Abstract: Random alloys exhibit a disordered atomic structure, composed of multiple elements distributed randomly at the atomic scale. The computational intensity of simulating heat transfer in such alloys stems from the intricacy of their atomic arrangements and the necessity to model interactions at this scale. This talk introduces two reduced-order modeling techniques tailored for these alloys. Focusing on local energy as coarse-grained variables, we propose two model-reduction approaches---Mori--Zwanzig and homogenization---to reduce the dimensionality of the dynamics. These approaches streamline computational complexity and retain essential physical insights, enabling more efficient simulations of heat transfer in random alloys for advanced materials design.