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…
Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain
Hendrik Kleikamp, Mario Ohlberger, Stephan Rave
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, li…
Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery
Tim Keil, Hendrik Kleikamp, Rolf J Lorentzen +2
In this contribution, we develop an efficient surrogate modeling framework for simulation-based optimization of enhanced oil recovery, where we particularly focus on polymer floodi…