Hybrid Physics-Spectral-Threshold Framework for Fluid Flow Analysis: Comprehensive Validation on Turbulent and Laminar Regimes

Physics-informed machine learning has emerged as a powerful paradigm for fluid flow analysis, yet existing methods struggle to balance accuracy, interpretability, and computational efficiency across diverse flow regimes. We present the Hybrid Physics-Spectral-Threshold (HPST) framework, which integrates three key innovations: (1) physics-based region identification using vorticity-aware spectral clustering, (2) adaptive thresholding via distance-weighted negative statistics, and (3) seamless integration with graph neural networks for velocity field prediction. Through comprehensive validation on six distinct flow configurations—ranging from laminar cylinder wakes (Re=100) to fully turbulent regimes (Re=3900), airfoil flows, backward-facing steps, and noisy experimental data—we demonstrate that HPST consistently matches or exceeds standard GNN performance across all configura- tions. The largest gains (4.4%) occur precisely in turbulent regimes where adaptive thresholding matters most. Statistical validation across 10 random seeds per exper- iment (120 individual trainings, each for 500 epochs) confirms robustness, with all experiments completing without numerical instability. Computational cost analysis shows HPST adds 3.7 seconds per dataset—a 7% overhead fully justified by accuracy gains in safety-critical applications. The framework’s built-in physics awareness provides interpretable thresholds that adapt to local flow conditions, offering a path toward trustworthy AI in computational fluid dynamics.