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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many control applications can be formulated as optimization constrained byconservation laws. Such optimization can be efficiently solved bygradient-based methods, where the gradient is obtained through the adjointmethod. Traditionally, the adjoint method has not been able to be implementedin "gray-box" conservation law simulations. In gray-box simulations, theanalytical and numerical form of the conservation law is unknown, but thespace-time solution of relevant flow quantities is available. Without theadjoint gradient, optimization can be challenging for problems with manycontrol variables. However, much information about the gray-box simulation iscontained in its space-time solution, which motivates us to estimate theadjoint gradient by leveraging the space-time solution. This article considersa type of gray-box simulations where the flux function is partially unknown. Amethod is introduced to estimate the adjoint gradient at a cost independent ofthe number of control variables. The method firstly infers a conservation law,named the twin model, from the space-time solution, and then applies theadjoint method to the inferred twin model to estimate the gradient. The methodis demonstrated to achieve good gradient estimation accuracies in severalnumerical examples. The main contributions of this paper are: a twin modelmethod that enables the adjoint gradient computation for gray-box conservationlaw simulations; and an adaptive basis construction scheme that fully exploitsthe information of gray-box solutions.

Adjoint-based Gradient Estimation Using the Space-time Solutions of Unknown Conservation Law Simulations