Applying physics-based loss functions to neural networks for improved generalizability in mechanics problemsPhysics-Informed Machine Learning (PIML) has gained momentum in the last 5
years with scientists and researchers aiming to utilize the benefits afforded
by advances in machine learning, particularly in deep learning. With large
scientific data sets with rich spatio-temporal data and high-performance
computing providing large amounts of data to be inferred and interpreted, the
task of PIML is to ensure that these predictions, categorizations, and
inferences are enforced by, and conform to the limits imposed by physical laws.
In this work a new approach to utilizing PIML is discussed that deals with the
use of physics-based loss functions. While typical usage of physical equations
in the loss function requires complex layers of derivatives and other functions
to ensure that the known governing equation is satisfied, here we show that a
similar level of enforcement can be found by implementing more simpler loss
functions on specific kinds of output data. The generalizability that this
approach affords is shown using examples of simple mechanical models that can
be thought of as sufficiently simplified surrogate models for a wide class of
problems.
arxiv.org