CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes
Abstract
High-fidelity Reynolds-averaged Navier--Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured mesh is computationally expensive, making many-query tasks such as design exploration, optimization, and multi-condition evaluation costly. Neural operators provide mesh-flexible surrogates for mapping geometry and operating conditions to flow fields; however, in many existing architectures, global parameters such as the freestream state and design variables are concatenated with pointwise inputs, leaving their influence on intermediate features implicit. This paper proposes CoPiT, a \textbf{Co}nditional \textbf{P}osition-induced \textbf{T}ransformer that builds on the Position-induced Transformer (PiT) as its geometric backbone and injects a global condition vector through multi-stage feature-wise linear modulation (FiLM), thereby making parametric modulation explicit while preserving geometry-based attention weights. The model is evaluated on two-dimensional AirfRANS airfoil fields, including scarce-data and extrapolation regimes, and on three-dimensional BlendedNet++ blended-wing-body surfaces. On the AirfRANS full-data test set, CoPiT reduces surface and volume losses by approximately 54\% and 24\% relative to Transolver, respectively, and achieves the lowest overall normalized test MSE among the compared baselines on BlendedNet++. Matched ablations show that FiLM conditioning generally improves upon input concatenation, while the preferred placement is task-dependent. CoPiT thus provides a practical operator-learning surrogate for parametric aerodynamics on unstructured meshes.
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BibTeX
@misc{chen2026copit,
title = {{CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes}},
author = {Junfeng Chen and Yongchen Fan and Zhonghua Qiao and Kailiang Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32299},
eprint = {2610.32299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32299},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - CoPiT: A conditional Position-induced Transformer for aerodynamic field prediction on unstructured meshes
AU - Junfeng Chen
AU - Yongchen Fan
AU - Zhonghua Qiao
AU - Kailiang Wu
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32299
UR - https://arxiv.org/abs/2610.32299
AB - High-fidelity Reynolds-averaged Navier--Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured mesh is computationally expensive, making many-query tasks such as design exploration, optimization, and multi-condition evaluation costly. Neural operators provide mesh-flexible surrogates for mapping geometry and operating conditions to flow fields; however, in many existing architectures, global parameters such as the freestream state and design variables are concatenated with pointwise inputs, leaving their influence on intermediate features implicit. This paper proposes CoPiT, a \textbf{Co}nditional \textbf{P}osition-induced \textbf{T}ransformer that builds on the Position-induced Transformer (PiT) as its geometric backbone and injects a global condition vector through multi-stage feature-wise linear modulation (FiLM), thereby making parametric modulation explicit while preserving geometry-based attention weights. The model is evaluated on two-dimensional AirfRANS airfoil fields, including scarce-data and extrapolation regimes, and on three-dimensional BlendedNet++ blended-wing-body surfaces. On the AirfRANS full-data test set, CoPiT reduces surface and volume losses by approximately 54\% and 24\% relative to Transolver, respectively, and achieves the lowest overall normalized test MSE among the compared baselines on BlendedNet++. Matched ablations show that FiLM conditioning generally improves upon input concatenation, while the preferred placement is task-dependent. CoPiT thus provides a practical operator-learning surrogate for parametric aerodynamics on unstructured meshes.
ER -