Unsteady flow predictions around an obstacle using Geometry-Parameterized Dual-Encoder Physics-Informed Neural Network

TL;DR

This work tackles the challenge of efficiently predicting unsteady flows around parameterized geometries by introducing the Geometry-Parameterized Dual-Encoder PINN (GP-DE-PINN). The method combines a geometry parameter encoder and a spatiotemporal coordinate encoder feeding a manifold decoder, trained under Navier–Stokes constraints to infer velocity and pressure fields without direct pressure data. Results on 2D petal-shaped cylinders show GP-DE-PINN significantly outperforms a geometry-augmented PINN, achieving sharper vortex structures, accurate pressure trends, and better second-order statistics, even for unseen shapes. The approach offers a robust, mesh-free surrogate for CFD in multi-query design contexts and points to future extensions with pressure data and varying Reynolds numbers.

Abstract

Machine learning-based flow field prediction is emerging as a promising alternative to traditional Computational Fluid Dynamics, offering significant computational efficiency advantage. In this work, we propose the Geometry-Parameterized Dual-Encoder Physics-Informed Neural Network (GP-DE-PINN) with a dual-encoder architecture for effective prediction of unsteady flow fields around parameterized geometries. This framework integrates a geometric parameter encoder to map low-dimensional shape parameters to high-dimensional latent features, coupled with a spatiotemporal coordinate encoder, and is trained under the Navier-Stokes equation constraints. Using 2D unsteady flow past petal-shaped cylinders as an example, we evaluate the model's reconstruction performance, generalization capability, and hyperparameter sensitivity. Results demonstrate that the GP-DE-PINN significantly outperforms the PINN with direct geometric input in flow field reconstruction, accurately capturing vortex shedding structures and pressure evolution, while exhibiting superior generalization accuracy on unseen geometric configurations. Furthermore, sensitivity analyses regarding geometric sampling and network width reveal the model's robustness to these hyperparameter variations. These findings illustrate that the proposed framework can serve as a robust and promising framework for predicting unsteady flows around complex geometric obstacles.

Figures (20)

• Figure 1: Schematic illustration of the geometric parameterization scheme. The continuous boundary is discretized into a high-dimensional feature vector $\mathbf{d} = [d_1, d_2, \dots, d_m]$, where each component $d_i$ represents the radial distance from the centroid to the boundary, sampled at uniformly spaced angular interval $\Delta \theta$.
• Figure 2: Schematic illustration of Geometry-Parameterized PINN architecture.
• Figure 3: GP-DE-PINN architecture. The two encoders $g_{\theta p}$ and $g_{\theta c}$ are employed to generate enhanced representations for the geometric parameters and the spatial/temporal coordinates. The concatenated features are then processed by the prediction network $g_{\theta n}$. The Navier-Stokes equations are provided as the governing physical constraints.
• Figure 4: Methods for generating petal-shaped cylinders.
• Figure 5: Training sets for evaluating the GP-PINN and the GP-DE-PINN.