Applying physics-based loss functions to neural networks for improved generalizability in mechanics problems
This work addresses the challenge of ensuring neural network predictions conform to physical laws in mechanics, offering an incremental improvement by simplifying loss function implementation.
The paper tackled the problem of improving generalizability in mechanics problems by applying physics-based loss functions to neural networks, showing that simpler loss functions can achieve similar enforcement of physical laws as more complex methods.
Physics-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.