Intratumoral heterogeneity presents a major challenge to diagnosis and treatment of glioblastoma (GBM). Such heterogeneity is further exacerbated upon the recurrence of GBM, where treatment-induced reactive changes produce additional intratumoral heterogeneity that is ambiguous to differentiate on clinical imaging. There is an urgent need to develop non-invasive approaches to map the heterogeneous landscape of histopathological alterations throughout the entire lesion for each patient. We propose to predictively fuse MRI with the underlying intratumoral heterogeneity in recurrent GBM using machine learning (ML) by leveraging unique image-localized biopsies with their associated locoregional MRI features. To this end, we develop BioNet, a biologically informed multi-task framework combining Bayesian neural networks and semi-supervised adversarial autoencoders, to predict regional distributions of three tissue-specific gene modules: proliferating tumor, reactive/inflammatory cells, and infiltrated brain tissue. BioNet provides insight into how to integrate implicit and hierarchical domain knowledge, which is difficult to incorporate into ML models through existing methods. The proposed architecture further addresses challenges in exploiting latent feature structures from limited labeled image-localized biopsy samples, which lead to improvements in prediction accuracy. BioNet performs significantly better than existing methods on cross-validation and blind test datasets, shows generalizability that surpasses other models, and is adaptable to different types of data or tasks. Prediction maps of gene modules from BioNet provide accurate predictions of intratumoral heterogeneity, which can improve surgical planning and localization of diagnostic biopsies, as well as inform neuro-oncological treatment assessment for each patient. These results also highlight the emerging role of ML in precision medicine.