MNO通过多尺度设计提升3D流体模拟精度与效率
MNO: Multiscale Neural Operator for 3D Computational Fluid Dynamics
- 分三层处理长程、局部和细微结构，显式建模多尺度特性
- 在含30万点的不规则网格上，误差降低5%至50%
- 适合需要高精度3D流体模拟的研究者或工业应用
神经算子作为求解偏微分方程的数据驱动范式已崭露头角，但在不规则域上其精度与可扩展性仍受限，尤其面对具有丰富多尺度结构的流体流动。本文提出多尺度神经算子（MNO），用于3D非结构化点云上的计算流体力学。MNO 显式分解信息为三个尺度：全局维度压缩注意力模块捕捉长程依赖，局部图注意力模块建模邻域交互，微粒点注意力模块保留细粒度特征。该设计在保持多尺度归纳偏置的同时实现高效计算。我们在多种基准上评估MNO，涵盖稳态与非稳态流场景，最大点数达30万。所有任务中，MNO均显著优于现有基线，预测误差降低5%至50%。结果表明，显式多尺度设计对神经算子至关重要，确立了MNO作为不规则域上复杂流体动力学学习的可扩展框架。
原文摘要 · Abstract (English)
Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, 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 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 diverse benchmarks, covering 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 50%. The 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.
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