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We propose an adaptive algorithm for identifying the unknown parameter in a linear exponentially stable single-input single-output infinite-dimensional system. We assume that the transfer function of the infinite-dimensional system can be…
In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
We develop data-driven dynamical models of the nonlinear aeroelastic effects on a long-span suspension bridge from sparse, noisy sensor measurements which monitor the bridge. Using the {\em sparse identification of nonlinear dynamics}…
Many studies on acoustic radiation forces focus on characterizing the behavior of acoustic fields. However, the dynamic response of objects, particularly those larger than the wavelength, remains underexplored. Here we bridge this gap by…
This research proposes a new method for approximating the solution of the inverse problem of finding a rational function that generates known local dynamics within distinct, disjoint closed balls in non-Archimedean fields. Although our…
Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…
Air vehicles of all scales are susceptible to large-amplitude gusts that may lead to vehicle damage and instability. Therefore, effective physics-based control strategies and an understanding of the dominant unsteady flow physics…
This paper presents an Adaptive Gain Nonlinear Observer (AGNO) for estimating the external interaction wrench (forces and torques) in human-UAV physical interaction for assistive payload transportation. The proposed AGNO uses the full…
This paper deals with the error processing problem of sparse identification of nonlinear dynamical systems(SINDy) through introducing the $L_\infty$ approximation to take place of the former $L_2$ approximation. The motivation is that the…
This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. Although SINDy is recognized as a remarkable approach for identifying nonlinear…
Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system…
The Sparse Identification of Nonlinear Dynamics (SINDy) framework has been frequently used to discover parsimonious differential equations governing natural and physical systems. This includes recent extensions to SINDy that enable the…
Using a perturbative approach, we investigate the parametric down-conversion process without the semi-classical approximation. A Wigner functional formalism, which incorporates both the spatiotemproal degrees of freedom and the…
We explore the issues of identification for nonlinear Impulse Response Functions in nonlinear dynamic models and discuss the settings in which the problem can be mitigated. In particular, we introduce the nonlinear autoregressive…
A new series expansion for the the Airy function is presented here that stems from the method of steepest descents and can be related to the Hadamard expansions as presented in prevous works cited in the manuscript, and which is convergent…
The classical theory of lift is confined to sharp edged airfoils. The search for a more general closure condition in potential flow remained elusive for over a century. Recently, a variational theory of lift, inspired by Gauss's principle…
Lagrangian descriptors provide a global dynamical picture of the geometric structures for arbitrarily time-dependent flows with broad applications. This paper develops a mathematical framework for computing Lagrangian descriptors when…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
Specific solutions of the nonlinear Schr\"odinger equation, such as the Peregrine breather, are considered to be prototypes of extreme or freak waves in the oceans. An important question is, whether these solutions also exist in the…