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Block-oriented models are often used to model nonlinear systems. These models consist of linear dynamic (L) and nonlinear static (N) sub-blocks. This paper addresses the generation of initial estimates for a Wiener-Hammerstein model (LNL…
Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…
Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance…
Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the…
The Loewner framework-(LF) in combination with Volterra series-(VS) offers a non-intrusive approximation method that is capable of identifying bilinear models from time-domain measurements. This method uses harmonic inputs which establish a…
Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse. Kernel matrices, which arise from discretizing a kernel…
The block-term tensor decomposition model with multilinear rank-$(L_r,L_r,1)$ terms (or, the "LL1 tensor decomposition" in short) offers a valuable alternative for hyperspectral unmixing (HU) under the linear mixture model. Particularly,…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
Wasserstein gradient and Hamiltonian flows have emerged as essential tools for modeling complex dynamics in the natural sciences, with applications ranging from partial differential equations (PDEs) and optimal transport to quantum…
In this paper, by mapping datasets to a set of non-linear coherent states, the process of encoding inputs in quantum states as a non-linear feature map is re-interpreted. As a result of this fact that the Radial Basis Function is recovered…
Kernel machines often yield superior predictive performance on various tasks; however, they suffer from severe computational challenges. In this paper, we show how to overcome the important challenge of speeding up kernel machines. In…
We present an algorithm for the identification of the relaxation kernel in the theory of diffusion systems with memory (or of viscoelasticity) which is linear, in the sense that we propose a linear Volterra integral equation of convolution…
In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…
While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the…
Integral equations are widely used in fields such as applied modeling, medical imaging, and system identification, providing a powerful framework for solving deterministic problems. While parameter identification for differential equations…
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…
Homogeneous polynomial dynamical systems (HPDSs), which can be equivalently represented by tensors, are essential for modeling higher-order networked systems, including ecological networks, chemical reactions, and multi-agent robotic…
We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. Remarkably, it is also possible to go…
The main focus of this paper is to approximate time series data based on the closed-loop Volterra series representation. Volterra series expansions are a valuable tool for representing, analyzing, and synthesizing nonlinear dynamical…
Our recent work lays out a general framework for inferring information about the parameters and associated dynamics of a differential equation model from a discrete set of data points collected from the system being modeled. Rigorous…