Advances in biomedicine are largely fueled by exploring uncharted territories of human biology. Machine learning can both enable and accelerate discovery, but faces a fundamental hurdle when applied to unseen data with distributions that differ from previously observed ones -- a common dilemma in scientific inquiry. We have developed a new deep learning framework, called {\textit{Portal Learning}}, to explore dark chemical and biological space. Three key, novel components of our approach include: (i) end-to-end, step-wise transfer learning, in recognition of biology's sequence-structure-function paradigm, (ii) out-of-cluster meta-learning, and (iii) stress model selection. Portal Learning provides a practical solution to the out-of-distribution (OOD) problem in statistical machine learning. Here, we have implemented Portal Learning to predict chemical-protein interactions on a genome-wide scale. Systematic studies demonstrate that Portal Learning can effectively assign ligands to unexplored gene families (unknown functions), versus existing state-of-the-art methods, thereby allowing us to target previously "undruggable" proteins and design novel polypharmacological agents for disrupting interactions between SARS-CoV-2 and human proteins. Portal Learning is general-purpose and can be further applied to other areas of scientific inquiry.