Prediction of 2D steady flow velocity fields with a CNN surrogate trained on RANS simulations

¹ Institute of Thermomechanics of the Czech Academy of Sciences, Prague, Czech Republic
² Department of Water Resources and Environmental Modeling, Faculty of Environmental Sciences, Czech University of Life Sciences Prague, Prague, Czech Republic

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 12 March 2026

Abstract

We present a data-driven surrogate modeling framework based on convolutional neural networks (CNNs) for predicting steady-state two-dimensional velocity fields in incompressible flows. The model was trained on a dataset of 120 Reynolds-averaged Navier–Stokes (RANS) simulations of flow past a rectangular obstacle, with systematic variation in inlet velocity, turbulence intensity, surface roughness, and obstacle orien-tation. Time-averaged velocity fields were extracted at z = 2 m, and subsequently interpolated onto a regular structured grid of 339 × 374 points. Only the horizontal velocity component U_x was retained for training the CNN. The surrogate model achieved a median MSE of 0.07 (m/s)² and R² of 0.75 on the test set, with most prediction errors localized in wake regions behind the obstacle. Cross-sectional velocity profiles and full-field error analyses confirmed high predictive accuracy across diverse flow configurations. Once trained, the CNN produces velocity field predictions within milliseconds, providing speed-ups of several orders of magnitude compared to RANS simulations and enabling rapid parametric exploration, design pre-screening, and real-time decision support.