Implicit-PointSAGE | Rajat Sarkar

Abstract

High-resolution computational fluid dynamics (CFD) simulations are essential for capturing complex fluid flow phenomena such as turbulent flows and shock-boundary layer interactions that are critical for aerospace applications. However, the high computational cost of obtaining simulation results at high resolution often limits their practicality.

Traditional deep learning-based super-resolution methods such as UNets have been explored to predict fine-mesh simulation results from coarse-mesh simulations, but they face challenges with unstructured meshes and require extensive amounts of training data. To address these limitations, we propose Implicit-PointSAGE, a mesh-independent super-resolution framework that leverages unordered, mesh-less structure of point clouds to simulate intricate fluid dynamics.

By integrating the strengths of PointSAGE with a Neural Implicit Learning module employing Galerkin-based attention, the framework efficiently captures the underlying physics and accurately predicts fine-mesh data directly from coarse-mesh inputs. Implicit-PointSAGE demonstrates significant computational efficiency, scalability to diverse point cloud sizes, and adaptability across various CFD scenarios.

Key Highlights

                                10-100x
                                Fewer Training Samples
                            

                                ~100
                                Samples Sufficient
                            

                                Mesh-Free
                                Point Cloud Based
                            

Architecture

Implicit-PointSAGE integrates three core modules: a Global Feature Extractor inspired by PointNet for capturing global flow patterns, a Local Feature Extractor using SAGEConv for neighborhood-aware representations, and a novel Pretrained Neural Implicit Learner employing Galerkin-based attention layers for continuous function representation.

Figure: Implicit-PointSAGE architecture showing Global Feature Extractor, Local Feature Extractor with SAGEConv, and Pretrained Neural Implicit Learner with Galerkin-based attention layers.

Key Contributions

Neural Implicit Learning: Integrates a Galerkin-based attention mechanism for learning continuous implicit representations of fluid flow fields.
Data Efficiency: Achieves state-of-the-art performance with 10 to 100 times fewer data samples, sometimes requiring as few as 100 samples.
Mesh Independence: Operates on unordered point clouds, eliminating dependency on mesh structure and enabling scalability across diverse point cloud sizes.
Versatility: Demonstrated across multiple CFD scenarios including lid-driven cavity, forward-facing step, and industrial applications.

Results

Implicit-PointSAGE matches the performance of state-of-the-art surrogate models in solving PDE-represented problems, while delivering substantial computational acceleration for high-resolution CFD simulations.

Velocity magnitude: Coarse mesh vs Fine mesh vs Prediction vs Error

Pressure field: Coarse mesh vs Fine mesh vs Prediction vs Error