Seeing Near and Far: A Neural Operator That Efficiently Tokenizes and Decodes on Industrial-Scale CFD Meshes

Industrial-scale computational fluid dynamics (CFD) simulations typically require more than a million mesh points to fully capture complex nonlinear physics. Consequently, recent efforts have focused on designing neural operators that can handle such large, complex meshes without sacrificing speed or accuracy. Approaches that aggregate only local information during tokenization and decoding are highly compute-efficient, especially as meshes grow larger. However, on 3D industrial-scale benchmarks, they are currently outperformed by models that retain global information through pointwise computation across the entire domain. We hypothesize that this performance gap is partly attributable to a mismatch between latent-point allocation and spatially varying reconstruction demands, and propose the use of a KD-tree algorithm for more efficient allocation. To further generalize this idea, we propose the Importance-Balanced Operator (IBO), which integrates an importance measure into the KD-tree algorithm to distribute latent points more effectively, substantially closing this performance gap while retaining computational efficiency. In our experiments, IBO achieves the best performance across multiple metrics on 2D single- and multi-airfoil aerodynamic problems. Crucially, on large-scale 3D datasets involving automotive aerodynamics (DrivAerML) and urban aerodynamics (the newly introduced UrbanWind dataset), IBO matches or outperforms state-of-the-art models across nearly all field metrics while requiring 5–40× fewer FLOPs per case, thereby establishing a new accuracy–compute Pareto frontier for learning industrial-scale CFD.