Implicit Neural Representation For Accurate CFD Flow Field Prediction

TL;DR

This work introduces an implicit neural representation framework for 3D CFD flow field prediction in turbomachinery, modeling the flow as a function $f:\mathbb{R}^3\to\mathbb{R}^D$ learned by a small backbone-net. A hyper-net conditions backbone-net weights on the blade geometry, enabling geometry-conditioned predictions independent of mesh parameterization and supporting rapid evaluation for unseen designs. The approach demonstrates accurate reconstruction of key flow features (boundary layers, wakes, shocks) and strong correlation with CFD-derived quantities-of-interest across four blade configurations, while maintaining a modest memory footprint. The proposed method offers a scalable, mesh-agnostic proxy suitable for low-cost multi-fidelity optimization and design exploration in industrial turbomachinery.

Abstract

Despite the plethora of deep learning frameworks for flow field prediction, most of them deal with flow fields on regular domains, and although the best ones can cope with irregular domains, they mostly rely on graph networks, so that real industrial applications remain currently elusive. We present a deep learning framework for 3D flow field prediction applied to blades of aircraft engine turbines and compressors. Crucially, we view any 3D field as a function from coordinates that is modeled by a neural network we call the backbone-net. It inherits the property of coordinate-based MLPs, namely the discretization-agnostic representation of flow fields in domains of arbitrary topology at infinite resolution. First, we demonstrate the performance of the backbone-net solo in regressing 3D steady simulations of single blade rows in various flow regimes: it can accurately render important flow characteristics such as boundary layers, wakes and shock waves. Second, we introduce a hyper-net that maps the surface mesh of a blade to the parameters of the backbone-net. By doing so, the flow solution can be directly predicted from the blade geometry, irrespective of its parameterization. Together, backbone-net and hyper-net form a highly-accurate memory-efficient data-driven proxy to CFD solvers with good generalization on unseen geometries.

Figures (23)

• Figure 1: Overview of the backbone-net and hyper-net. At the top in black, we have the usual tool chain: From the blade design vector $\theta$, a 3D mesh is generated (only the surface mesh is depicted), then the CFD solver computes the full 3D flow solution and eventually the postprocessor aggregates the local information at the cell-centers and outputs quantities of interest denoted by $q$ like massflow and efficiency. At the bottom in red, we have our model that comprises the backbone-net and the hyper-net. The backbone-net maps the coordinates of a point of the computational domain to its flow features. It is specialized to a configuration. We make it capable of dealing with any blade by predicting its weights and biases from the surface mesh of a blade given as input. First, a graph neural network (GNN) extracts a fixed-sized vector representation of the blade, $\theta'$. This representation can be thought of as a pseudo design vector. Afterwards, the hyper-net generates the weights and biases, $\phi$, of the backbone-net. Finally, the backbone-net yields the 3D flow solution that is compared to the ground truth.
• Figure 2: Left: Predictions with MAE loss; middle: predictions with MSE loss; right: ground-truth, for the backbone-net trained solo on comp-rotor. We show the axial velocity component $V_x$ at the leading edge (top row) and the pressure $p$ at the trailing edge (bottom row), both at $r_{S_1} = 0.8$.
• Figure 3: Predictions of the axial velocity component $V_x$ for the configuration comp-rotor using the backbone trained solo (left) versus ground-truth (middle); absolute differences on the right. Top row: Near hub ($r_{S_1}=0.1$). Bottom row: Near tip ($r_{S_1}=0.8$).
• Figure 4: Predictions of the circumferential velocity component $V_\theta$ for the configuration turb-rotor using the backbone trained solo (left) versus ground-truth (middle) at midspan; absolute differences on the right. Top row: at leading edge; bottom row: at trailing edge.
• Figure 5: Predictions using the backbone trained solo with only 1% (left), 5% (middle) of the dataset versus ground-truth (right) of variable $V_x$ for comp-rotor near tip ($r_{S_1}=0.8$).