  Machine learning models can be used to predict physical quantities like
homogenized elasticity stiffness tensors, which must always be symmetric
positive definite (SPD) based on conservation arguments. Two datasets of
homogenized elasticity tensors of lattice materials are presented as examples,
where it is desired to obtain models that map unit cell geometric and material
parameters to their homogenized stiffness. Fitting a model to SPD data does not
guarantee the model's predictions will remain SPD. Existing Cholsesky
factorization and Eigendecomposition schemes are abstracted in this work as
transformation layers which enforce the SPD condition. These layers can be
included in many popular machine learning models to enforce SPD behavior. This
work investigates the effects that different positivity functions have on the
layers and how their inclusion affects model accuracy. Commonly used models are
considered, including polynomials, radial basis functions, and neural networks.
Ultimately it is shown that a single SPD layer improves the model's average
prediction accuracy.
