Modern simulation scenarios frequently require multi-query or real-time
responses of simulation models for statistical analysis, optimization,
or process control. However, the underlying simulation models may
be very time-consuming rendering the simulation task difficult or
infeasible. This motivates the need for rapidly computable surrogate
models. We address the case of surrogate modeling of functions from
vectorial input to vectorial output spaces. These appear, for instance,
in simulation of coupled models or in the case of approximating general
input--output maps. We review some recent methods and theoretical
results in the field of greedy kernel approximation schemes. In particular,
we recall the vectorial kernel orthogonal greedy algorithm (VKOGA)
for approximating vector-valued functions. We collect some recent
convergence statements that provide sound foundation for these algorithms,
in particular quasi-optimal convergence rates in case of kernels
inducing Sobolev spaces. We provide some initial experiments that
can be obtained with non-symmetric greedy kernel approximation schemes.
The results indicate better stability and overall more accurate models
in situations where the input data locations are not equally distributed.
%0 Book Section
%1 HS2017a
%A Haasdonk, Bernard
%A Santin, Gabriele
%B Reduced-Order Modeling (ROM) for Simulation and Optimization: Powerful Algorithms as Key Enablers for Scientific Computing
%C Cham
%D 2018
%E Keiper, Winfried
%E Milde, Anja
%E Volkwein, Stefan
%I Springer International Publishing
%K anm ians imported
%P 21--45
%R 10.1007/978-3-319-75319-5_2
%T Greedy Kernel Approximation for Sparse Surrogate Modeling
%U https://doi.org/10.1007/978-3-319-75319-5_2
%X Modern simulation scenarios frequently require multi-query or real-time
responses of simulation models for statistical analysis, optimization,
or process control. However, the underlying simulation models may
be very time-consuming rendering the simulation task difficult or
infeasible. This motivates the need for rapidly computable surrogate
models. We address the case of surrogate modeling of functions from
vectorial input to vectorial output spaces. These appear, for instance,
in simulation of coupled models or in the case of approximating general
input--output maps. We review some recent methods and theoretical
results in the field of greedy kernel approximation schemes. In particular,
we recall the vectorial kernel orthogonal greedy algorithm (VKOGA)
for approximating vector-valued functions. We collect some recent
convergence statements that provide sound foundation for these algorithms,
in particular quasi-optimal convergence rates in case of kernels
inducing Sobolev spaces. We provide some initial experiments that
can be obtained with non-symmetric greedy kernel approximation schemes.
The results indicate better stability and overall more accurate models
in situations where the input data locations are not equally distributed.
%@ 978-3-319-75319-5
@inbook{HS2017a,
abstract = {Modern simulation scenarios frequently require multi-query or real-time
responses of simulation models for statistical analysis, optimization,
or process control. However, the underlying simulation models may
be very time-consuming rendering the simulation task difficult or
infeasible. This motivates the need for rapidly computable surrogate
models. We address the case of surrogate modeling of functions from
vectorial input to vectorial output spaces. These appear, for instance,
in simulation of coupled models or in the case of approximating general
input--output maps. We review some recent methods and theoretical
results in the field of greedy kernel approximation schemes. In particular,
we recall the vectorial kernel orthogonal greedy algorithm (VKOGA)
for approximating vector-valued functions. We collect some recent
convergence statements that provide sound foundation for these algorithms,
in particular quasi-optimal convergence rates in case of kernels
inducing Sobolev spaces. We provide some initial experiments that
can be obtained with non-symmetric greedy kernel approximation schemes.
The results indicate better stability and overall more accurate models
in situations where the input data locations are not equally distributed.},
added-at = {2021-09-29T14:33:27.000+0200},
address = {Cham},
author = {Haasdonk, Bernard and Santin, Gabriele},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/219813e9fb637b35cc6e2d66407e07a53/britsteiner},
booktitle = {Reduced-Order Modeling (ROM) for Simulation and Optimization: Powerful Algorithms as Key Enablers for Scientific Computing},
doi = {10.1007/978-3-319-75319-5_2},
editor = {Keiper, Winfried and Milde, Anja and Volkwein, Stefan},
file = {:PDF/HS2017_www_preprint.pdf:PDF},
groups = {santin, haasdonk_misc, haasdonk_all_papers},
interhash = {e733ee8f462c3f7fafc29e26940192a2},
intrahash = {19813e9fb637b35cc6e2d66407e07a53},
isbn = {978-3-319-75319-5},
keywords = {anm ians imported},
owner = {santinge},
pages = {21--45},
publisher = {Springer International Publishing},
timestamp = {2021-09-29T12:35:04.000+0200},
title = {Greedy Kernel Approximation for Sparse Surrogate Modeling},
url = {https://doi.org/10.1007/978-3-319-75319-5_2},
year = 2018
}