Intratumoral heterogeneity poses a significant challenge to the diagnosis and treatment of glioblastoma (GBM). This heterogeneity is further exacerbated during GBM recurrence, as 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 Magnetic Resonance Imaging (MRI) with the underlying intratumoral heterogeneity in recurrent GBM using machine learning (ML) by leveraging image-localized biopsies with their associated locoregional MRI features. To this end, we develop BioNet, a biologically-informed neural network model, to predict regional distributions of three tissue-specific gene modules: proliferating tumor, reactive/inflammatory cells, and infiltrated brain tissue. BioNet offers valuable insights into the integration of multiple implicit and qualitative biological domain knowledge, which are challenging to describe in mathematical formulations. BioNet performs significantly better than a range of existing methods on cross-validation and blind test datasets. Voxel-level prediction maps of the gene modules by BioNet help reveal intratumoral heterogeneity, which can improve surgical targeting of confirmatory biopsies and evaluation of neuro-oncological treatment effectiveness. The non-invasive nature of the approach can potentially facilitate regular monitoring of the gene modules over time, and making timely therapeutic adjustment. These results also highlight the emerging role of ML in precision medicine.