A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs
We present a new surrogate modeling technique for efficient approximation of input-output
maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order …
maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order …
[HTML][HTML] Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps
We propose a local, non-intrusive model order reduction technique to accurately
approximate the solution of coupled multi-component parametrized systems governed by …
approximate the solution of coupled multi-component parametrized systems governed by …
Data-driven kernel designs for optimized greedy schemes: A machine learning perspective
Thanks to their easy implementation via radial basis functions (RBFs), meshfree kernel
methods have proved to be an effective tool for, eg, scattered data interpolation, PDE …
methods have proved to be an effective tool for, eg, scattered data interpolation, PDE …
Classifier-dependent feature selection via greedy methods
The purpose of this study is to introduce a new approach to feature ranking for classification
tasks, called in what follows greedy feature selection. In statistical learning, feature selection …
tasks, called in what follows greedy feature selection. In statistical learning, feature selection …
An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations
In this paper we propose an enhanced version of the residual sub-sampling method (RSM)
in Driscoll and Heryudono (2007) for adaptive interpolation by radial basis functions (RBFs) …
in Driscoll and Heryudono (2007) for adaptive interpolation by radial basis functions (RBFs) …
Goal‐Oriented Two‐Layered Kernel Models as Automated Surrogates for Surface Kinetics in Reactor Simulations
Multi‐scale modeling allows the description of real reactive systems under industrially
relevant conditions. However, its application to rational catalyst and reactor design is …
relevant conditions. However, its application to rational catalyst and reactor design is …
Hermite kernel surrogates for the value function of high-dimensional nonlinear optimal control problems
T Ehring, B Haasdonk - Advances in Computational Mathematics, 2024 - Springer
Numerical methods for the optimal feedback control of high-dimensional dynamical systems
typically suffer from the curse of dimensionality. In the current presentation, we devise a …
typically suffer from the curse of dimensionality. In the current presentation, we devise a …
Learning theory convergence rates for observers and controllers in native space embedding
J Burns, A Kurdila, D Oesterheld… - 2023 American …, 2023 - ieeexplore.ieee.org
This paper derives rates of convergence of approximations of observers and controllers
arising in the native space embedding method for adaptive estimation and control of a class …
arising in the native space embedding method for adaptive estimation and control of a class …
A review of radial kernel methods for the resolution of Fredholm integral equations of the second kind
The paper presents an overview of the existing literature concerning radial kernel meshfree
methods for the numerical treatment of second-kind Fredholm integral equations. More in …
methods for the numerical treatment of second-kind Fredholm integral equations. More in …
Learning a robust shape parameter for RBF approximation
MH Veiga, FN Mojarrad, FN Mojarrad - arxiv preprint arxiv:2408.05081, 2024 - arxiv.org
Radial basis functions (RBFs) play an important role in function interpolation, in particular in
an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a …
an arbitrary set of interpolation nodes. The accuracy of the interpolation depends on a …