Uncertainty quantification for safety-relevant engineering systems is often limited by the high computational cost of large-scale, high-fidelity simulations and by the high dimensionality of the associated stochastic state space. In particular, probabilistic safety assessments require surrogate models that are not only efficient but also robust, bounded, and strictly consistent with physically admissible simulation results. This contribution presents an adaptive, surrogate-based uncertainty quantification framework tailored to safety assessment applications. The approach follows a two-stage surrogate construction strategy. In a first stage, a global sensitivity analysis is employed to identify the dominant sources of uncertainty for selected quantities of interest, allowing the elimination of non-influential input parameters with minimal loss of global variance. This results in a significantly reduced stochastic input space. In a second stage, the reduced space is approximated using an adaptive sparse grid surrogate with locally linear basis functions [1]. By construction, the surrogate response is strictly bounded by the available high-fidelity simulation results. A key feature of the proposed methodology is its ability to interpolate complete post-processing results from complex engineering simulations [2], including spatially and temporally resolved fields, without additional model evaluations. The resulting surrogate model enables real-time reconstruction of complete simulation outputs across the stochastic state space, facilitating interactive exploration of uncertainty effects and rapid assessment of system responses, allowing critical system responses to be identified without prior assumptions on their location in the physical domain. The framework is demonstrated using a computationally demanding probabilistic safety assessment [3] of a deep geological repository system. The results show that the proposed surrogate approach provides an efficient, physically consistent basis for uncertainty-aware analysis and supports transparent, simulation-based decision-making in safety-critical engineering applications. REFERENCES [1] M. Bittens, R.L. Gates. DistributedSparseGrids.jl: A Julia library implementing an Adaptive Sparse Grid collocation method. Journal of Open Source Software, 2023 Mar 7;8(83):5003. [2] M. Bittens. A VTU library in the Julia language that implements an algebra for basic mathematical operations on VTU data. Journal of Open Source Sof