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Machine learning models can be used to predict physical quantities likehomogenized elasticity stiffness tensors, which must always be symmetricpositive definite (SPD) based on conservation arguments. Two datasets ofhomogenized elasticity tensors of lattice materials are presented as examples,where it is desired to obtain models that map unit cell geometric and materialparameters to their homogenized stiffness. Fitting a model to SPD data does notguarantee the model's predictions will remain SPD. Existing Cholseskyfactorization and Eigendecomposition schemes are abstracted in this work astransformation layers which enforce the SPD condition. These layers can beincluded in many popular machine learning models to enforce SPD behavior. Thiswork investigates the effects that different positivity functions have on thelayers and how their inclusion affects model accuracy. Commonly used models areconsidered, including polynomials, radial basis functions, and neural networks.Ultimately it is shown that a single SPD layer improves the model's averageprediction accuracy.

Neural Network Layers for Prediction of Positive Definite Elastic Stiffness Tensors