PGD-NO: A Neural Operator with Precomputed Geometry Decomposition for 3D Million-Scale Physics Simulations

While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the "singlenode bottleneck," where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit. To address these challenges, we propose PGD-NO, a neural operator with Precomputed Geometry Decomposition, that relocates the computational overhead of geometric encoding to a deterministic pre-computation phase. By utilizing an iterative geometry decomposition algorithm to extract "geometry tokens," our model decouples feature extraction from solution querying. This architecture enables linear memory scalability, allowing high-fidelity learning on meshes exceeding 10 million nodes-a scale where existing architectures typically encounter memory exhaustion. PGD-NO demonstrates competitive predictive accuracy across diverse industrial benchmarks and provides intrinsic interpretability through attention mechanisms. By effectively overcoming traditional mesh-size constraints, PGD-NO offers a robust and efficient solution for the next generation of large-scale, high-fidelity industrial design applications. Our codes and datasets are available at https://github.com/WeihengZ/PGD-NO .