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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2504.18591 |
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| _version_ | 1866912607018942464 |
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| author | Catalani, Giovanni Bauerheim, Michael Tost, Frédéric Bertrand, Xavier Morlier, Joseph |
| author_facet | Catalani, Giovanni Bauerheim, Michael Tost, Frédéric Bertrand, Xavier Morlier, Joseph |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations Catalani, Giovanni Bauerheim, Michael Tost, Frédéric Bertrand, Xavier Morlier, Joseph Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition 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. |
| title | Geometry aware inference of steady state PDEs using Equivariant Neural Fields representations |
| topic | Machine Learning Artificial Intelligence Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2504.18591 |