Grid-transferable learning-based scheme for interface normal prediction from the volume fraction field on non-uniform Cartesian meshes

Accurate estimation of interface orientation is critical for the performance of Volume of Fluid (VOF) methods in multiphase flow simulations, particularly on non-uniform Cartesian grids. Traditional gradient reconstruction techniques, such as least-squares (LSQ), often exhibit significant errors and oscillations when applied to highly stretched meshes. This study presents a grid-transferable learning-based scheme that predicts the unit normal vector of the interface directly from the volume-fraction field on non-uniform structured Cartesian meshes using a compact feedforward neural network. The model is trained on a synthetically generated dataset constructed from radially symmetric star-shaped geometries with analytically defined normals, using non-uniform grids spanning cell aspect ratios up to 1000. In addition, specialized models are trained on subsets restricted to moderate aspect ratios for comparative evaluation and to probe sensitivity to grid stretching. Performance is assessed using the mean angular error, with improvements exceeding 78.3% relative to conventional LSQ methods, and with markedly reduced oscillatory behaviour on highly stretched meshes. The proposed approach generalizes well to unseen grid configurations and maintains high accuracy even on uniform meshes not included in training. Grid-convergence analysis reveals second-order accuracy for the learned predictor, in contrast to the poor convergence behaviour observed with LSQ. Feature-engineering studies highlight the importance of embedding local geometric descriptors of the grid within the input stencil. Overall, the method offers a robust, scalable, and readily integrable foundation for enhancing interface-normal prediction in VOF solvers and improving the accuracy of multiphase simulations on challenging non-uniform Cartesian grids.