We formulate mold filling in metal casting as a 2D neural operator learning problem that maps geometry and boundary data on an unstructured mesh to time resolved flow quantities, replacing expensive transient CFD. In the proposed method, a graph based encoder aggregates local neighborhood information on the input mesh and encodes geometry and boundary data, a Fourier spectral core operates on a regular latent grid to capture global interactions across the domain, and a graph based decoder projects the latent fields to a target mesh. The model is trained to jointly predict velocity components, pressure, and liquid volume fraction over a fixed rollout horizon and generalizes across different ingate locations and process settings. On held out geometries and inlet conditions, it reproduces large scale advection and the fluid-air interface evolution with localized errors near steep gradients. The mean relative L2 error is about 5% across all fields, and inference is two to three orders of magnitude faster than conventional CFD, enabling design in the loop exploration. Ablation studies show monotonic accuracy degradation under stronger spatial subsampling of input vertices and a smoother decline under temporal subsampling. Halving the training set yields only a small increase in error. These results establish neural operators as accurate and data efficient surrogates for 2D mold filling and enable rapid optimization of gating systems in casting workflows.

翻译：本文将金属铸造中的模具充型过程构建为一个二维神经算子学习问题，该算子将非结构化网格上的几何与边界数据映射为时间分辨的流动参量，从而替代昂贵的瞬态计算流体动力学模拟。所提方法中，基于图的编码器聚合输入网格的局部邻域信息以编码几何与边界数据；傅里叶谱核心在规则潜空间网格上运算以捕捉全域相互作用；基于图的解码器将潜场映射至目标网格。该模型经训练可联合预测固定推演时段内的速度分量、压力与液相体积分数，并能泛化至不同浇口位置与工艺参数。在未见过的几何与入口条件下，模型能复现大尺度平流运动与气液界面演化，仅在陡梯度附近存在局部误差。所有场量的平均相对L2误差约为5%，推理速度比传统计算流体动力学快两到三个数量级，支持设计闭环探索。消融研究表明：输入顶点空间采样越稀疏，精度呈单调下降；时间采样越稀疏，精度下降较平缓。训练集减半仅导致误差小幅上升。这些结果证实神经算子可作为二维充型过程精确且数据高效的代理模型，为铸造流程中的浇注系统快速优化提供支持。