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A computational methodology based on supervised machine learning (ML) is described for characterizing and designing anisotropic refractory composite alloys with desired thermal conductivities (TCs). The structural design variables are parameters of our fast computational microstructure generator, which were linked to the physical properties. Based on the Sobol sequence, a sufficiently large dataset of artificial microstructures with a fixed volume fraction (VF) was created. The TCs were calculated using our previously developed fast Fourier transform (FFT) homogenization approach. The resulting dataset was used to train our optimal autoencoder, establishing the intricate links between the material’s structure and properties. Specifically, the trained ML model’s inverse design of tungsten-30% (VF) copper with desired TCs was investigated. According to our case studies, our computational model accurately predicts TCs based on two perpendicular cut-section images of the experimental microstructures. The approach can be expanded to the robust inverse design of other material systems based on the target TCs.