  We present a machine learning framework to train and validate neural networks
to predict the anisotropic elastic response of the monoclinic organic molecular
crystal $\beta$-HMX in the geometrical nonlinear regime. A filtered molecular
dynamic (MD) simulations database is used to train the neural networks with a
Sobolev norm that uses the stress measure and a reference configuration to
deduce the elastic stored energy functional. To improve the accuracy of the
elasticity tangent predictions originating from the learned stored energy, a
transfer learning technique is used to introduce additional tangential
constraints from the data while necessary conditions (e.g. strong ellipticity,
crystallographic symmetry) for the correctness of the model are either
introduced as additional physical constraints or incorporated in the validation
tests. Assessment of the neural networks is based on (1) the accuracy with
which they reproduce the bottom-line constitutive responses predicted by MD,
(2) detailed examination of their stability and uniqueness, and (3)
admissibility of the predicted responses with respect to continuum mechanics
theory in the finite-deformation regime. We compare the neural networks'
training efficiency under different Sobolev constraints and assess the models'
accuracy and robustness against MD benchmarks for $\beta$-HMX.
