  Incorporating scientific knowledge into deep learning (DL) models for
materials-based simulations can constrain the network's predictions to be
within the boundaries of the material system. Altering loss functions or adding
physics-based regularization (PBR) terms to reflect material properties informs
a network about the physical constraints the simulation should obey. The
training and tuning process of a DL network greatly affects the quality of the
model, but how this process differs when using physics-based loss functions or
regularization terms is not commonly discussed. In this manuscript, several PBR
methods are implemented to enforce stress equilibrium on a network predicting
the stress fields of a high elastic contrast composite. Models with PBR
enforced the equilibrium constraint more accurately than a model without PBR,
and the stress equilibrium converged more quickly. More importantly, it was
observed that independently fine-tuning each implementation resulted in more
accurate models. More specifically, each loss formulation and dataset required
different learning rates and loss weights for the best performance. This result
has important implications on assessing the relative effectiveness of different
DL models and highlights important considerations when making a comparison
between DL methods.
