Higher-order constants of β-HMX needed for high-fidelity continuum models: A neural network guide to curve-fitting thermoelasticity data from molecular dynamics

We present, for the first time, a complete set of third-order and four-order elastic coefficients as well as higher-order thermal stress coefficients of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) using the P2_1/n space group convention at 300 K and atmospheric pressure. These higher-order constants are computed from a neural network model that not only has good stress predictions but also shows good agreement with the second-order elastic stiffness tensor, specific heat, and Gruneisen parameter inferred from molecular dynamics. Leveraging the spectral bias of neural networks, we directly train the model on the fluctuating stress data homogenized from molecular dynamics, satisfying the stress-free and energy normalization conditions associated with a reference configuration. We further employ higher-order Sobolev norms to enforce a consistent specific heat and explore several activation functions to produce a smooth, positive-definite tangent stiffness, leading the model to perform well on adiabatic data acquired from unseen loading paths while being trained on only isothermal data at various temperatures. While this expressive neural network model can directly be used for high-fidelity hydrocodes, we provide an analytical polynomial model constructed via Taylor expansion that respects the monoclinic symmetry of β-HMX and is roughly just as accurate but is also guaranteed to be faster for inference.