LRQ-Solver: A Transformer-Based Neural Operator for Fast and Accurate Solving of Large-scale 3D PDEs
Sponsor
This work was supported in part by the Key-Area Research and Development Program of Guangdong Province under Grant 2021B0101190004 and 2021B0101190003, and in part by the National Natural Science Foundation of China under Grant 62472106
Published In
Computer-Aided Design
Document Type
Pre-Print
Publication Date
11-2026
Subjects
Computer-aided design, Aerodynamic drag coefficient, Deep learning, Three-dimensional geometry
Abstract
Solving large-scale PDEs on complex three-dimensional geometries remains a central challenge in scientific and engineering computing, often due to expensive pre-processing stages and high computational overhead. We present Low-Rank Query-based PDE Solver (LRQ-Solver), a physics-integrated deep learning framework for efficient CAE simulations of complex three-dimensional geometries in CAD-driven design analysis. Built upon the Parameter-Conditioned Lagrangian Modeling (PCLM) that embeds physical consistency into the learning process and the Low-Rank Query Attention (LR-QA) module that reduces attention complexity from O(N2) to O(NC2+C3) via covariance decomposition, LRQ-Solver supports multi-configuration analysis within iterative design workflows. On two benchmark datasets, it achieves a 28.6% error reduction on DrivAerNet++ and 28.76% on the 3D Beam dataset, while supporting simulations with 2 million points under a 40 GB memory budget. These results indicate its potential for accelerating PDEs-based CAE tasks, such as aerodynamic drag estimation and structural stress analysis, in computational design pipelines.
Rights
© Copyright the author(s) 2026
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DOI
10.1016/j.cad.2026.104151
Persistent Identifier
https://archives.pdx.edu/ds/psu/45110
Citation Details
Published as: Zeng, P., Wang, G., Gu, H., Hu, X., Gao, T., Wang, Z., ... & Song, X. (2026). LRQ-Solver: A transformer-based neural operator for fast and accurate solving of large-scale 3D PDEs. Computer-Aided Design, 104151.
Description
This is the author’s version of a work that was accepted for publication. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published as: Zeng, P., Wang, G., Gu, H., Hu, X., Gao, T., Wang, Z., ... & Song, X. (2026). LRQ-Solver: A transformer-based neural operator for fast and accurate solving of large-scale 3D PDEs. Computer-Aided Design, 104151.