A cold-start meshing strategy guided by residuals from partially trained physics-informed neural networks

Traditional adaptive mesh refinement in computational fluid dynamics typically relies on a posteriori error estimators. These iterative methods are tightly coupled to the solver and heavily depend on the quality of the initial mesh. However, standard initialization strategies, including uniform and geometric refinement, are fundamentally physics-blind. They often fail to capture critical flow features, leading to poor performance in subsequent adaptive steps. To address this, we introduce a novel a priori framework termed PPR-GM (Partially Trained Physics-Informed Neural Network Residual-Guided Meshing), which decouples physical complexity sensing from the numerical solver. This approach uses a physics-informed neural network (PINN) as a mesh-free physics sensor to probe the intrinsic physical complexity of the domain. A key finding is that the residual field from the partially trained PINN correlates better with global flow structures than the fully converged residual field, which tends to concentrate on localized singularities. This residual field is mapped to a mesh-size function to guide mesh generation. Validated on laminar steady flow benchmarks, PPR-GM meshes enable a standard finite element method solver to achieve significantly higher accuracy across a wide range of degrees of freedom compared to those generated by traditional initialization strategies. The proposed framework correctly captures flow features, providing a robust, physics-driven method for cold-start mesh generation without manual intervention or pre-computed simulation data.