Advances in high-fidelity numerical modeling, combined with the increasing availability of observational and experimental data, are revolutionizing the integration of data and simulation in scientific and engineering analyses. However, the computational cost of high-fidelity models can be prohibitive for outer-loop tasks such as inference, uncertainty quantification, design, and control, which require repeated model evaluations. To address this challenge, recent research has focused on developing data-driven approximation methods that replace expensive models in the outer loop, enabling efficient and scalable analysis with limited evaluations of the high-fidelity model. This session will explore innovative approaches to leveraging data-driven surrogate models to improve accuracy and reduce computational costs in simulation-aided analysis. Discussions will focus on three key categories: finite-dimensional function approximation, operator learning, and generative modeling. As advances in these areas continue to evolve rapidly, it is essential to explore the relative strengths and trade-offs of these approaches. Presentations will highlight strategies for accelerating surrogate and generative model training, theoretical error estimation, and uncertainty quantification, alongside practical applications in areas such as risk analysis of multi-scale, multi-physics systems and predictive digital twins. Special attention will be given to experimental design for training data, the costs of surrogate construction and interrogation, and hybrid approaches that integrate high-fidelity models with surrogate models to balance the trustworthiness of high-fidelity predictions with the efficiency of low-fidelity models, enabling more outer-loop iterations. This session will showcase advances in this rapidly evolving field and their successful applications in areas ranging from fusion energy systems to materials discovery.