Foundations of Uncertainty Quantification for Science and Engineering

In engineering, science, and data analysis, making predictions without accounting for real-world variability can lead to critical system failures. This text-based course introduces you to Uncertainty Quantification, the essential discipline of mathematically measuring, analyzing, and reducing uncertainty in complex systems. You will transition from making deterministic assumptions to developing robust, probabilistic models. By studying foundational probability, sensitivity analysis, and modern computational workflows, you will gain the skills to evaluate risk and improve decision-making in any technical project. What you'll learn: Understand the fundamental concepts of aleatory and epistemic uncertainty; Apply probability theory and random variables to model real-world variability; Perform uncertainty propagation using Monte Carlo methods and modern Python-based computational tools; Build basic surrogate models, including Gaussian processes, to approximate complex system behaviors; Analyze system reliability and execute sensitivity analysis to identify key sources of risk; Explore Bayesian inference for model calibration and parameter estimation. The course begins with core definitions and essential mathematical concepts before guiding you through practical simulation techniques, surrogate modeling, and reliability assessments. You will read structured explanations and analyze code snippets designed to build your confidence step-by-step. This course is designed for beginning engineers, data scientists, and researchers looking for a clear, accessible entry point into risk analysis, with no prior experience in uncertainty quantification required. Start reading today to build more reliable, resilient models.