Making reliable predictions in the presence of uncertainty is critical to high-consequence modeling and simulation activities, such as those encountered at Sandia National Laboratories. Surrogate or reduced-order models are often used to mitigate the expense of performing quality uncertainty analyses with high-fidelity, physics-based codes. However, phenomenological surrogate models do not always adhere to important physics and system properties. This project develops surrogate models that integrate physical theory with experimental data through a maximally-informative framework that accounts for the many uncertainties present in computational modeling problems. Correlations between relevant outputs are preserved through the use of multi-output or co-predictive surrogate models; known physical properties (specifically monotoncity) are also preserved; and unknown physics and phenomena are detected using a causal analysis. By endowing surrogate models with key properties of the physical system being studied, their predictive power is arguably enhanced, allowing for reliable simulations and analyses at a reduced computational cost.