Natural systems display extraordinary capacities for learning, adaptation, and environmental responsiveness, capabilities that have inspired the use of artificial neural networks (ANNs) across diverse scientific and engineering domains. Leveraging the biomimetic paradigm, our work explores how ANNs, originally inspired by biological neural processes, are increasingly employed to model gene expression in molecular biology and to develop intelligent, behaviour-responsive built environments. We conducted a comparative study of recent ANN-based approaches in systems biology, particularly in modelling gene regulatory networks, transcriptional dynamics, and epigenetic modulation, and architectural systems, including adaptive lighting, smart HVAC control, and occupant-driven space optimization. By examining the underlying data flows, feedback mechanisms, and functional architectures, we identified significant conceptual and computational parallels between these domains. Our findings reveal that, in both cases, ANNs serve as effective tools for capturing non-linear relationships, learning from high-dimensional input data, and enabling system-level adaptability. In biological systems, deep learning models accurately predict gene expression patterns from genomic features, while in architecture, recurrent reinforcement learning frameworks enable buildings to anticipate and respond to environmental and user stimuli in real-time. These insights accentuate the utility of ANNs not merely as analytical tools but as design frameworks for creating responsive, learning-enabled systems. We conclude that viewing gene networks and built environments through a unified lens of adaptive intelligence opens new frontiers for cross-disciplinary innovation in biomimetics, where principles of learning and responsiveness evolve seamlessly from genomes to geometry.