Physics-Informed Graph Learning for Spatially Contiguous and Capacity-Constrained Hospital Service Area Delineation.

Delineating Hospital Service Areas (HSAs) is critical for healthcare resource allocation and policymaking. However, existing methods struggle to simultaneously capture patient flow patterns, spatial contiguity, and multiple capacity constraints. Traditional spatial clustering fails to integrate flow networks effectively, while standard Graph Neural Networks (GNNs) often lack the capability to strictly enforce hard capacity constraints. Even the Spatially constrained Leiden algorithm, which couples flow and adjacency, often yields communities with near-zero inflow. We propose a novel framework, SGCN-MST, integrating physics-informed graph learning with constraint-based regionalization. It leverages a physics-informed GNN to simulate patient flow as a spatial diffusion process, explicitly capturing the spatial decay of interactions. The resulting "interaction-aware" embedding is fed into a spatial Minimum Spanning Tree (MST) using a Depth-First Search (DFS) strategy to dynamically balance modularity optimization with multiple constraints. Applied to the Florida inpatient database, our model reveals a nested, hierarchical spatial structure where large regional referral centers coexist with compact local communities, closely mirroring functional medical hierarchies. Comparative analysis shows that SGCN-MST provides a more balanced and policy-ready solution than baselines such as ScLeiden and Region2Vec when localization, contiguity, and capacity feasibility must be considered jointly. This study provides a statistically robust and administratively practical tool for health geography.