Predicting Melting of Gallium in Nickel Porous Media Using Fourier Neural Operator

Abstract This study presents a data-driven surrogate modeling framework using the Fourier Neural Operator (FNO) to predict the spatiotemporal evolution of melting in Gallium-filled Nickel porous media. The surrogate model is trained on a compact dataset of two-dimensional computational fluid dynamics (CFD) simulations, covering a wide spectrum of porous configurations generated from randomly placed circular inclusions. Each configuration is encoded as a binary mask and simulated under fixed boundary conditions to capture the time-resolved evolution of temperature, pressure, velocity, and liquid fraction fields. The trained FNO model demonstrates strong generalization capabilities across unseen geometries and extrapolated physical settings, including extended simulation durations and increased spatial resolutions. In particular, the model achieves high accuracy in low-porosity domains, where phase-change dynamics are compact and less coupled. The architecture leverages spectral convolution to learn global spatial correlations efficiently, enabling fast and resolution-invariant inference without retraining. Despite its success, the model exhibits limitations in high-porosity scenarios, where melting fronts become diffuse, and nonlinearities intensify. Minor nonphysical artifacts, such as artificial cooling at long prediction horizons, are attributed to the absence of embedded physics constraints. Nevertheless, the FNO produces smooth, stable predictions and offers significant computational speedups over traditional solvers. These features make it highly suitable for early-stage conceptual design, where rapid and reasonably accurate predictions are essential for iterative thermal analysis and system optimization. The full implementation is publicly accessible via the Neural Operator library at this link.2