Reliability estimation of nonlinear dynamical systems with high physical and stochastic dimensionality poses a significant computational challenge. To cut computational costs, a projection-based reduced-order model (ROM) can serve as an efficient surrogate for the full model, where the high dimensional model (HDM) is solved only at certain parameter points to form a snapshot matrix and a proper orthogonal decomposition (POD) is carried out to extract reduced bases. Choosing those parameter values become crucial for computational efficiency of the model, since the performance is sensitive to the choice and distribution of training samples, especially in high-dimensional or nonlinear problems. Adaptive sampling strategies are used to dynamically identify new training points in key regions of the parameter space. Some of these techniques include checking error–without invoking HDM–at potential parameter values and choosing the critical ones to integrate into the snapshot matrix. For intrusive ROMs which have access to HDM source code, a posteriori error estimators are often based on, among others, the residual of the governing differential equation. However, the community has increasingly moved towards non intrusive ROMs (NIROMs) that merely require a ‘black-box’ solver as opposed to the source code which in turn poses a challenge in developing analytical error estimators. In this work, a data-driven a posteriori error estimator is developed for NIROMs, integrated into an adaptive framework. Several machine learning based techniques are tried and compared to choose the best path. Transfer learning is employed to update the model to incorporate new points rather than retrain the entire model. The method is demonstrated on a benchmark reliability problem of a nonlinear Duffing-type oscillator with ten degrees of freedom. For a specific type of problem–for example, reliability analysis–the concern is primarily the failure zone; therefore, the parameter sampling is focused there to build an accurate ROM to estimate probability of failure. The work suggests that data-driven approaches are a promising avenue for tracking error as opposed to analytical methods in adaptive training.