3 citations · 6 across the 14 of their papers we have counts for
5 papers · 1 filter
Adaptive Model Hierarchies for Multi-Query Scenarios
Hendrik Kleikamp, Mario Ohlberger
In this contribution we present an abstract framework for adaptive model hierarchies together with several instances of hierarchies for specific applications. The hierarchy is part…
Kernel Methods in the Deep Ritz framework: Theory and practice
Hendrik Kleikamp, Tizian Wenzel
In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential…
Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems
Hendrik Kleikamp, Lukas Renelt
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully…
Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics
Björn Schembera, Frank Wübbeling, Hendrik Kleikamp +8
Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorit…
Application of an adaptive model hierarchy to parametrized optimal control problems
Hendrik Kleikamp
In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized…