6 research outputs found
A Generalized Probabilistic Learning Approach for Multi-Fidelity Uncertainty Propagation in Complex Physical Simulations
Two of the most significant challenges in uncertainty propagation pertain to
the high computational cost for the simulation of 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 for uncertainty
quantification either fail or are not feasible. To overcome the current
limitations, we propose a probabilistic multi-fidelity framework that can
exploit lower-fidelity model versions of the original problem in a small data
regime. The approach circumvents the curse of dimensionality by learning
dependencies between the outputs of high-fidelity models and lower-fidelity
models instead of explicitly accounting for the high-dimensional inputs. We
complement the information provided by a low-fidelity model with a
low-dimensional set of informative features of the stochastic input, which are
discovered by employing a combination of supervised and unsupervised
dimensionality reduction techniques. The goal of our analysis is an efficient
and accurate estimation of the full probabilistic response for a high-fidelity
model. Despite the incomplete and noisy information that low-fidelity
predictors provide, we demonstrate that accurate and certifiable estimates for
the quantities of interest can be obtained in the small data regime, i.e., with
significantly fewer high-fidelity model runs than state-of-the-art methods for
uncertainty propagation. We illustrate our approach by applying it to
challenging numerical examples such as Navier-Stokes flow simulations and
monolithic fluid-structure interaction problems.Comment: 31 pages, 14 figure