Mechanically ventilated patients generate waveform data that corresponds to patient interaction with unnatural forcing. This breath information includes both patient and apparatus sources, imbuing data with broad heterogeneity resulting from ventilator settings, patient efforts, patient-ventilator dyssynchronies, injuries, and other clinical therapies. Lung-protective ventilator settings outlined in respiratory care protocols lack personalization, and the connections between clinical outcomes and injuries resulting from mechanical ventilation remain poorly understood. Intra- and inter-patient heterogeneity and the volume of data comprising lung-ventilator system (LVS) observations limit broader and longer-time analysis of such systems. This work presents a computational pipeline for resolving LVS systems by tracking the evolution of data-conditioned model parameters and ventilator information. For individuals, the method presents LVS trajectory in a manageable way through low-dimensional representation of phenotypic breath waveforms. More general phenotypes across patients are also developed by aggregating patient-personalized estimates with additional normalization. The effectiveness of this process is demonstrated through application to multi-day observational series of 35 patients, which reveals the complexity of changes in the LVS over time. Considerable variations in breath behavior independent of the ventilator are revealed, suggesting the need to incorporate care factors such as patient sedation and posture in future analysis. The pipeline also identifies structural similarity in pressure-volume (pV) loop characterizations at the cohort level. The design invites active learning to incorporate clinical practitioner expertise into various methodological stages and algorithm choices.