Factorized Implicit Global Convolution for Automotive Computational Fluid Dynamics Prediction

TL;DR

This work tackles the challenge of accurate, scalable CFD prediction on large automotive meshes by introducing Factorized Implicit Global Convolution (FIGConv). FIGConv factorizes the high-resolution domain into multiple implicit grids and performs efficient global 3D convolution via 2D reparameterization, achieving quadratic complexity $O(N^2)$ while preserving global context. The architecture combines factorized grids, grid fusion, and a UNet-like design to predict per-face pressure and drag, achieving state-of-the-art results on DrivAerNet ($R^2=0.95$ for drag) and Ahmed body (normalized pressure error $0.89\%$) with favorable speed and memory footprints. This approach enables high-resolution CFD predictions for automotive design, potentially accelerating aerodynamic optimization while maintaining accuracy.

Abstract

Computational Fluid Dynamics (CFD) is crucial for automotive design, requiring the analysis of large 3D point clouds to study how vehicle geometry affects pressure fields and drag forces. However, existing deep learning approaches for CFD struggle with the computational complexity of processing high-resolution 3D data. We propose Factorized Implicit Global Convolution (FIGConv), a novel architecture that efficiently solves CFD problems for very large 3D meshes with arbitrary input and output geometries. FIGConv achieves quadratic complexity $O(N^2)$, a significant improvement over existing 3D neural CFD models that require cubic complexity $O(N^3)$. Our approach combines Factorized Implicit Grids to approximate high-resolution domains, efficient global convolutions through 2D reparameterization, and a U-shaped architecture for effective information gathering and integration. We validate our approach on the industry-standard Ahmed body dataset and the large-scale DrivAerNet dataset. In DrivAerNet, our model achieves an $R^2$ value of 0.95 for drag prediction, outperforming the previous state-of-the-art by a significant margin. This represents a 40% improvement in relative mean squared error and a 70% improvement in absolute mean squared error over previous methods.

Figures (6)

• Figure 1: FIGConvNet: ConvNet for drag prediction using FIG convolution blocks. The encoder and decoder consist of a set of FIG convolution blocks and we connect the encoder and decoder with skip connections. The output of the encoder is used for drag prediction and the output of the decoder is used for pressure prediction.
• Figure 2: From left to right, we have a regular convolution, a separable convolution, and our proposed factorized implicit global (FIG) convolution. Regular Convolution: Requires $O(N^2k^2)$ computation and the convolution kernel is not global. Separable Convolution: Involves a sequence of $O(N^2k)$ convolutions, but the convolution kernel is still not global. FIG Convolution: Requires $O(Nk)$ computation in parallel, with convolution kernels that are global in one axis in the respective factorized domain.
• Figure 3: Factorized Implicit Global Convolution 3D: The FIG convolution first creates a set of voxel grids that factorizes the domain. This allows representing a high resolution voxel grid domain implicitly that can be computationally prohibitive to save explicitly. Then, a set of global convolution operations are applied in parallel to these voxel grids to capture the global context. Finally, the voxel grids are aggregated to predict the output.
• Figure 4: Point Convolution: The features from source and target nodes as well as offset are fed into an MLP to lift the features, which are then aggregated and projected back to the original feature space using an MLP.
• Figure 5: Normalized Pressure Prediction and Error Visualization on DrivAerNet. Our network predicts both drag coefficients and per vertex pressure. We visualize the ground truth pressure and prediction along with the absolute error of the pressure. Note that the pressures are normalized to highlight the errors clearly.