  The widespread integration of deep neural networks in developing data-driven
surrogate models for high-fidelity simulations of complex physical systems
highlights the critical necessity for robust uncertainty quantification
techniques and credibility assessment methodologies, ensuring the reliable
deployment of surrogate models in consequential decision-making. This study
presents the Occam Plausibility Algorithm for surrogate models
(OPAL-surrogate), providing a systematic framework to uncover predictive neural
network-based surrogate models within the large space of potential models,
including various neural network classes and choices of architecture and
hyperparameters. The framework is grounded in hierarchical Bayesian inferences
and employs model validation tests to evaluate the credibility and prediction
reliability of the surrogate models under uncertainty. Leveraging these
principles, OPAL-surrogate introduces a systematic and efficient strategy for
balancing the trade-off between model complexity, accuracy, and prediction
uncertainty. The effectiveness of OPAL-surrogate is demonstrated through two
modeling problems, including the deformation of porous materials for building
insulation and turbulent combustion flow for the ablation of solid fuels within
hybrid rocket motors.
