This paper shows that neural networks trained to predict fluid flow in small parts of an airway tree can be locally accurate but still fail to conserve mass when their predictions are pieced together. The authors study steady, incompressible flow in simplified two‑dimensional airway trees. They warn that training separate models for individual components does not automatically produce a consistent global simulator for the whole tree.

The team trained three family‑specific neural operators called DeepONets for three primitive geometries: a straight Tube, a bifurcation (one branch splitting into two), and a trifurcation (one branch splitting into three). Training used 4,872 computational fluid dynamics (CFD) examples. In addition to matching field values, the losses included auxiliary penalties that nudge physical behavior: a divergence penalty to encourage incompressibility (zero net local mass creation), a port‑flux penalty to match flow through component boundaries, component‑balance to keep mass balance inside a piece, and port‑pressure to match pressures at connection points. After choosing models on validation data, the authors froze them and ran a “single‑pass” assembly: they predicted fields for each primitive and assembled them into whole‑tree fields without any further coupling, iterative correction, or CFD‑informed adjustment.

Assembled predictions kept the major flow patterns and responded sensibly to pathology scenarios. Inference was fast: about 0.204–0.215 seconds on a CPU. But when the authors audited global conservation they found a large error: a 22.68% prescribed‑inlet‑normalized external residual. That residual measures how much the assembled solution violates mass conservation across the whole tree relative to the inlet flow. In short, the model looked reasonable locally yet did not enforce correct global mass balance.