Neural operator-based super-fidelity: A warm-start approach for accelerating steady-state fluid flow simulations*

Neural operators have emerged as a powerful tool for approximating mappings between infinite-dimensional function spaces, gaining attention in both research and industry. However, relying solely on neural operators as surrogate models may fall short in scientific tasks that prioritize computational precision and deterministic outcomes. In this study, we demonstrate that despite visual fidelity in flow field predictions, integral quantities can significantly deviate from ground truths. Consequently, we emphasize the necessity of numerically solving governing equations and present a novel warm-start approach, termed neural operator-based super-fidelity, to accelerate steady-state fluid flow simulations. The concept of super-fidelity, inspired by super-resolution in computer vision, involves mapping low-fidelity model solutions to high-fidelity ones through a vector-cloud neural network with equivariance (VCNN-e). The VCNN-e preserves all desired invariance/equivariance properties for solutions and adapts to different spatial resolutions. We evaluate the approach in two scenarios: (1) simulating incompressible laminar flows over parameterized elliptical cylinders and (2) simulating compressible flows over various airfoils at different angles of attack using a turbulence model. By utilizing the network's prediction as refined initial conditions, both simulations achieve speed-up ratios of no less than two times while maintaining the same level of accuracy compared to iterative convergence from potential flows. The robustness of this approach is evidenced across diverse CPU configurations and various iterative algorithms. Moreover, this method offers distinct advantages and practicality, bypassing the need for extensive high-quality data during training, leading to substantial time savings in data preparation, particularly for industrial applications. This study highlights the benefits of initializing traditional CFD solvers with neural operator-based predictions, enhancing computational efficiency while ensuring outcome accuracy.