Surrogate Neural Networks (NN) now routinely serve as substitutes for computationally demanding simulations (e.g., finite element). They enable faster analyses in industrial applications e.g., manufacturing processes, performance assessment. The verification of surrogate models is a critical step to assess their robustness under different scenarios. We explore the combination of empirical and formal methods in one NN verification pipeline. We showcase its efficiency on an industrial use case of aircraft predictive maintenance. We assess the local stability of surrogate NN designed to predict the stress sustained by an aircraft part from external loads. Our contribution lies in the complete verification of the surrogate models that possess a high-dimensional input and output space, thus accommodating multi-objective constraints. We also demonstrate the pipeline effectiveness in substantially decreasing the runtime needed to assess the targeted property.