MNO: Multiscale Neural Operator for 3D Computational Fluid Dynamics

Abstract

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.