The design of the blade-disk interface in a jet engine is crucial, as the stresses on both disk and blade directly affect the engine’s service life and potentially lead to catastrophic failure. In particular, any variation in design parameters can have a significant impact on the life of the components. While finite element (FE) analysis is commonly used to analyze the effects of each variation on the geometry separately, surrogate models can be a much more efficient alternative to explore these effects and thus the design space, as long as they can describe the system behavior well.This paper addresses the challenge of surrogate modeling a high-dimensional parameterized FE model of a turbine blade-disk interface using deep neural networks (DNNs) to describe the system behavior. Sampling methods as a part of Monte Carlo simulation (MCS), are used for training to evaluate the efficiency of using DNNs.In applications such as FE analysis, where interactions between neighboring nodes are essential, DNNs are advantageous due to their ability to account for these interactions and to process a large amount of data simultaneously and for all nodes in an FE model, so that there is only one DNN model for the entire FE model. They can adapt to different mesh topologies, eliminating the need for topologically identical positions, unlike conventional approaches such as node-based least squares. This advantage of DNNs is demonstrated in this work by a comparative analysis of geometry variation due to manufacturing tolerances and its impact on stress values using an in-house probabilistic tool MetamodelGUI. With this tool, the FE results of an MCS can be visualized in a much easier and faster way and the components can be preliminary designed using surrogate models. In addition, the ability of using DNNs to perform sensitivity analyses is evaluated. Furthermore, the robustness of DNN models for describing the system behavior is discussed, as well as the feasibility of using this method for robust optimization and failure probability estimation.