  To improve predictive models for STEM applications, supplemental
physics-based features computed from input parameters are introduced into
single and multiple layers of a deep neural network (DNN). While many studies
focus on informing DNNs with physics through differential equations or
numerical simulation, much may be gained through integration of simplified
relationships. To evaluate this hypothesis, a number of thin rectangular plates
simply-supported on all edges are simulated for five materials. With plate
dimensions and material properties as input features and fundamental natural
frequency as the sole output, predictive performance of a purely data-driven
DNN-based model is compared with models using additional inputs computed from
simplified physical relationships among baseline parameters, namely plate
weight, modulus of rigidity, and shear modulus. To better understand the
benefit to model accuracy, these additional features are injected into various
single and multiple DNN layers, and trained with four different dataset sizes.
When these physics-enhanced models are evaluated against independent data of
the same materials and similar dimensions to the training sets, supplementation
with simplified physics-based parameters provides little reduction in
prediction error over the baseline for models trained with dataset sizes of 60
and greater, although small improvement from 19.3% to 16.1% occurs when trained
with a sparse size of 30. Conversely, notable accuracy gains occur when the
independent test data is of material and dimensions not conforming to the
training set. Specifically, when physics-enhanced data is injected into
multiple DNN layers, reductions in error from 33.2% to 19.6%, 34.9% to 19.9%,
35.8% to 22.4%, and 43.0% to 28.4% are achieved for training dataset sizes of
261, 117, 60, and 30, respectively, demonstrating attainment of a degree of
generalizability.
