相关论文: Constructive interpolation points selection in the…
The Loewner framework is one of the most successful data-driven model order reduction techniques. If $N$ is the cardinality of a given data set, the so-called Loewner and shifted Loewner matrices $\mathbb{L}\in\mathbb{C}^{N\times N}$ and…
Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…
In this paper, we address an extension of the Loewner framework for learning quadratic control systems from input-output data. The proposed method first constructs a reduced-order linear model from measurements of the classical transfer…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
We here introduce a novel classification approach adopted from the nonlinear model identification framework, which jointly addresses the feature selection and classifier design tasks. The classifier is constructed as a polynomial expansion…
High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…
The Loewner framework is an interpolatory approach for the approximation of linear and nonlinear systems. The purpose here is to extend this framework to linear parametric systems with an arbitrary number n of parameters. To achieve this, a…
In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order…
Prototype methods seek a minimal subset of samples that can serve as a distillation or condensed view of a data set. As the size of modern data sets grows, being able to present a domain specialist with a short list of "representative"…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
Model selection in latent block models has been a challenging but important task in the field of statistics. Specifically, a major challenge is encountered when constructing a test on a block structure obtained by applying a specific…
Low discrepancy point sets have been widely used as a tool to approximate continuous objects by discrete ones in numerical processes, for example in numerical integration. Following a century of research on the topic, it is still unclear…
In this paper, we extend the structure-preserving interpolatory model reduction framework, originally developed for linear systems, to structured bilinear control systems. Specifically, we give explicit construction formulae for the model…
We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
This paper presents a Sparse Hierarchical Fourier Interaction Networks, an architectural building block that unifies three complementary principles of frequency domain modeling: A hierarchical patch wise Fourier transform that affords…
This paper addresses problems on the structural design of control systems taking explicitly into consideration the possible application to large-scale systems. We provide an efficient and unified framework to solve the following major…
This work brings together the moment matching approach based on Loewner functions and the classical Loewner framework based on the Loewner pencil in the case of bilinear systems. New Loewner functions are defined based on the bilinear…
We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural…
Feature selection is used in machine learning to improve predictions, decrease computation time, reduce noise, and tune models based on limited sample data. In this article, we present FeatureExplorer, a visual analytics system that…