The production of high-quality fiber reinforced polymer parts is an important aspect in several industrial areas. However, due to unavoidable uncertainties in material and manufacturing processes, the part quality scatters. One important aspect here is the fiber orientation, being crucial for the thermo-mechanical properties of the part and being influenced by the uncertain material state and process conditions. Process simulations are an important tool for predicting the fiber orientation, but state-of-the-art simulations are normally deterministic and represent only one specific case. Performing enough deterministic simulations to model manufacturing uncertainties requires high numerical effort. Therefore, this work presents methods to quickly and efficiently approximate the fiber orientation under varying material and process parameters, requiring only a few simulations as input. Different schemes for approximation are evaluated and compared with each other and with 3D process simulations.