Neural Signed Distance Surrogates for Cut-Cell Finite-Volume Solvers

Cut-cell and ghost-cell finite-volume methods require an accurate boundary distance field, available in closed form only for simple shapes and otherwise obtained through costly nearest-neighbor search. Prior work embeds learned distance fields as an auxiliary component inside a larger neural architecture; this study instead tests the numerical consequences of substituting the distance function alone within an otherwise unmodified classical discretization. We propose a compact trained neural network as a drop-in surrogate for this field, evaluated against exact and classical alternatives, including a KD-tree baseline, on four problems of increasing difficulty ending with a three-dimensional mechanical flange. A truncation analysis bounds the surrogate’s intercept error and identifies the training accuracy needed to preserve the scheme’s formal order. The surrogate matches second-order accuracy in every example, with fitted orders of 2.0 to 2.1 in two dimensions and, in three dimensions, a wider but still order-consistent 1.9 to 2.5, the extra width traced to identified, shared mesh- and timestep-resolution effects rather than to the surrogate itself. Query cost overtakes the KD-tree beyond roughly one hundred thousand points, with speedups up to 26.1 times, and gradient fields are substantially smoother than nearest-point construction throughout, tracking geometric severity in two dimensions and feature scale in three.