MNO: Multiscale Neural Operator for Computational Fluid Dynamics with 3D Point Cloud Data
This work addresses challenges in CFD for fluid dynamics on irregular domains, offering a scalable framework with significant performance gains, though it is incremental as it builds on existing neural operator paradigms.
The paper tackled the problem of limited accuracy and scalability in neural operators for solving Partial Differential Equations (PDEs) in Computational Fluid Dynamics (CFD) on 3D unstructured point clouds, introducing the Multiscale Neural Operator (MNO) which reduced prediction errors by 5% to 40% across diverse benchmarks.
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.