Mathematical models of the circulation continue to be an essential tool to study how the cardiovascular (CV) system maintains homeostasis. The utility of these models is ultimately limited by how much we can trust the accuracy of their predictions. The predictive capability of a model can be measured by uncertainty quantification (UQ). A challenge in implementing UQ procedures is that many publ...

The modelling of dynamic effects for flight dynamics analysis typically makes use of dynamic derivatives. A single value for the derivative is used and is assumed to be independent of the conditions for which it is calculated. This is however not the case. This work looks to quantify the uncertainty introduced as a result for an arbitrary manoeuvre within the flight envelope. The manoeuvres can...

Parametrized surrogate models are used in alloy modeling to quickly obtain otherwise expensive properties such as quantum mechanical energies, and thereafter used to optimize, or simply compute, some alloy quantity of interest, e.g., a phase transition, subject to given constraints. Once learned on a data set, the surrogate can compute alloy properties fast, but with an increased uncertainty co...

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a “pointwise” large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered.

Bargaining with reading habit is no need. Reading is not kind of something sold that you can take or not. It is a thing that will change your life to life better. It is the thing that will give you many things around the world and this universe, in the real world and here after. As what will be given by this uncertainty quantification in computational fluid dynamics, how can you bargain with th...

In this paper we demonstrate the only available scalable information bounds for quantities of interest of high dimensional probabilistic models. Scalability of inequalities allows us to (a) obtain uncertainty quantification bounds for quantities of interest in the large degree of freedom limit and/or at long time regimes; (b) assess the impact of large model perturbations as in nonlinear respon...

Consider approximating a “black box” function f by an emulator f̂ based on n noiseless observations of f . Let w be a point in the domain of f . How big might the error |f̂(w) − f(w)| be? If f could be arbitrarily rough, this error could be arbitrarily large: we need some constraint on f besides the data. Suppose f is Lipschitz with a known constant. We find a lower bound on the number of observa...