PointSAGE: Mesh-independent superresolution approach to fluid flow predictions

TL;DR

PointSAGE introduces a mesh-independent CFD super-resolution framework that operates on unstructured point clouds to predict fine-mesh flow data from coarse simulations. The method fuses global (PointNet-inspired) and local (GraphSAGE-based) features, with an IDW upsampling step that maps coarse point clouds $C \in \mathbb{R}^{m \times d}$ to fine clouds $F \in \mathbb{R}^{n \times d}$, trained with $MSE$ loss. Across forward-facing step, lid-driven cavity, and methane combustion cases, PointSAGE achieves high-accuracy predictions while delivering large speedups (up to $\sim$100X) over conventional CFD, and it generalizes to unseen geometries without relying on mesh information. The work highlights a paradigm shift toward mesh-agnostic, point-cloud-based CFD predictions, with future directions including scalability via advanced GNNs and potential unsupervised learning to broaden applicability.

Abstract

Computational Fluid Dynamics (CFD) serves as a powerful tool for simulating fluid flow across diverse industries. High-resolution CFD simulations offer valuable insights into fluid behavior and flow patterns, aiding in optimizing design features or enhancing system performance. However, as resolution increases, computational data requirements and time increase proportionately. This presents a persistent challenge in CFD. Recently, efforts have been directed towards accurately predicting fine-mesh simulations using coarse-mesh simulations, with geometry and boundary conditions as input. Drawing inspiration from models designed for super-resolution, deep learning techniques like UNets have been applied to address this challenge. However, these existing methods are limited to structured data and fail if the mesh is unstructured due to its inability to convolute. Additionally, incorporating geometry/mesh information in the training process introduces drawbacks such as increased data requirements, challenges in generalizing to unseen geometries for the same physical phenomena, and issues with robustness to mesh distortions. To address these concerns, we propose a novel framework, PointSAGE a mesh-independent network that leverages the unordered, mesh-less nature of Pointcloud to learn the complex fluid flow and directly predict fine simulations, completely neglecting mesh information. Utilizing an adaptable framework, the model accurately predicts the fine data across diverse point cloud sizes, regardless of the training dataset's dimension. We have evaluated the effectiveness of PointSAGE on diverse datasets in different scenarios, demonstrating notable results and a significant acceleration in computational time in generating fine simulations compared to standard CFD techniques.

Figures (18)

• Figure 1: PointSAGE Architecture : The coarse data undergoes dimension matching with the fine data through the IDW Up-sampler technique. Subsequently, the up-sampled coarse data is concurrently processed by two modules: the Global (PointNet) and Local (GraphSAGE) feature extractors. These outputs are then fused through concatenation to accurately predict the fine mesh data.
• Figure 2: Scenario 1: Pressure and Velocity prediction at t= 3.5s for inlet velocity 4.465 m/s for an AR 3 dataset.
• Figure 3: Scenario 1: Velocity prediction for the case of Reynolds number interpolation
• Figure 4: Comparison of Speedup Achieved by PointSAGE in Accelerated CFD Simulations: The blue bars represent the time taken for coarse mesh simulation along with the inference time of PointSAGE for predicting fine mesh simulation, while the red bars represent the simulation time for fine mesh simulation using the CFD solver OpenFOAM.
• Figure 5: Computational Domain of a 2D Forward Facing Step Simulation