Computational mechanics are a core pillar of modern simulation-driven design. As modelling fidelity increases in approaches such as Finite Element (FE) analysis and Computational Fluid Dynamics (CFD), the computational effort per simulation rises accordingly. While advances in hardware and solver implementations improve simulation efficiency, the number of model evaluations required for design-space exploration and optimisation remains a significant time driver. Surrogate modelling has therefore emerged as a key enabling technology for accelerating solver-based workflows, particularly when rapid evaluation of complex response fields is required. However, widely applicable Machine Learning (ML) approaches such as neural networks typically lack uncertainty estimates, leading to predictions of unknown reliability. Building on the established framework of stochastic process emulation for computer experiments, this contribution introduces a probabilistic surrogate modelling framework that augments digital engineering pipelines with uncertainty-aware prediction and adaptive data acquisition. The proposed methodology is applicable to a broad range of numerical quantities, from scalar outputs to high-dimensional spatial fields, and is therefore independent of the underlying physical domain. Applications span structural and fluid mechanics as well as electromagnetics, acoustics, optics, and multiphysics problems. To handle multi-dimensional data, such as mesh-based simulation results, the probabilistic surrogate architecture is extended by concepts of graph neural networks. This enables learning mappings between input and output fields while explicitly accounting for geometric and spatial structure. Combined with an optimisation strategy based on Bayesian Optimisation principles, these uncertainty estimates drive adaptive sampling and active learning, prioritising data with the highest expected information gain. Summarising, the framework allows uncertainty-aware learning from complex data, offering a scalable foundation for advanced analysis and decision-making in computational mechanics and related simulation-driven disciplines.