Convolutional Neural Network-Based Numerical Stability Prediction in Computational Fluid Dynamics Using Multi-Channel Spatial Inputs

Abstract

Numerical instability remains a fundamental problem in computational fluid dynamics (CFD), because it can cause the solver to diverge and increase the computational expense . In this paper, we introduce the CNN based classification framework StabilityPredictor, which uses six-channel spatial representations of flow variables (velocity, pressure, and discretization parameters) to characterize the state of the flow at the end of the CFD simulation as numerically stable or unstable. Proposed architecture is three blocks of convolution, batch normalization, ReLU activation, adaptive pooling, and fully connected classification layers.

The model was trained on a synthetic set of CFD experiments and tested with the multi-seed experiments, the ablation experiments and compared to the classical Courant–Friedrichs–Lewy (CFL) stability criterion. StabilityPredictor performed better than the rule-based baseline in all of the evaluation metrics with an average test accuracy of 94.72 ± 0.78%.

The trained network was also tested without retraining on the independently generated OpenFOAM simulations with icoFoam finite-volume solver, to investigate its real-world applicability. Though the numerical formulation, mesh representation, and coupling of pressure and velocity differ significantly, the model achieved 76.3% zero-shot classification accuracy, showing that it generalizes across solvers, between synthetic finite-difference simulations and an industrial CFD framework.

The results show that deep learning is able to extract transferable representations of numerical stability from a single simulation environment, suggesting that CNN-based stability prediction could be used to adaptively control the solver and in practical scientific computing workflows.