Related papers: A kernel-based approach to physics-informed nonlin…

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…

Physics-informed machine learning (PIML) has emerged as a promising alternative to conventional numerical methods for solving partial differential equations (PDEs). PIML models are increasingly built via deep neural networks (NNs) whose…

Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…

This chapter deals with kernel methods as a special class of techniques for surrogate modeling. Kernel methods have proven to be efficient in machine learning, pattern recognition and signal analysis due to their flexibility, excellent…

Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…

Amidst the array of quantum machine learning algorithms, the quantum kernel method has emerged as a focal point, primarily owing to its compatibility with noisy intermediate-scale quantum devices and its promise to achieve quantum…

A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the…

Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary…

This article presents a three-step framework for learning and solving partial differential equations (PDEs) using kernel methods. Given a training set consisting of pairs of noisy PDE solutions and source/boundary terms on a mesh, kernel…

Model misspecification can create significant challenges for the implementation of probabilistic models, and this has led to development of a range of robust methods which directly account for this issue. However, whether these more…

This paper introduces a novel statistical regression framework that allows the incorporation of consistency constraints. A linear and nonlinear (kernel-based) formulation are introduced, and both imply closed-form analytical solutions. The…

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the…

Kernel methods are ubiquitous tools in machine learning. However, there is often little reason for the common practice of selecting a kernel a priori. Even if a universal approximating kernel is selected, the quality of the finite sample…

In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…

In this draft, fault diagnosis in nonlinear dynamic systems is addressed. The objective of this work is to establish a framework, in which not only model-based but also data-driven and machine learning based fault diagnosis strategies can…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

In this paper, we consider the problem of system identification when side-information is available on the steady-state (or DC) gain of the system. We formulate a general nonparametric identification method as an infinite-dimensional…

The aim of quantum system identification is to estimate the ingredients inside a black box, in which some quantum-mechanical unitary process takes place, by just looking at its input-output behavior. Here we establish a basic and general…