The work is devoted to the improvement of the k-ω BSL turbulence model for the closure of Reynolds averaged Navier-Stokes (RANS) equations with the use of machine learning (ML) methods. The correction developed for this  model enhances its accuracy in calculating airfoil flows at stall angles of attack. Testing of the modified model on the flows around different airfoils reveals its superiority for this type of flows. The results demonstrate efficiency of the ML methods for turbulence model improvement.