Fourier Neural Operators for Two-Phase, 2D Mold-Filling Problems Related to Metal Casting

This work reframes mold filling in metal casting as a simplified 2D operator learning surrogate to avoid costly transient CFD simulations. The method combines a graph based encoder that aggregates neighborhood information on an unstructured input mesh to encode geometry and boundary data, a Fourier spectral core that operates on a regular latent grid to capture global interactions, and a graph based decoder that maps latent fields back to a target mesh. The model jointly predicts velocities, pressure, and volume fraction over a fixed horizon and generalizes across varied ingate locations and process settings. On held out geometries and inlet conditions it reproduces large scale advection and the fluid air interface with errors concentrated near steep gradients. Mean relative L2 errors are about 5 percent across all fields. Inference is roughly 100 to 1000 times faster than conventional CFD simulations, thereby enabling rapid in-the-loop design exploration. Ablation studies show accuracy drops monotonically with stronger spatial subsampling of input vertices while temporal subsampling causes a gentler decline. Cutting the training data by 50 percent yields only small error growth. Overall the results demonstrate neural operators as efficient surrogates for 2D mold filling and related filling problems and enable fast exploration and optimization of gating system designs in casting workflows.