A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs

B Haasdonk, H Kleikamp, M Ohlberger… - SIAM Journal on …, 2023 - SIAM
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 …

[HTML][HTML] Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

N Discacciati, JS Hesthaven - Computer Methods in Applied Mechanics …, 2024 - Elsevier
We propose a local, non-intrusive model order reduction technique to accurately
approximate the solution of coupled multi-component parametrized systems governed by …

Data-driven kernel designs for optimized greedy schemes: A machine learning perspective

T Wenzel, F Marchetti, E Perracchione - SIAM Journal on Scientific Computing, 2024 - SIAM
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 …

Classifier-dependent feature selection via greedy methods

F Camattari, S Guastavino, F Marchetti, M Piana… - Statistics and …, 2024 - Springer
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 …

An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations

R Cavoretto, A De Rossi - Journal of Computational and Applied …, 2023 - Elsevier
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) …

Goal‐Oriented Two‐Layered Kernel Models as Automated Surrogates for Surface Kinetics in Reactor Simulations

F Döppel, T Wenzel, R Herkert… - Chemie Ingenieur …, 2024 - Wiley Online Library
Multi‐scale modeling allows the description of real reactive systems under industrially
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 …

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 …

A review of radial kernel methods for the resolution of Fredholm integral equations of the second kind

R Cavoretto, A De Rossi… - Constructive Mathematical …, 2024 - dergipark.org.tr
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 …

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 …