  In this paper, we introduce a physics-driven regularization method for
training of deep neural networks (DNNs) for use in engineering design and
analysis problems. In particular, we focus on prediction of a physical system,
for which in addition to training data, partial or complete information on a
set of governing laws is also available. These laws often appear in the form of
differential equations, derived from first principles, empirically-validated
laws, or domain expertise, and are usually neglected in data-driven prediction
of engineering systems. We propose a training approach that utilizes the known
governing laws and regularizes data-driven DNN models by penalizing divergence
from those laws. The first two numerical examples are synthetic examples, where
we show that in constructing a DNN model that best fits the measurements from a
physical system, the use of our proposed regularization results in DNNs that
are more interpretable with smaller generalization errors, compared to other
common regularization methods. The last two examples concern metamodeling for a
random Burgers' system and for aerodynamic analysis of passenger vehicles,
where we demonstrate that the proposed regularization provides superior
generalization accuracy compared to other common alternatives.
