SMART: Scalable Mesh-free Aerodynamic Simulations from Raw Geometries using a Transformer-based Surrogate Model

TL;DR

SMART tackles the cost and rigidity of CFD mesh generation by introducing a mesh-free surrogate that predicts aerodynamic fields from a geometry point cloud. A Transformer-based encoder–decoder learns a shared latent geometry and uses cross-layer attention to couple geometric context with evolving physics, enabling accurate predictions at arbitrary query points without a CFD mesh. The model employs modulated positional encodings, coarse geometry scaffolds, and FiLM-conditioned MLPs, with training-time subsampling and memory-aware inference. Across automotive and aerospace datasets, SMART matches or surpasses mesh-dependent baselines while eliminating mesh reliance, offering a scalable, industry-ready workflow for rapid design iterations.

Abstract

Machine learning-based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an additional input, thereby reducing prediction errors. However, generating a simulation mesh for new geometries is computationally costly. In contrast, mesh-free methods, which do not rely on the simulation mesh, typically incur higher errors. Motivated by these considerations, we introduce SMART, a neural surrogate model that predicts physical quantities at arbitrary query locations using only a point-cloud representation of the geometry, without requiring access to the simulation mesh. The geometry and simulation parameters are encoded into a shared latent space that captures both structural and parametric characteristics of the physical field. A physics decoder then attends to the encoder's intermediate latent representations to map spatial queries to physical quantities. Through this cross-layer interaction, the model jointly updates latent geometric features and the evolving physical field. Extensive experiments show that SMART is competitive with and often outperforms existing methods that rely on the simulation mesh as input, demonstrating its capabilities for industry-level simulations.

Figures (31)

• Figure 1: The proposed SMART model maps a geometry G, represented as a point cloud, and simulation parameters $\boldsymbol{\xi}$ to physical quantities (e.g., surface pressure and velocity in the volume) for arbitrary query positions $P$ without relying on the simulation mesh.
• Figure 2: SMART is an encoder-decoder architecture that encodes the geometry $G$ and simulation parameters $\boldsymbol{\xi}$ into a shared latent space. The decoder attends to the encoder's intermediate latent geometries $E^{(l)}_{G}$ to map arbitrary spatial coordinates $P$ to physical quantities $\textbf{u}(P,G, \boldsymbol{\xi})$. This cross-layer interaction enables a joint update of the latent geometry and the evolving physics field.
• Figure 3: True and predicted pressure field and velocity field (as streamlines) for a random sample from the SHIFT-SUV dataset.
• Figure 4: Geometries can be either represented in an application-specific CAD format, a derived geometry mesh (STL file), or a point cloud. The geometry mesh and point cloud are subsampled solely for visualization purposes.
• Figure 5: The geometry mesh (i.e., STL file) is used as input to generate the simulation mesh consisting of the surface mesh $P_S$ and volume mesh $P_V$. The simulation mesh generation is both computationally expensive and slow. A numerical solver resolves the governing physics on the simulation mesh, producing physical quantities $\mathbf{u}((x,y,z), G, \boldsymbol{\xi})$ for each of the mesh locations.