Near-wall behaviour of particle trickle release graph network simulators (PTR-GNS) in out-of-distribution geometries

Purpose This paper aims to investigate how a particle trickle release graph network simulator (PTR-GNS) represents near-wall flow and material-dependent interactions when evaluated on geometries that differ from those present in the training data. The study focuses on analysing the behaviour exhibited by trained PTR-GNS models in boundary-layer-type regions under such out-of-distribution (OOD) conditions. Design/methodology/approach Two PTR-GNS models, WaterRamps (WR) and MultiMaterial (MM), are analysed. WR is trained on single-material water rollouts with obstacle-particle walls, whereas MM is trained on water, sand and goop rollouts without obstacle-particle walls. A moving–least–squares (MLS) diagnostic is defined on fixed probe points along a vertical probe line above walls and steps; nodal velocity is obtained by distance-weighted averaging within a prescribed sampling radius. Findings Four test cases are evaluated: a flat wall (Case 1), a backward-facing step with and without outflow (Cases 2–3), and a reverse-inflow forward-facing step with alternative step materials (Case 4). On the continuous-wall layout, WR and MM yield similar near-wall velocity profiles under identical inflow. With an obstacle-particle wall, the near-wall velocity is reduced relative to the continuous-wall case, indicating differences in the effective wall interaction behaviour learned by the model. For the backward- and forward-facing steps, rigid and deformable steps produce distinct near-wall profiles and material response, including entrainment and downstream transport of sand-like particles. Originality/value The paper introduces an MLS-based reporting protocol for learned particle simulators and applies it to OOD evaluation using explicit near-wall profiles and transport measures, enabling like-for-like comparison across wall representations, material configurations and boundary-condition variants in PTR-GNS rollouts.