of​​ Strasbourg, Inria
  • Raphaël Bulle, postdoctoral researcher, MIMESIS project-team, Inria Branch‌​‌ at the University of​​ Strasbourg, Inria
  • Stéphane Cotin, researcher, MIMESIS project-team, Inria Branch‌​‌ at the University of​​ Strasbourg, Inria
  • Michel Duprez, researcher, NeuralFEM coordinator, MIMESIS project-team, Inria Branch‌​‌ at the University of​​ Strasbourg, Inria
  • Virginie Ehrlacher, researcher, NeuralFEM coordinator, CERMICS
  • Alexandre Ern, researcher, CERMICS
  • Martin Genet, researcher, École Polytechnique, M3DISIM project-team, Inria Saclay Centre, Inria

In Chile: 

  • Jorge Aguayo, researcher, Universidad del Bío-Bío
  • Rodolfo Araya, researcher, NeuralFEM coordinator, Universidad de Concepción
  • Patrick Vega, researcher, Universidad de Santiago

In Uruguay: 

  • Juan Pablo Borthagaray, researcher, Universidad de la República
  • Franz Chouly, researcher, NeuralFEM coordinator, Universidad de la República

In Colombia: 

  • Manuela Bastidas, researcher, NeuralFEM coordinator, Universidad Nacional de Colombia
  • Nicolás Guarín-Zapata, researcher, Universidad EAFIT
  • Diego Alejandro Muñoz Durango, researcher, Universidad Nacional de Colombia

Workshops