We consider the problem of using scientific machine learning (SciML) to rapidly predict solutions to systems of nonlinear partial differential equations (PDEs) defined over complex geometries. In particular, we focus on modeling how airflow in operating rooms (ORs) is affected as the position of an object within the OR varies. We develop data-driven and physics-informed operator-learning models based on the deep operator network (DeepONet) architecture. The DeepONet models are able to accurately and rapidly predict airflow solutions to novel parameter configurations, and they surpass the accuracy of a random forest (RF) baseline. Interestingly, we find that physics-informed regularization (PIR) does not enhance model accuracy, partially because of misspecification of the physical prior compared to the data’s governing equations. Existing SciML models struggle in predicting flow when complex geometries determine localized behavior.