Graph sample and aggregate-based deep operator network for accelerating one-dimensional human breathing simulations

Neural network (NN)-based surrogate models represent a promising tool for accelerating human lung airflow simulations. However, the highly hierarchical branching structure of the lung airway produces flow rates ranging from liters to microliters per second, which, along with the geometric complexity of the airway, complicates the design of appropriate NN models.

We introduce a novel model combining Deep Operator Network (DeepONet) with Graph Sample and Aggregate (GraphSAGE), called GraphDeepONet, to accelerate simulations of one-dimensional (1D) human airway models. We also develop a volume-based normalization technique to eliminate the effects of multiscale flow rate variations during model training. We design three different types of models and compare their predictions with a conventional 1D solver as a reference. Model 1 employs a dual-model GraphDeepONet to predict the flow rate and static pressure simultaneously. Model 2 predicts the flow rate first and then computes the static pressure accordingly. Model 3 predicts the flow rates in the acinar regions, hierarchically aggregates them to obtain the remaining flow rates, and then calculates the static pressure, similar to Model 2.

Model 3 provided the most accurate predictions for healthy subjects, achieving median (Q1-Q3) L₂ relative errors of 7.0% (6.6-14.4%) in flow rate, 5.9% (5.6-14.3%) in static pressure, and 6.8% (6.3-12.8%) in pleural pressure. These NN models significantly lower computation costs (<1 s) compared with conventional solvers (∼12 min).

The proposed surrogate modeling strategy ensures efficient simulation of airflow in 1D human airways, potentially enabling real-time respiratory analysis and personalized treatment.