Genomic selection and gene editing in crops could be enhanced by multi-species, mechanistic models predicting effects of changes in gene regulation. Current expression abundance prediction models require extensive computational resources, hard-to-measure species-specific training data, and often fail to incorporate data from multiple species. We hypothesize that gene expression prediction models that harness the regulatory network structure ofArabidopsis thalianatranscription factor-target gene interactions will improve on the present maize models. To this end, we collect 147Oryza sativaand 99Sorghum bicolorgene expression assays and assign them to maize family-based orthologous groups. Using three popular graph-based machine learning frameworks, including a shallow graph convolutional autoencoder, a deep graph convolutional autoencoder, and the inductive GraphSage strategy, we encode anArabidopsis thalianaintegrated gene regulatory network (iGRN) structure and TF gene expression values to predict gene expression both within and between species. We then evaluate the network methods against a partial least-squares baseline. We find that the baseline gives the best predictions within species, with Spearman correlations averaging between 0.74 and 0.78. The graph autoencoder methods were more variable with correlations between -0.1 and 0.65. In particular, the GraphSage and deep autoencoders performed the worst, and the shallow autoencoders performed the best. In the most challenging prediction context, where predictions were in new species and on genes that were not seen, we found that the shallow graph autoencoder framework averaged around 0.65. Unlike initial thoughts about preserved network structure improving gene expression predictions, this study shows that within-species predictions only need simple models, such as partial least squares, to capture expression variations. In cross-species predictions, the best model is often a more complex strategy utilizing regulatory network structure and other studies' expressions.