Geo-PhysNet: A Geometry-Aware and Physics-Constrained Graph Neural Network for Aerodynamic Pressure Prediction on Vehicle Fluid-Solid Surfaces

The aerodynamic pressure of a car is crucial for its shape design. To overcome the time-consuming and costly bottleneck of wind tunnel tests and computational fluid dynamics (CFD) simulations, deep learning-based surrogate models have emerged as highly promising alternatives. However, existing methods that only predict on the surface of objects only learn the mapping of pressure. In contrast, a physically realistic field has values and its gradients that are structurally unified and self-consistent. Therefore, existing methods ignore the crucial differential structure and intrinsic continuity of the physical field as a whole. This oversight leads to their predictions, even if locally numerically close, often showing unrealistic gradient distributions and high-frequency oscillations macroscopically, greatly limiting their reliability and practicality in engineering decisions. To address this, this study proposes the Geo-PhysNet model, a graph neural network framework specifically designed for complex surface manifolds with strong physical constraints. This framework learns a differential representation, and its network architecture is designed to simultaneously predict the pressure scalar field and its tangential gradient vector field on the surface manifold within a unified framework. By making the gradient an explicit learning target, we force the network to understand the local mechanical causes leading to pressure changes, thereby mathematically ensuring the self-consistency of the field's intrinsic structure, rather than merely learning the numerical mapping of pressure. Finally, to solve the common noise problem in the predictions of existing methods, we introduce a physical regularization term based on the surface Laplacian operator to penalize non-smooth solutions, ensuring the physical rationality of the final output field. Experimental verification results show that Geo-PhysNet not only outperforms existing benchmark models in numerical accuracy but, more importantly, demonstrates superior advantages in the physical authenticity, field continuity, and gradient smoothness of the generated pressure fields.