Title: Physics-Informed Regularization of Deep Neural Networks,
Abstract: This paper presents a novel physics-informed regularization method for
training of deep neural networks (DNNs). In particular, we focus on the DNN
representation for the response of a physical or biological system, for which a
set of governing laws are known. These laws often appear in the form of
differential equations, derived from first principles, empirically-validated
laws, and/or domain expertise. We propose a DNN training approach that utilizes
these known differential equations in addition to the measurement data, by
introducing a penalty term to the training loss function to penalize divergence
form the governing laws. Through three numerical examples, we will show that
the proposed regularization produces surrogates that are physically
interpretable with smaller generalization errors, when compared to other common
regularization methods.