  The unprecedented amount of data generated from experiments, field
observations, and large-scale numerical simulations at a wide range of
spatio-temporal scales have enabled the rapid advancement of data-driven and
especially deep learning models in the field of fluid mechanics. Although these
methods are proven successful for many applications, there is a grand challenge
of improving their generalizability. This is particularly essential when
data-driven models are employed within outer-loop applications like
optimization. In this work, we put forth a physics-guided machine learning
(PGML) framework that leverages the interpretable physics-based model with a
deep learning model. The PGML framework is capable of enhancing the
generalizability of data-driven models and effectively protect against or
inform about the inaccurate predictions resulting from extrapolation. We apply
the PGML framework as a novel model fusion approach combining the physics-based
Galerkin projection model and long-short term memory (LSTM) network for
parametric model order reduction of fluid flows. We demonstrate the improved
generalizability of the PGML framework against a purely data-driven approach
through the injection of physics features into intermediate LSTM layers. Our
quantitative analysis shows that the overall model uncertainty can be reduced
through the PGML approach especially for test data coming from a distribution
different than the training data. Moreover, we demonstrate that our approach
can be used as an inverse diagnostic tool providing a confidence score
associated with models and observations. The proposed framework also allows for
multi-fidelity computing by making use of low-fidelity models in the online
deployment of quantified data-driven models.
