How to Model What We Don’t Know

Probabilistic Foundations of Uncertainty Quantification

Engineering simulation is often used to support decisions before all relevant information is known. Material properties vary, loads are uncertain, measurements are limited, and models are always simplified representations of reality. This course introduces a probabilistic way of thinking about these uncertainties, showing how probability, data, and simulation can be combined to make more informed engineering judgements. It then introduces Bayes’ theorem and marginalisation, using an accessible example to show why evidence can be misleading if base rates are ignored. The course later moves from hand calculation to numerical simulation, showing how Monte Carlo methods and probabilistic programming can be used when problems become too complex for analytical solutions.

After completing this segment, you should be able to:

• Explain why uncertainty is unavoidable in engineering simulation.
• Describe, in general terms, what uncertainty quantification is used for.
• Recognise the difference between deterministic and probabilistic modelling.
• Understand the pathway from theory to an engineering probability-of-failure example.
• Identify the role of tools such as R and Stan in probabilistic modelling.

Course Author

Dr. Frank Günther

Dr. Frank Günther is Director of Analysis & Simulations at Knorr-Bremse Rail Systems, with extensive experience in numerical simulation, virtual testing, uncertainty quantification, and physics-informed machine learning. He is an active contributor to the NAFEMS technical community as a member of both the NAFEMS Stochastics Working Group and the NAFEMS Simulation Governance & Management Working Group.

Keywords

Uncertainty Quantification; Probabilistic Modelling; Bayesian Inference; Monte Carlo Simulation; Machine Learning; Virtual Testing; Simulation Governance; Fatigue; Reliability