Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulations

TL;DR

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs), which achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures.

Abstract

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains for different flow conditions, handle non-parametric 3D geometric variations, and generalize to unseen shapes at test time. The coordinate-based formulation naturally leads to robustness with respect to discretization, allowing an excellent trade-off between computational cost (memory footprint and training time) and accuracy. The method is demonstrated on two industrially relevant applications: a RANS dataset of the two-dimensional compressible flow over a transonic airfoil and a dataset of the surface pressure distribution over 3D wings, including shape, inflow condition, and control surface deflection variations. On the considered test cases, our approach achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures. Remarkably, the method can perform inference five order of magnitude faster than the high fidelity solver on the RANS transonic airfoil dataset. Code is available at https://gitlab.isae-supaero.fr/gi.catalani/aero-nepf

Figures (13)

• Figure 1: Left: Illustration of the multiscale architecture. Right: Experimental results for fitting a single signal using a 3-layer INR with different Fourier encoding. This experiment can be easily reproduced using the notebook provided in the accompanying Git repository (https://gitlab.isae-supaero.fr/gi.catalani/aero-nepf).
• Figure 2: Top: The geometry is encoded by the input INR, where the spatial coordinates $x, y, z$ are processed by a modulated neural network parameterized by $\theta_{in}$ to produce a Signed Distance Function (SDF). The output INR, parameterized by $\theta_{out}$, learns the mapping between the spatial coordinates and the output physical fields $p$, for each training sample through modulation. The modulation vectors $\phi$ are obtained from the (input or output) latent codes $z$ through a hypernetwork parameterized by $\psi$. The latent map, where $z_{in}$ and parameters $\mu$ is transformed into $z_{out}$, is approximated via a Multilayer Perceptron (MLP). Bottom: In this setup, the input parameters $\mu$ are directly fed into a hypernetwork $h_{\psi}$ to produce the modulations $\phi$. This modulation, along with the spatial coordinates, is then processed by a neural network parameterized by $\theta_{out}$ to output the physical fields $p$.
• Figure 3: At inference time, few gradient steps are needed to optimize the input shape descriptors $\hat{z}^{in}$ to produce good reconstructions of the Signed Distance Function. The processor network $p_{\delta}$ maps the input latent and the parameters $\mu$ to the output $\hat{z}_{out}$, which allows decoding the output fields everywhere in the spatial domain.
• Figure 4: Pressure field distribution prediction with different surrogate models and comparison with CFD. Top: Angle of Attack 6.2 [deg], Mach Number 0.60. Center: Angle of Attack 4.94 [deg], Mach Number 0.84. Bottom: Angle of Attack 7.2 [deg], Mach Number 0.85
• Figure 5: Surface Pressure Coefficient distribution prediction with different surrogate models and comparison with CFD. Left: Angle of Attack [6.2 deg], Mach Number [0.60]. Center: Angle of Attack [4.94 deg], Mach Number [0.84]. Right: Angle of Attack [7.2 deg], Mach Number [0.85]