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Granular energetic materials exhibit complex chaotic behavior due to the coexistence of a wide range of energy scales without scale separation. The main challenges involved in modeling the physical processes leading to initiation of explosive reactions are (i) the lack of a general model for heterogeneous granular media under compaction and (ii) the lack of a reliable multi-scale discrete-to-continuum framework for describing diffusion-advection-reaction processes in heterogeneous particulate media. This heterogeneity plays a major role in stress and heat localization, which is responsible for initiating reactions in energetic materials. In particular, hot-spots emerge as a consequence of visco-plastic pore collapse, intergranular friction, and granular compaction. We developed a number of computation tools for stochastic analysis of granular materials dynamics. These include a continuum-discrete model of heat dissipation/diffusion and a continuum-discrete model of compaction of a granular material with macro-pores. We have also proposed a class of randomly fluctuating macroscopic equations of motion for granular materials and powders.