The ambient solar wind flows and fields influence the complex propagation dynamics of coronal mass ejections in the interplanetary medium and play an essential role in shaping Earths space weather environment. A critical scientific goal in the space weather research and prediction community is to develop, implement and optimize numerical models for specifying the large-scale properties of solar wind conditions at the inner boundary of the heliospheric model domain. Here we present an adaptive prediction system that fuses information from in situ measurements of the solar wind into numerical models to better match the global solar wind model solutions near the Sun with prevailing physical conditions in the vicinity of Earth. In this way, we attempt to advance the predictive capabilities of well-established solar wind models for specifying solar wind speed, including the Wang-Sheeley-Arge (WSA) model. In particular, we use the Heliospheric Upwind eXtrapolation (HUX) model for mapping the solar wind solutions from the near-Sun environment to the vicinity of Earth. In addition, we present the newly developed Tunable HUX (THUX) model which solves the viscous form of the underlying Burgers equation. We perform a statistical analysis of the resulting solar wind predictions for the time 2006-2015. The proposed prediction scheme improves all the investigated coronal/heliospheric model combinations and produces better estimates of the solar wind state at Earth than our reference baseline model. We discuss why this is the case, and conclude that our findings have important implications for future practice in applied space weather research and prediction.