Related papers: Structure Discrimination in Block-Oriented Models …
The Koopman operator approach provides a powerful linear description of nonlinear dynamical systems in terms of the evolution of observables. While the operator is typically infinite-dimensional, it is crucial to develop finite-dimensional…
This text aims at providing a bird's eye view of system identification with special attention to nonlinear systems. The driving force is to give a feeling for the philosophical problems facing those that build mathematical models from data.…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
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…
Nonlinear approximation from regular piecewise polynomials (splines) of degree $<k$ supported on rings in $\R^2$ is studied. By definition a ring is a set in $\R^2$ obtained by subtracting a compact convex set with polygonal boundary from…
We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group…
In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links.…
Nonlinear topological insulators have garnered substantial recent attention as they have both enabled the discovery of new physics due to interparticle interactions, and may have applications in photonic devices such as topological lasers…
Complex dynamical systems are notoriously difficult to model because some degrees of freedom (e.g., small scales) may be computationally unresolvable or are incompletely understood, yet they are dynamically important. For example, the small…
Scientific studies increasingly collect multiple modalities of data to investigate a phenomenon from several perspectives. In integrative data analysis it is important to understand how information is heterogeneously spread across these…
Curvilinear structures, which include line-like continuous objects, are fundamental geometrical elements in image-based applications. Reconstructing these structures from images constitutes a pivotal research area in computer vision.…
Nonlinear adaptive filtering allows for modeling of some additional aspects of a general system and usually relies on highly complex algorithms, such as those based on the Volterra series. Through the use of the Kronecker product and some…
We introduce a Bayesian extension of the latent block model for model-based block clustering of data matrices. Our approach considers a block model where block parameters may be integrated out. The result is a posterior defined over the…
An emerging class of trajectory optimization methods enforces collision avoidance by jointly optimizing the robot's configuration and a separating hyperplane. However, as linear separators only apply to convex sets, these methods require…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…
We propose a probabilistic extension of Wiener-Laguerre models for causal operator learning. Classical Wiener-Laguerre models parameterize stable linear dynamics using orthonormal Laguerre bases and apply a static nonlinear map to the…
Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…