arXiv subjects

Yiye Zou

Publications and source records attributed to Yiye Zou.

4 recordsLinked to original sources

arXiv2026

A multi-scale feature enhanced graph neural network for fluid dynamics prediction in complex geometries

Industrial design in fields such as vehicle and aerospace engineering often relies on large-scale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs. Deep neural networks have shown promise in improving simulation efficiency, especially graph neural networks (GNNs), which demonstrate great potential due to their flexibility with unstructured data. However, GNNs face challenges when dealing with tasks involving complex geometries and large-scale meshes. In this paper, we propose the Multi-scale Feature Enhanced Graph Neural Network (ME-GNN) to tackle these challenges. ME-GNN employs a graph neural network with a two-step message-passing mechanism to capture detailed local features effectively. Additionally, it integrates an Attention U-Net with uniform grid discretization, enabling the extraction of both fine and coarse features. The model also utilizes K-hop sampling to construct subgraphs, facilitating efficient training on large datasets while preserving detailed local features. We evaluated ME-GNN on three benchmark datasets and achieved state-of-the-art results: a relative L2 error of 0.0196 for the velocity field and 0.0556 for the surface pressure on ShapeNet-Car, a normalized mean squared error of 0.0033 for the flow field on AirfRANS, and a relative L2 error of 0.1416 for the surface pressure on DrivAerNet.

cs.LG↗

arXiv2026

Optimize discrete loss with finite-difference physics constraint and time-stepping for PDE solving

Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on computational grids. Physics-informed neural networks(PINNs) have emerged as a popular optimization-based approach for solving PDEs, but they often suffer from ill-conditioned objectives and the high cost of automatic differentiation. Optimization-based discretizations such as ODIL mitigate several PINN drawbacks by optimizing discrete variables directly, yet accuracy and efficiency remain limited on body-fitted geometries and for time-dependent problems. This paper proposes FDTO, a finite-difference time-stepping loss-optimization solver that defines physics losses from discrete residuals. FDTO couples curvilinear coordinate transforms with body-fitted structured grids and decomposes long-horizon evolution into sequential, well-conditioned subproblems consistent with time marching. The method is primarily evaluated on incompressible Navier-Stokes flows, including lid-driven cavity benchmarks, external airfoil aerodynamics (lift/drag consistency), and a cylinder case on a multi-block structured mesh with cross-block coherent solutions. Additional validations on diffusion and flow-mixing problems further demonstrate generality. Compared with representative PINN-based solvers, FDTO reduces GPU memory by about 82.6% on the lid-driven cavity case and achieves 3-5 times lower relative error on the flow-mixing problem. These results indicate that FDTO enables accurate, stable, and memory-efficient discrete-loss optimization for incompressible-flow solutions, while remaining applicable to other PDE models.

physics.flu-dyn↗

arXiv2024

Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured grids

Advances in deep learning have enabled physics-informed neural networks to solve partial differential equations. Numerical differentiation using the finite-difference (FD) method is efficient in physics-constrained designs, even in parameterized settings. In traditional computational fluid dynamics(CFD), body-fitted block-structured grids are often employed for complex flow cases when obtaining FD solutions. However, convolution operators in convolutional neural networks for FD are typically limited to single-block grids. To address this issue, \blueText{graphs and graph networks are used} to learn flow representations across multi-block-structured grids. \blueText{A graph convolution-based FD method (GC-FDM) is proposed} to train graph networks in a label-free physics-constrained manner, enabling differentiable FD operations on unstructured graph outputs. To demonstrate model performance from single- to multi-block-structured grids, \blueText{the parameterized steady incompressible Navier-Stokes equations are solved} for a lid-driven cavity flow and the flows around single and double circular cylinder configurations. When compared to a CFD solver under various boundary conditions, the proposed method achieves a relative error in velocity field predictions on the order of $10^{-3}$. Furthermore, the proposed method reduces training costs by approximately 20\% compared to a physics-informed neural network. \blueText{To} further verify the effectiveness of GC-FDM in multi-block processing, \blueText{a 30P30N airfoil geometry is considered} and the \blueText{predicted} results are reasonable compared with those given by CFD. \blueText{Finally, the applicability of GC-FDM to three-dimensional (3D) case is tested using a 3D cavity geometry.

cs.LG↗

arXiv2024

A fully differentiable GNN-based PDE Solver: With Applications to Poisson and Navier-Stokes Equations

In this study, we present a novel computational framework that integrates the finite volume method with graph neural networks to address the challenges in Physics-Informed Neural Networks(PINNs). Our approach leverages the flexibility of graph neural networks to adapt to various types of two-dimensional unstructured grids, enhancing the model's applicability across different physical equations and boundary conditions. The core innovation lies in the development of an unsupervised training algorithm that utilizes GPU parallel computing to implement a fully differentiable finite volume method discretization process. This method includes differentiable integral and gradient reconstruction algorithms, enabling the model to directly solve partial-differential equations(PDEs) during training without the need for pre-computed data. Our results demonstrate the model's superior mesh generalization and its capability to handle multiple boundary conditions simultaneously, significantly boosting its generalization capabilities. The proposed method not only shows potential for extensive applications in CFD but also establishes a new paradigm for integrating traditional numerical methods with deep learning technologies, offering a robust platform for solving complex physical problems.

physics.flu-dyn↗