This study explored the potential of an AlN/$\beta -Ga_{2}O_{3}$ MOSHEMT (Metal Oxide Semiconductor High Electron Mobility Transistor) as a biosensor. An analytical framework was developed to effectively detect biomolecules, with the biosensor operating by modifying electrical parameters in response to changes in the dielectric constant of these biomolecules. The findings demonstrate significant sensitivity to various biomolecules, with Uricase displaying the highest sensitivity. In comparison to the AlGaN/GaN MOSHEMT, the AlN/$\beta -Ga_{2}O_{3}$ MOSHEMT showed improved sensitivity in terms of drain current. Additionally, the machine learning (ML) model created for this investigation correlates strongly with the simulation results. It can accurately predict outcomes within its trained range. Implementing the ML model leads to considerable reductions in both computational costs and time for similar simulations. Furthermore, it eliminates empirical adjustments typically required in traditional physics-based models.