Evaluate and express the uncertainty in (computational) model predictions based on limited knowledge, data, and uncertain model inputs.
Uncertainty Quantification (UQ)
Uncertainty quantification (UQ) is a method to quantify the uncertainty in the output of numerical simulations. UQ becomes challenging in expensive simulations such as those used in biomechanics, where the cost of conducting multiple simulations may be prohibitive. On the other hand, especially in complex models, it is essential to understand how the uncertain inputs (such as material properties or initial conditions) affect the simulation’s output and quantify the uncertainty in that output. This is usually done with sampling-based approaches, such as the Monte Carlo method, by drawing samples from the uncertain model inputs, realizing simulations for these inputs, and then quantifying the uncertainty in the resulting model output samples. The propagated uncertainty in the model’s output is then given as samples or a distribution estimate. It allows for quantifying the confidence level in the simulation results, which is helpful for decision-making and understanding the simulation’s limitations.
Bayesian Multi-Fidelity Monte Carlo (BMFMC)
Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of these problems are encountered, and standard methods either fail or are not feasible. To overcome the current limitations, Bayesian multi-fidelity Monte Carlo (BMFMC) exploits lower-fidelity model versions in a small data regime. The goal is an efficient and accurate estimation of the complete probabilistic response for high-fidelity models. BMFMC circumvents the curse of dimensionality by learning the relationship between the outputs of a reference high-fidelity model and potentially several lower-fidelity models. Despite the inaccurate and noisy information that some low-fidelity models provide, we demonstrated using QUEENS that accurate and certifiable estimates for the quantities of interest can be obtained for uncertainty quantification problems in high stochastic dimensions, with significantly fewer high-fidelity model runs than state-of-the-art methods for uncertainty quantification.
Features in QUEENS
- Monte Carlo (MC)
- Bayesian Multi-Fidelity Monte Carlo (BMFMC)
- Several surrogate-based sampling approaches, such as Gaussian Processes, Polynomial Chaos Expansions (PCE) or (Bayesian) Neural Networks