Frédéric Tost

Giovanni Catalani, Michael Bauerheim, Frédéric Tost et al.

Advances in neural operators have introduced discretization invariant surrogate models for PDEs on general geometries, yet many approaches struggle to encode local geometric structure and variable domains efficiently. We introduce enf2enf, a neural field approach for predicting steady-state PDEs with geometric variability. Our method encodes geometries into latent features anchored at specific spatial locations, preserving locality throughout the network. These local representations are combined with global parameters and decoded to continuous physical fields, enabling effective modeling of complex shape variations. Experiments on aerodynamic and structural benchmarks demonstrate competitive or superior performance compared to graph-based, neural operator, and recent neural field methods, with real-time inference and efficient scaling to high-resolution meshes.

Giovanni Catalani, Jean Fesquet, Xavier Bertrand et al.

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.