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This paper introduces PGD-NO, a neural operator that utilizes Precomputed Geometry Decomposition to alleviate the memory limitations of existing neural PDE solvers in 3D physics simulations. By shifting the computational burden of geometric encoding to a pre-computation phase, PGD-NO achieves linear memory scalability, enabling it to handle meshes with over 10 million nodes without running into memory exhaustion. The architecture not only maintains competitive predictive accuracy across various industrial benchmarks but also enhances interpretability through attention mechanisms, making it a promising tool for large-scale industrial design applications.
PGD-NO breaks the memory barrier for neural PDE solvers, enabling high-fidelity simulations on meshes with over 10 million nodes.
While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node 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.
