A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils (2412.09399v2)

Abstract: Computational modeling of aerodynamics is a key problem in aerospace engineering, often involving flows interacting with solid objects such as airfoils. Deep surrogate models have emerged as purely data-driven approaches that learn direct mappings from simulation conditions to solutions based on either simulation or experimental data. Here, we consider modeling of incompressible flows over solid objects, wherein geometric structures are a key factor in determining aerodynamics. To effectively incorporate geometries, we propose a message passing scheme that efficiently and expressively integrates the airfoil shape with the mesh representation. Under this framework, we first obtain a representation of the geometry in the form of a latent graph on the airfoil surface. We subsequently propagate this representation to all collocation points through message passing on a directed, bipartite graph. We demonstrate that this framework supports efficient training by downsampling the solution mesh while avoiding distribution shifts at test time when evaluated on the full mesh. To enable our model to be able to distinguish between distinct spatial regimes of dynamics relative to the airfoil, we represent mesh points in both a leading edge and trailing edge coordinate system. We further enhance the expressiveness of our coordinate system representations by embedding our hybrid Polar-Cartesian coordinates using sinusoidal and spherical harmonics bases. We additionally find that a change of basis to canonicalize input representations with respect to inlet velocity substantially improves generalization. Altogether, these design choices lead to a purely data-driven machine learning framework known as GeoMPNN, which won the Best Student Submission award at the NeurIPS 2024 ML4CFD Competition, placing 4th overall. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

• The paper introduces GeoMPNN, a novel neural network that leverages geometric features for precise CFD modeling of airfoil aerodynamics.
• It employs a directed bipartite graph with specialized coordinate transforms to enhance accuracy across diverse flow conditions.
• The approach reduces computational costs significantly while maintaining high fidelity in simulating incompressible aerodynamic flows.

A Geometry-Aware Message Passing Neural Network for Modeling Aerodynamics over Airfoils

The paper presents a novel approach for modeling incompressible aerodynamic flows over airfoils using a Geometry-Aware Message Passing Neural Network (GeoMPNN), addressing challenges in computational fluid dynamics (CFD) relevant to airfoil design. GeoMPNN introduces an innovative message passing scheme on latent graphs of airfoil surfaces, incrementally building upon existing neural surrogate models for the numerical solution of Partial Differential Equations (PDEs) in aerospace engineering.

GeoMPNN's core innovation lies in its geometry-aware architecture, which leverages the airfoil's shape to predict surrounding field conditions accurately. This approach utilizes a directed bipartite graph to propagate geometric representations to all mesh points, improving generalization across diverse flow conditions and geometries. Strategies such as leading and trailing edge coordinate systems, combined with polar-Cartesian coordinate enhancements, further refine spatial distinction and flow dynamics representation.

The methodology involves training on subsampled mesh points without sacrificing prediction accuracy on the full mesh, effectively managing computational costs. The framework supports efficient processing by separately handling surface-to-volume and volume-to-volume communication, thereby minimizing distribution shifts during inference. As a result, GeoMPNN performs robustly in the NeurIPS 2024 ML4CFD competition, delivering effective solutions even in out-of-distribution scenarios.

The results validate the strong numerical accuracy of the proposed method, showing significant improvements in error metrics across simulated conditions while maintaining computational efficiency. The paper’s findings suggest that explicit geometric acknowledgment in neural networks can enhance model precision, opening avenues for optimization applications, such as inverse design processes focused on aerodynamic efficiency metrics like drag and lift coefficients.

GeoMPNN's architecture has implications for future AI developments in CFD by exemplifying how domain-specific enhancements—such as tailored coordinate transforms and basis changes—can significantly impact model effectiveness. Adoption across other CFD challenges, particularly those involving complex boundary conditions or requiring high-fidelity PDE solutions, could be transformative.

This research positions geometry-aware neural networks as a crucial tool for advancing CFD simulations in aerospace applications. However, further exploration into scale adaptation and integration with more extensive system-level simulations could broaden its applicability and impact on design automation and optimization in engineering.