Abstract Traditional artificial intelligence (AI) models in healthcare focus on point predictions without quantifying uncertainty, leading to unreliable clinical decision-making in high-stakes environments. This paper presents a comprehensive mathematical framework linking stochastic noise control in biological systems to uncertainty-aware AI for clinical decision-making, research and development, and healthcare delivery. We formalize predictability as a conditional probability measure over trajectories, integrating differential equations, statistical inference, stochastic modeling, and decision theory with rules-based knowledge systems and retrieval-augmented generation. We provide formal stability proofs via Lyapunov analysis, regulatory crosswalks mapping mathematical control mechanisms to compliance requirements, and executable algorithms. The framework decomposes total uncertainty into aleatoric (irreducible biological variability) and epistemic (model limitations) components, enabling risk-proportional interventions. The noise-aware framework enables explicit modeling of predictive variance, supporting risk-stratified decisions across oncology immunotherapy, adaptive dose trials, pharmacovigilance, and intensive care unit monitoring. Formal Lyapunov stability conditions ensure bounded variance and mean-square stability. By transforming uncertainty from an implicit limitation into an explicit, monitorable safety variable, noise-aware AI operationalizes regulatory expectations from the U.S. Food and Drug Administration Good Machine Learning Practice, European Medicines Agency AI Act, and ISO 62304, providing mathematically defensible mechanisms for risk control, transparency, and lifecycle governance in regulated healthcare environments.