Large Geometry Models Are Priors For Fast Physics Pretraining
Abstract
Language and vision models became data-efficient by pretraining on plentiful unlabelled data; physical field models have such data, over ten million 3D shapes, but geometry pretraining designs its targets rather than deriving them from the physics. Euler-Lagrange geometry pretraining derives them: for attached flow, a shape enters the flow's Euler-Lagrange equation only through coefficients that distance and normal line (the normal up to sign) fix to first order. Their reconstruction error therefore bounds what a representation loses about any field, and fine-tuning on costly simulations need only assemble the global field. We realise it in AREALS, a masked surface autoencoder whose areal tokens carry position, normal and area, pretrained self-supervised and sign-free on 61,822 raw meshes. Because the operating condition enters only through the far field, sensors can supply it: AREALS completes a hidden field in one forward pass without condition labels. It matches the accuracy of the same architecture trained from scratch with half the simulations on DrivAerML and DrivAerNet++ and about a quarter on WindsorML. On DoubleDelta wings, 20 sensors give 3.9× and 4.0× lower field and force error than GABI, a Bayesian inversion method with a learned prior, and beyond the training angles pretraining halves the error.
Related
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- Quantum field theory and four-manifolds: Perspectives from physics and geometry
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BibTeX
@misc{chlon2026large,
title = {{Large Geometry Models Are Priors For Fast Physics Pretraining}},
author = {Maggie Chlon and Leon Chlon},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02066},
eprint = {2611.02066},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02066},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large Geometry Models Are Priors For Fast Physics Pretraining
AU - Maggie Chlon
AU - Leon Chlon
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02066
UR - https://arxiv.org/abs/2611.02066
AB - Language and vision models became data-efficient by pretraining on plentiful unlabelled data; physical field models have such data, over ten million 3D shapes, but geometry pretraining designs its targets rather than deriving them from the physics. Euler-Lagrange geometry pretraining derives them: for attached flow, a shape enters the flow's Euler-Lagrange equation only through coefficients that distance and normal line (the normal up to sign) fix to first order. Their reconstruction error therefore bounds what a representation loses about any field, and fine-tuning on costly simulations need only assemble the global field. We realise it in AREALS, a masked surface autoencoder whose areal tokens carry position, normal and area, pretrained self-supervised and sign-free on 61,822 raw meshes. Because the operating condition enters only through the far field, sensors can supply it: AREALS completes a hidden field in one forward pass without condition labels. It matches the accuracy of the same architecture trained from scratch with half the simulations on DrivAerML and DrivAerNet++ and about a quarter on WindsorML. On DoubleDelta wings, 20 sensors give 3.9× and 4.0× lower field and force error than GABI, a Bayesian inversion method with a learned prior, and beyond the training angles pretraining halves the error.
ER -