English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We demonstrate that the recently developed Optimal Uncertainty Quantification(OUQ) theory, combined with recent software enabling fast global solutions ofconstrained non-convex optimization problems, provides a methodology forrigorous model certification, validation, and optimal design under uncertainty.In particular, we show the utility of the OUQ approach to understanding thebehavior of a system that is governed by a partial differential equation --Burgers' equation. We solve the problem of predicting shock location when weonly know bounds on viscosity and on the initial conditions. Through thisexample, we demonstrate the potential to apply OUQ to complex physical systems,such as systems governed by coupled partial differential equations. We compareour results to those obtained using a standard Monte Carlo approach, and showthat OUQ provides more accurate bounds at a lower computational cost. Wediscuss briefly about how to extend this approach to more complex systems, andhow to integrate our approach into a more ambitious program of optimalexperimental design.

Optimal Bounds on Nonlinear Partial Differential Equations in Model Certification, Validation, and Experimental Design