We propose a graph-based, multi-fidelity learning framework for the prediction of stationary Navier--Stokes solutions in non-parametrized two-dimensional geometries. The method is designed to guide the learning process through successive approximations, starting from reduced-order and full Stokes models, and progressively approaching the Navier--Stokes solution. To effectively capture both local and long-range dependencies in the velocity and pressure fields, we combine graph neural networks with Transformer and Mamba architectures. While Transformers achieve the highest accuracy, we show that Mamba can be successfully adapted to graph-structured data through an unsupervised node-ordering strategy. The Mamba approach significantly reduces computational cost while maintaining performance. Physical knowledge is embedded directly into the architecture through an encoding -- processing -- physics informed decoding pipeline. Derivatives are computed through algebraic operators constructed via the Weighted Least Squares method. The flexibility of these operators allows us not only to make the output obey the governing equations, but also to constrain selected hidden features to satisfy mass conservation. We introduce additional physical biases through an enriched graph convolution with the same differential operators describing the PDEs. Overall, we successfully guide the learning process by physical knowledge and fluid dynamics insights, leading to more regular and accurate predictions

翻译：本文提出了一种基于图的多保真度学习框架，用于预测非参数化二维几何中的稳态Navier-Stokes解。该方法旨在通过逐次逼近的方式引导学习过程：从降阶模型和完整Stokes模型出发，逐步逼近Navier-Stokes解。为有效捕捉速度场与压力场的局部及长程依赖关系，我们将图神经网络与Transformer及Mamba架构相结合。虽然Transformer实现了最高精度，但我们证明了通过无监督节点排序策略，Mamba能成功适配图结构数据。Mamba方法在保持性能的同时显著降低了计算成本。物理知识通过编码-处理-物理信息解码的流程直接嵌入架构中。导数计算通过基于加权最小二乘法构建的代数算子实现。这些算子的灵活性不仅使输出满足控制方程，还能约束选定的隐藏特征以满足质量守恒。我们通过采用与描述偏微分方程相同的微分算子进行增强图卷积，引入了额外的物理偏置。总体而言，我们成功利用物理知识和流体动力学原理引导学习过程，从而获得更规整且精确的预测结果。