Related papers: Homogeneous Models of Nonlinear Circuits
Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to…
We consider an additive partially linear framework for modelling massive heterogeneous data. The major goal is to extract multiple common features simultaneously across all sub-populations while exploring heterogeneity of each…
We outline an approach that streamlines considerably the construction and analysis of well-behaved nonlinear quantum dynamics, with completely positive extensions to entangled systems. A few notes are added on the issue of quantum…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…
We analyze the effect of adding a weak, localized, inhomogeneity to a two dimensional array of oscillators with nonlocal coupling. We propose and also justify a model for the phase dynamics in this system. Our model is a generalization of a…
Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
In this paper, a practicable simulation-free model order reduction method by nonlinear moment matching is developed. Based on the steady-state interpretation of linear moment matching, we comprehensively explain the extension of this…
Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited…
Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas…
In this contribution, we propose a data-driven procedure to fit quadratic-bilinear surrogate models from data. Although the dynamics characterizing the original model are strongly nonlinear, we rely on lifting techniques to embed the…
This paper proposes a framework for analysis of generalized homogeneous control systems under state quantization. In particular, it addresses the challenge of maintaining finite/fixed-time stability of nonlinear systems in the presence of…
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…
Generalized linear models are flexible tools for the analysis of diverse datasets, but the classical formulation requires that the parametric component is correctly specified and the data contain no atypical observations. To address these…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
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 provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…
Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…