High-speed turbocharger rotors are often supported on double film floating ring bearings. In recent times, foil bearings are increasingly used as an alternative to floating ring bearings for supporting such lightweight rotors. Present work aims at the dynamic modeling and stability studies of the automotive turbocharger rotor system supported on the airfoil bearings under varying operating conditions. The effects of different parameters including rotor spin speed, bearing clearance, bump foil thickness, and foil pitch on the dynamic response of the rotor system are illustrated. The nonlinear relationship between the bearing parameters and vibration response data is modeled using supervised neural network scheme. With the use of counter propagation neural network model, inverse identification methodology of the bearing parameters is performed. Further, an optimal design of foil bearing parameters using a surrogate model is proposed with a modified particle swarm optimization scheme. The resultant design parameters are employed, and the percentage reductions in vibration amplitudes of dynamic response are reported. © 2021, Springer-Verlag GmbH Germany, part of Springer Nature.