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

arXiv: https://arxiv.org/abs/2501.17081 · HTML: https://mlsanity.com/paper/2501.17081/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2025.

## Built on by (most cited first, 5 of 5)

- [Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later](https://mlsanity.com/paper/2509.19929/) (2025)
- [Bayesian Inference for PDE-based Inverse Problems using the Optimization of a Discrete Loss](https://mlsanity.com/paper/2510.15664/) (2025)
- [PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty](https://mlsanity.com/paper/2604.26593/) (2026)
- [Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions](https://mlsanity.com/paper/2605.06861/) (2026)
- [Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processing](https://mlsanity.com/paper/2608.21677/) (2026)

## Abstract (arXiv)

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.