Higher ‐Order Elastic and Thermal Stress Coefficients of <i>β</i> ‐HMX for High‐Fidelity Continuum Models: A Neural Network Guide to Calibrating Thermoelasticity Data From Molecular Dynamics

ABSTRACT We present a complete set of isothermal third‐ and fourth‐order elastic coefficients, as well as higher‐order thermal stress coefficients, for the monoclinic molecular crystal β‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocane (β‐HMX) in the P2 1 /n space group setting at 300 K and atmospheric pressure. These higher‐order coefficients are obtained from a neural network model. Leveraging the spectral bias property of neural networks, the model is trained directly on temporally fluctuating stress data homogenized from isothermal molecular dynamics (MD) simulations of the mechanical response of single‐crystal samples during imposed isothermal strain to failure. Once trained, the model accurately reproduces not only the stress history of the samples but also their second‐order tangent stiffness tensor, specific heat, and Grüneisen parameter, all while satisfying the stress‐free and energy normalization conditions associated with a single reference configuration. We further employ a higher‐order Sobolev norm to enforce a specific heat consistent with MD and explore the ability of several different activation functions to produce smooth, positive definite elastic moduli, which, in turn, enable the model to perform well in predicting the adiabatic response for unseen, nonisothermal MD loading paths, despite being trained solely on isothermal data acquired at various discrete temperatures. Although this expressive neural network model is suitable for direct use in high‐fidelity hydrocodes, we provide an analytical polynomial approximation, constructed via Taylor expansion, that respects the monoclinic symmetry of β‐HMX, is practically as accurate as the learned model, and is guaranteed to be faster for inference.