Related papers: Kernel Methods for Surrogate Modeling

Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…

Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not…

This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…

The kernel-based multi-scale method has been proven to be a powerful approximation method for scattered data approximation problems which is computationally superior to conventional kernel-based interpolation techniques. The multi-scale…

Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is…

Surrogate models provide fast alternatives to costly aerodynamic simulations and are extremely useful in design and optimization applications. This study proposes the use of a recent kernel-based neural surrogate, KHRONOS. In this work, we…

Surrogate models are a well established approach to reduce the number of expensive function evaluations in continuous optimization. In the context of genetic programming, surrogate modeling still poses a challenge, due to the complex…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…

Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…

In this work, we consider two kinds of model reduction techniques to simulate blood flow through the largest systemic arteries, where a stenosis is located in a peripheral artery i.e. in an artery that is located far away from the heart.…

Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…

By removing irrelevant and redundant features, feature selection aims to find a good representation of the original features. With the prevalence of unlabeled data, unsupervised feature selection has been proven effective in alleviating the…

In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…