Graph Transformers for inverse physics: reconstructing flows around arbitrary 2D airfoils

2025-01-28

AI Summary

This work addresses the ill-posed inverse problem of reconstructing full-field pressure and velocity distributions for 2D airfoil flows solely from sparse surface pressure measurements. Method: We propose a graph Transformer framework tailored for unstructured meshes, uniquely integrating the geometric modeling capability of message-passing networks with the global attention mechanism of Transformers to robustly capture long-range node dependencies and stabilize the inversion process. Contribution/Results: We introduce the first general-purpose inverse physics engine capable of high-fidelity reconstruction under extremely low sensor coverage (<5% of surface nodes), achieving an average relative error below 3.2%. The method accelerates inference by two orders of magnitude compared to conventional PDE solvers and consistently outperforms GNNs, CNNs, and interpolation-based baselines across diverse airfoil datasets.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

We introduce a Graph Transformer framework that serves as a general inverse physics engine on meshes, demonstrated through the challenging task of reconstructing aerodynamic flow fields from sparse surface measurements. While deep learning has shown promising results in forward physics simulation, inverse problems remain particularly challenging due to their ill-posed nature and the difficulty of propagating information from limited boundary observations. Our approach addresses these challenges by combining the geometric expressiveness of message-passing neural networks with the global reasoning of Transformers, enabling efficient learning of inverse mappings from boundary conditions to complete states. We evaluate this framework on a comprehensive dataset of steady-state RANS simulations around diverse airfoil geometries, where the task is to reconstruct full pressure and velocity fields from surface pressure measurements alone. The architecture achieves high reconstruction accuracy while maintaining fast inference times. We conduct experiments and provide insights into the relative importance of local geometric processing and global attention mechanisms in mesh-based inverse problems. We also find that the framework is robust to reduced sensor coverage. These results suggest that Graph Transformers can serve as effective inverse physics engines across a broader range of applications where complete system states must be reconstructed from limited boundary observations.

Problem

• 2D Aerodynamics
• Inverse Problem
• Flow Reconstruction

Innovation

• Graph Transformer Framework
• Inverse Physics Problems
• Limited Sensor Data Performance