Geometry-Informed Neural Operator Transformer

2025-04-28

AI Summary

Solving partial differential equations (PDEs) on arbitrary geometries via traditional forward simulation incurs high computational cost due to repeated numerical evaluation. Method: We propose a point-cloud-geometry-aware neural operator surrogate model. For the first time, we integrate Transformers into the neural operator framework, designing a geometry-aware sampling-grouping-attention encoding mechanism that yields order-invariant and density-robust representations of 2D/3D surface point clouds. We further introduce joint geometric-query attention decoding to ensure geometric invariance and generalization. Contribution/Results: Extensive experiments on diverse complex-geometry datasets demonstrate significant improvements in prediction accuracy and cross-geometry generalization—especially on unseen topologies. Our approach establishes a scalable, geometry-adaptive paradigm for high-dimensional PDE surrogate modeling, overcoming limitations of mesh-dependent methods and enabling efficient learning directly from unstructured geometric data.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT

Abstract

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations. This work introduces the Geometry-Informed Neural Operator Transformer (GINOT), which integrates the transformer architecture with the neural operator framework to enable forward predictions for arbitrary geometries. GINOT encodes the surface points cloud of a geometry using a sampling and grouping mechanism combined with an attention mechanism, ensuring invariance to point order and padding while maintaining robustness to variations in point density. The geometry information is seamlessly integrated with query points in the solution decoder through the attention mechanism. The performance of GINOT is validated on multiple challenging datasets, showcasing its high accuracy and strong generalization capabilities for complex and arbitrary 2D and 3D geometries.

Problem

• Develops Geometry-Informed Neural Operator Transformer for PDEs
• Enables forward predictions for arbitrary geometries efficiently
• Ensures robustness to point density and order variations

Innovation

• Transformer architecture with neural operator framework
• Surface points cloud encoding via attention mechanism
• Robust handling of arbitrary 2D/3D geometries