Towards scalable surrogate models based on Neural Fields for large scale aerodynamic simulations

Abstract

This paper introduces a novel surrogate modeling framework for aerodynamic applications based on Neural Fields. The proposed approach, MARIO (Modulated Aerodynamic Resolution Invariant Operator), addresses non parametric geometric variability through an efficient shape encoding mechanism and exploits the discretization-invariant nature of Neural Fields. It enables training on significantly downsampled meshes, while maintaining consistent accuracy during full-resolution inference. These properties allow for efficient modeling of diverse flow conditions, while reducing computational cost and memory requirements compared to traditional CFD solvers and existing surrogate methods. The framework is validated on two complementary datasets that reflect industrial constraints. First, the AirfRANS dataset consists in a two-dimensional airfoil benchmark with non-parametric shape variations. Performance evaluation of MARIO on this case demonstrates an order of magnitude improvement in prediction accuracy over existing methods across velocity, pressure, and turbulent viscosity fields, while accurately capturing boundary layer phenomena and aerodynamic coefficients. Second, the NASA Common Research Model features three-dimensional pressure distributions on a full aircraft surface mesh, with parametric control surface deflections. This configuration confirms MARIO's accuracy and scalability. Benchmarking against state-of-the-art methods demonstrates that Neural Field surrogates can provide rapid and accurate aerodynamic predictions under the computational and data limitations characteristic of industrial applications.

Figures (12)

• Figure 1: MARIO's conditional neural field architecture. The framework handles two types of geometric variability: (1) Parametric case (e.g., NASA CRM), where $\mu_{\text{geom}}$ is directly obtained from explicit parameters like control surface deflections; and (2) Non-parametric case (e.g., AirfRANS), where $\mu_{\text{geom}}$ is learned by encoding SDF fields as described in Section \ref{['sec:Geometry Encoding']}. The conditions $z$ are formed by concatenating operating conditions $\mu$ (e.g., $M$, $\alpha$, $Re$) with $\mu_{\text{geom}}$. Spatial coordinates $x_x,x_y,..$ and optional auxiliary fields (e.g., normals, SDF) are processed through Fourier feature encoding ($\gamma$). The hypernetwork $h_\psi$ generates modulation vectors $\boldsymbol{\phi}$ from $z$, which are applied to each layer of the main network to condition the output.
• Figure 2: Geometry encoding process used in MARIO for non-parametric geometric variability. The neural field $f_{\theta_{in},\phi_{in}}$ with modulation vectors from hypernetwork $h_{\psi}$ takes points (in red) $x \in \mathcal{V}$ and the current latent code $z_{in}^{(k)}$ to predict the SDF field. The loss between the true and predicted SDF fields is used to compute the gradient with respect to $z_{in}^{(k)}$, which is then used for $K$ gradient descent steps. The final latent code $z_{in}^{(K)}$ becomes the geometric descriptor $\mu_{geom}$.
• Figure 3: Left: Example of the computational mesh for a single airfoil geometry in the AirfRANS dataset, with a zoomed view highlighting the refined mesh resolution near the airfoil surface. Right: Representative sample of diverse airfoil geometries from the dataset.
• Figure 4: Comparison of pressure field predictions between MARIO and Transolver models for a test sample. Top: Pressure contour plots showing the full field predictions. Bottom: Error contour plots and pressure coefficient ($C_p$) distribution along the airfoil surface. $\alpha=9.39 ^\circ$, $M=0.17$
• Figure 5: Comparison of all four predicted fields ($u_x$, $u_y$, $p$, $\nu_t$) for an in-distribution airfoil test case. First row: MARIO predictions; Second row: Ground truth CFD results; Third row: Absolute error contour plots. Operating conditions: $\alpha=9.94^\circ$, $M=0.18$.