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 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.

Attention to Detail: Fine-Scale Feature Preservation-Oriented Geometric Pre-training for AI-Driven Surrogate Modeling

AI-driven surrogate modeling has become an increasingly effective alternative to physics-based simulations for 3D design, analysis, and manufacturing. These models leverage data-driven methods to predict physical quantities traditionally requiring computationally expensive simulations. However, the scarcity of labeled CAD-to-simulation datasets has driven recent advancements in self-supervised and foundation models, where geometric representation learning is performed offline and later fine-tuned for specific downstream tasks. While these approaches have shown promise, their effectiveness is limited in applications requiring fine-scale geometric detail preservation. This work introduces a self-supervised geometric representation learning method designed to capture fine-scale geometric features from non-parametric 3D models. Unlike traditional end-to-end surrogate models, this approach decouples geometric feature extraction from downstream physics tasks, learning a latent space embedding guided by geometric reconstruction losses. Key elements include the essential use of near-zero level sampling and the innovative batch-adaptive attention-weighted loss function, which enhance the encoding of intricate design features. The proposed method is validated through case studies in structural mechanics, demonstrating strong performance in capturing design features and enabling accurate few-shot physics predictions. Comparisons with traditional parametric surrogate modeling highlight its potential to bridge the gap between geometric and physics-based representations, providing an effective solution for surrogate modeling in data-scarce scenarios.