It is a story as old as time. Models rife with uncertainty are developed for intriguing applications while simultaneously uncertainty quantification (UQ) methods are rapidly advanced. Yet, when the developers of the models and methods meet, it is rarely love at first sight. Either the UQ questions the modeler asks are like the third cousin to those the methods are intended to answer or the methods require certain types or quantities of data for which the modeler is not prepared to deliver. This minisymposium brings together pairs of collaborative researchers giving coordinated presentations on how an application and UQ method were finally joined in harmony. The first presentation focuses on the application, modeling, and types of UQ questions the researchers seek to answer. The second presentation focuses on how a UQ method was tailored to answer these questions under the constraints of the model.
08:30
Striking the Right Chord (Part I): What note is this?
Harri Hakula | Aalto University | Finland
Show details
Author:
Harri Hakula | Aalto University | Finland
How does the sound of the drum depend on its material properties? We model the drum as an elastic membrane and compute the associated variable diffusion eigenproblem, where the diffusion can be interpreted for instance as the tension of the drum. We choose as the shape of a drum a disk with a cut sector. In this case the exact eigenvalues for the constant coefficient problem are known, and the non-symmetric domain guarantees that there are no clusters of eigenvalues at the low end of the spectrum. This is an important property of the problem, since as the diffusion coefficient is perturbed, not only do the eigenvalues change but the order of the modes can change too. This phenomenon is referred to as mixing of modes. The numerical experiments are computed with hp-FEM where it is ensured that the discretisation is such that in the reference case all first 60 eigenpairs are in correct order. Thus, when in the perturbed cases mixing is observed, we can with high confidence say that it is due to the variation of the tension of the drum. Using this setup we can sample the coefficients from given distributions and observe the responses.
09:00
Striking the Right Chord (Part II): Learning to hear
Troy Butler | University of Colorado Denver | United States
Show details
Author:
Troy Butler | University of Colorado Denver | United States
In this follow-up to the presentation "Striking the Right Chord (Part I): What note is this?" we discuss how a novel data-consistent approach is modified to "hear" the properties associated with the tension of a drum. Particular attention is paid to applying feature extraction techniques commonly associated with machine learning to construct the parameter-to-observable maps required in this data-consistent approach. In the context of the application discussed here, we are identifying the most informative "chords" (a harmonious sound made up of individual "notes") to listen to from the striking of a drum that help us determine how tightly stretched the drum is over its frame. Numerical results demonstrate our ability to reconstruct the distributions of different families of tensions through the hearing of the correct chords.
09:30
Data-consistent computational modeling of the mechanical behavior of abdominal aortic aneurysms
Lukas Bruder | Technical University of Munich | Germany
Show details
Authors:
Lukas Bruder | Technical University of Munich | Germany
Michael W. Gee | Technical University of Munich | Germany
Recent advances in personalized medicine and biomechanical modeling of the cardiovascular system have encouraged patient-specific simulations in order to predict in-vivo quantities of interest or the future progression of a disease. The lack of precise knowledge about all the parameters that define the computational model motivates the exploitation of obtainable data for model calibration purposes and necessitates the quantification of uncertainties on the predictions. In this work, we consider abdominal aortic aneurysms (AAAs), pathological dilations of the infrarenal aorta that can be fatal in case of rupture. Our goal is to establish data-consistent computational models of the biomechanical behavior of AAAs to provide rupture risk indicators for decision making in clinical practice.
10:00
A mathematical and computational framework for developing data-consistent probability densities with application to abdominal aortic aneurysms
Tim Wildey | Sandia National Labs | United States
Show details
Author:
Tim Wildey | Sandia National Labs | United States
Uncertainty is ubiquitous in computational science and engineering. Often, parameters of interest cannot be measured directly and must be inferred from observable data. The mapping between these parameters and the measurable data is often referred to as the forward model and the goal is to use the forward model to gain knowledge about the parameters given the observations on the data. Bayesian inference is the most common approach for incorporating stochastic data into probabilistic descriptions of the input parameters. In this presentation, we discuss the utilization of a recently developed approach for stochastic inversion based on measure theory and Bayes’ rule to construct a data-consistent distribution of model input parameters. This distribution is consistent in the sense that the push-forward of the distribution through the computational model matches the distribution of data collected across a population. We demonstrate this data-consistent approach on series of simple problems to build intuition and then on an application in computational modeling of abdominal aortic aneurysms.