Abstract Parker Solar Probe's (PSP's) unique orbital path allows us to observe the solar wind closer to the Sun than ever before. Essential to advancing our knowledge of solar wind and energetic particle formation is identifying the sources of PSP observations. We report on results for the first two PSP solar encounters derived using the Wang–Sheeley–Arge (WSA) model driven by Air Force Data Assimilative Photospheric Flux Transport (ADAPT) model maps. We derive the coronal magnetic field and the 1 R _⊙ source regions of the PSP-observed solar wind. We validate our results with the solar wind speed and magnetic polarity observed at PSP. When modeling results are very reliable, we derive time series of model-derived spacecraft separation from the heliospheric current sheet, magnetic expansion factor, coronal hole boundary distance, and photospheric field strength along the field lines estimated to be connected to the spacecraft. We present new results for Encounter 1, which show time evolution of the far-side mid-latitude coronal hole that PSP corotates with. We discuss how this evolution coincides with solar wind speed, density, and temperature observed at the spacecraft. During Encounter 2, a new active region emerges on the solar far side, making it difficult to model. We show that ADAPT-WSA output agrees well with PSP observations once this active region rotates onto the near side, allowing us to reliably estimate the solar wind sources retrospectively for most of the encounter. We close with ways in which coronal modeling enables scientific interpretation of these encounters that would otherwise not have been possible.