  Determining the proper level of details to develop and solve physical models
is usually difficult when one encounters new engineering problems. Such
difficulty comes from how to balance the time (simulation cost) and accuracy
for the physical model simulation afterwards. We propose a framework for
automatic development of a family of surrogate models of physical systems that
provide flexible cost-accuracy tradeoffs to assist making such determinations.
We present both a model-based and a data-driven strategy to generate surrogate
models. The former starts from a high-fidelity model generated from first
principles and applies a bottom-up model order reduction (MOR) that preserves
stability and convergence while providing a priori error bounds, although the
resulting reduced-order model may lose its interpretability. The latter
generates interpretable surrogate models by fitting artificial constitutive
relations to a presupposed topological structure using experimental or
simulation data. For the latter, we use Tonti diagrams to systematically
produce differential equations from the assumed topological structure using
algebraic topological semantics that are common to various lumped-parameter
models (LPM). The parameter for the constitutive relations are estimated using
standard system identification algorithms. Our framework is compatible with
various spatial discretization schemes for distributed parameter models (DPM),
and can supports solving engineering problems in different domains of physics.
