Uncertainty Quantification
Uncertainty Quantification (UQ) focuses on characterizing and estimating uncertainties in computational models and real-world applications. Its goal is to predict the likelihood of specific outcomes when certain elements of a system are not precisely known. These uncertainties can arise from model parameter variability, measurement inaccuracies, or incomplete understanding of the underlying physics. UQ uses statistical and computational methods to assess how these variations affect system outcomes.
A key distinction in UQ is between aleatoric and epistemic uncertainty. Aleatoric uncertainty refers to inherent randomness, such as the scatter in outcomes from repeating an experiment under the same conditions. Epistemic uncertainty, on the other hand, stems from incomplete knowledge or imperfect models. Both types often coexist, and UQ techniques aim to quantify and manage them effectively.
UQ typically addresses two main problem types: forward and inverse problems. Forward UQ focuses on propagating known uncertainties through a model to predict their impact on outcomes, which is critical for fields like reliability engineering. Inverse UQ, a more complex approach, involves refining model parameters and correcting biases based on experimental data to improve model accuracy.
To tackle these challenges, researchers use various probabilistic and non-probabilistic methods, including Monte Carlo simulations, surrogate modeling, polynomial chaos expansions, and interval analysis. Integrating machine learning techniques, like Gaussian processes, has also enhanced the ability to manage uncertainties in complex systems, making UQ a powerful tool for both predictive modeling and system design.