Hybrid Neural Interpolation of a Sequence of Wind Flows

TL;DR

This work tackles real-time urban wind field prediction by building surrogate models for Reynolds-averaged Navier–Stokes solutions as boundary-condition–dependent interpolants. It introduces a hybrid Tucker–NN framework that embeds a Tucker tensor decomposition into the network to compress high-dimensional wind-field data and learns a neural residual to suppress interpolation artifacts, achieving $R^2$ near 1 across velocity, pressure, and eddy viscosity. The approach yields substantial training speedups (from ~$2.82$ s/epoch to ~0.45 s/epoch) and reduces parameter counts (approximately $16{,}197$ vs $50{,}949$) while maintaining accuracy close to a pure neural-network benchmark, and it suppresses spurious oscillations in wakes. The resulting surrogate supports real-time wind-field updates suitable for emergency response and urban-scale pollutant transport studies, with clear pathways for extending to more complex geometries and additional parameterizations.

Abstract

Rapid and accurate urban wind field prediction is essential for modeling particle transport in emergency scenarios. Traditional Computational Fluid Dynamics (CFD) approaches are too slow for real-time applications, necessitating surrogate models. We develop a hybrid neural interpolation method for constructing surrogate models that can update urban wind maps on timescales aligned with meteorological variations. Our approach combines Tucker tensor decomposition with neural networks to interpolate Reynolds-Averaged Navier-Stokes (RANS) solutions across varying inlet wind angles. The method decomposes high-dimensional velocity, pressure, and eddy viscosity field datasets into a core tensor and factor matrices, then uses Fourier interpolation for angular modes and k-nearest neighbors convolution for spatial interpolation. A neural network correction mitigates interpolation artifacts while preserving physical consistency. We validate the approach on a simple cylinder-sphere configuration and, relative to a strong pure neural network benchmark, achieve comparable or improved accuracy ($R^2 > 0.99$) with significantly reduced training time. The pure NN remains a feasible reference model; the hybrid provides an accelerated approximate alternative that suppresses spurious oscillations, maintains wake dynamics, and demonstrates computational efficiency suitable for real-time urban wind simulation.

Figures (10)

• Figure 1: Cylinder-sphere test configuration: (a) Side view showing a wall-mounted cylinder (15 m diameter, 65 m height) and a floating sphere (10 m diameter, centered at 50 m elevation); (b) Top view of the configuration showing the relative positioning of obstacles. The inlet wind angle $\theta$ is measured counterclockwise from the positive x-axis; (c) Computational grid for the cylinder-sphere test case, consisting of 317,551 cells. The domain is discretized using tetrahedral elements with prismatic inflation layers near solid surfaces to resolve boundary layer flows. Mesh refinement is concentrated in the wake regions.
• Figure 2: Wind speed magnitude and streamlines on the horizontal plane at $z=50\,\mathrm{m}$ for the cylinder-sphere configuration. (a) $\theta=0^\circ$: sphere shielded by cylinder, wake interaction suppresses sphere vortices; (b) $\theta=60^\circ$: independent wake development with dual vortex pairs; (c) $\theta=120^\circ$: similar to $\theta=60^\circ$ but rotated; (d) $\theta=180^\circ$: cylinder minimally affected by sphere in the upstream due to size difference. Streamlines are all in black, they are however overlaid on a horizontal slice colored by velocity magnitude.
• Figure 3: Three-dimensional streamlines for the cylinder-sphere configuration: (a) $\theta = 0^\circ$ — sphere positioned downstream of the cylinder. The sphere is completely enclosed within the cylinder’s turbulent wake, suppressing the formation of independent sphere vortices; (b) $\theta = 180^\circ$ — cylinder positioned downstream of the sphere. The smaller sphere wake has minimal influence on the cylinder’s wake structure due to the size difference.
• Figure 4: Architecture of the pure neural network regression model with four hidden layers of 128 neurons each, using ELU activation functions. Input layer receives 5 features: spatial coordinates ($x, y, z$) and encoded wind angle ($\cos\theta, \sin\theta$). Output layer predicts 5 RANS field variables: velocity components ($u_x, u_y, u_z$), pressure ($p$), and eddy viscosity ($\nu_t$). Total trainable parameters: $\sim$50,000.
• Figure 5: Regression results for RANS fields using a fully connected neural network, shown at $Z=50\,\mathrm{m}$. Each image includes two rows corresponding to wind angles $7.5^\circ$ and $157.5^\circ$, and three columns showing ground truth (left), prediction (middle), and absolute error (right).

Theorems & Definitions (1)

• proof