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MNO: Multiscale Neural Operator for Computational Fluid Dynamics with 3D Point Cloud Data

Qinxuan Wang, Chuang Wang, Mingyu Zhang, Jingwei Sun, Peipei Yang, Shuo Tang, Shiming Xiang

TL;DR

MNO introduces a multiscale neural operator for CFD on unstructured 3D point clouds by combining global dimension-shrinkage, local graph, and micro point-wise attention within a mesh-free encoder–decoder framework. The three-scale blocks enable simultaneous capture of long-range dependencies, neighborhood interactions, and high-frequency details, leading to robust accuracy improvements across four challenging 3D CFD benchmarks with up to 300K points. Ablation and visualization confirm the complementary roles of the three modules and highlight the practical benefits of explicit multiscale design for irregular geometries. Overall, MNO provides a scalable, high-precision approach for learning complex fluid dynamics directly from unstructured data, with potential impact on real-time CFD design and analysis.

Abstract

Neural operators have emerged as a powerful data-driven paradigm for solving Partial Differential Equations (PDEs), offering orders-of-magnitude acceleration over traditional solvers. However, existing approaches still suffer from limited accuracy and scalability, particularly on irregular domains where fluid flows exhibit rich multiscale structures. In this work, we introduce the Multiscale Neural Operator (MNO), a new architecture for Computational Fluid Dynamics (CFD) on three-dimensional (3D) unstructured point clouds. MNO explicitly decomposes information across three scales: a global dimension-shrinkage attention module for long-range dependencies, a local graph attention module for neighborhood-level interactions, and a micro point-wise attention module for fine-grained details. This design preserves multiscale inductive biases while remaining computationally efficient. We evaluate MNO on four diverse benchmarks, covering both steady-state and unsteady flow scenarios with up to 300K points. Across all tasks, MNO consistently outperforms state-of-the-art baselines, reducing prediction errors by 5% to 40% and demonstrating improved robustness in challenging 3D CFD problems. Our results highlight the importance of explicit multiscale design for neural operators and establish MNO as a scalable framework for learning complex fluid dynamics on irregular domains.

MNO: Multiscale Neural Operator for Computational Fluid Dynamics with 3D Point Cloud Data

TL;DR

MNO introduces a multiscale neural operator for CFD on unstructured 3D point clouds by combining global dimension-shrinkage, local graph, and micro point-wise attention within a mesh-free encoder–decoder framework. The three-scale blocks enable simultaneous capture of long-range dependencies, neighborhood interactions, and high-frequency details, leading to robust accuracy improvements across four challenging 3D CFD benchmarks with up to 300K points. Ablation and visualization confirm the complementary roles of the three modules and highlight the practical benefits of explicit multiscale design for irregular geometries. Overall, MNO provides a scalable, high-precision approach for learning complex fluid dynamics directly from unstructured data, with potential impact on real-time CFD design and analysis.

Abstract

Neural operators have emerged as a powerful data-driven paradigm for solving Partial Differential Equations (PDEs), offering orders-of-magnitude acceleration over traditional solvers. However, existing approaches still suffer from limited accuracy and scalability, particularly on irregular domains where fluid flows exhibit rich multiscale structures. In this work, we introduce the Multiscale Neural Operator (MNO), a new architecture for Computational Fluid Dynamics (CFD) on three-dimensional (3D) unstructured point clouds. MNO explicitly decomposes information across three scales: a global dimension-shrinkage attention module for long-range dependencies, a local graph attention module for neighborhood-level interactions, and a micro point-wise attention module for fine-grained details. This design preserves multiscale inductive biases while remaining computationally efficient. We evaluate MNO on four diverse benchmarks, covering both steady-state and unsteady flow scenarios with up to 300K points. Across all tasks, MNO consistently outperforms state-of-the-art baselines, reducing prediction errors by 5% to 40% and demonstrating improved robustness in challenging 3D CFD problems. Our results highlight the importance of explicit multiscale design for neural operators and establish MNO as a scalable framework for learning complex fluid dynamics on irregular domains.
Paper Structure (27 sections, 7 equations, 6 figures, 5 tables)

This paper contains 27 sections, 7 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Physics-Informed Neural Networks
  4. Neural Operators
  5. Regular Domain Neural Operators
  6. Irregular Domain Neural Operators
  7. Multiscale Neural Operators
  8. Method
  9. Overview of the MNO model
  10. Global Dimension-Shrinkage Attention Module
  11. Local Graph Attention Module
  12. Micro Point-wise Attention Module
  13. Remarks on other multiscale models
  14. Experiments
  15. Benchmarks
  16. ...and 12 more sections

Figures (6)

  • Figure 1: (a) The overview of the proposed MNO model with a sequence of three-scale blocks, and (b) each block combines three complementary, parallel modules: (c) a global dimension-shrinkage attention module for long-range dependencies, (d) a local graph attention module for neighborhood-level interactions, and (e) a micro point-wise attention module for fine-grained details.
  • Figure 2: The visualization of Global, Local and Micro Attention modules. The red circle serves as a reference for areas with obvious differences. Rows show the error maps for different benchmarks. For each row: (a) ShapeNet Car. The arrow represents the direction of the wind, and the color denotes the prediction error; (b) Ahmed body; (c) DrivAerNet++; (d) Parachute. For each column: (first column) prediction of only Global Attention module; (second column) prediction of Global and Local Attention modules together; (third column) identical values to the second column but with a different color scale; (fourth column) prediction of the full MNO with Global, Local, and Micro Attention modules together.
  • Figure 3: The display of prediction results on ShapeNet Car dataset. The pred represents the predicted velocity and pressure fields, the true denotes the ground truth, and the error stands for the absolute error of the prediction fluid fields. The arrows represent the wind direction, and the color of arrows denotes the magnitude of wind speed.
  • Figure 4: The display of prediction results on DrivAerNet++ dataset. The pred represents the predicted pressure fields, the true denotes the ground truth, and the error stands for the absolute error of the prediction fluid fields.
  • Figure 5: The display of prediction results on Ahmed body dataset. The pred represents the predicted pressure fields, the true denotes the ground truth, and the error stands for the absolute error of the prediction fluid fields.
  • ...and 1 more figures