Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations
This addresses the challenge of efficiently modeling PDEs on variable geometries for applications like aerodynamics and structural analysis, representing an incremental improvement over existing neural operator and neural field methods.
The paper tackles the problem of predicting steady-state PDEs with geometric variability by introducing enf2enf, a neural field approach that encodes geometries into local latent features. The method achieves competitive or superior performance on aerodynamic and structural benchmarks compared to existing methods, with real-time inference and efficient scaling to high-resolution meshes.
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.