Geometry Aware Inference of Steady State PDEs Using Equivariant Neural Field Representations

Giovanni Catalani, Xavier BERTRAND, Frédéric TOST, Michael BAUERHEIM, Joseph Morlier

Additional Submission Instructions: For the camera-ready version, please include the author names and affiliations, funding disclosures, and acknowledgements.

Track: Track 1: Original Research/Position/Education/Attention Track

Keywords: Partial Differential Equations, Operator Learning, Computational Fluid Dynamics, Neural Fields

Abstract:

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.

Submission Number: 74