相关论文: Approximating a flexible beam model in the Loewner…

The problem of data-driven control is addressed here in the context of switched affine systems. This class of nonlinear systems is of particular importance when controlling many types of applications in electronic, biology, medicine, etc.…

This paper employs a fully adaptive and semi-adaptive frequency sweep algorithm using the Loewner matrix-based state model for the electromagnetic simulation. The proposed algorithms use two Loewner matrix models with different or the same…

In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…

Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In…

We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…

We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…

The Loewner equation (LE) is used to obtain conformal mappings that lead to exact and analytical expressions for several electrostatic properties of realistic quasi-unidimensional nanoelectromechanical systems (NEMS). The LE approach also…

We propose a trajectory-based quasiclassical method for approximating dynamics in condensed phase systems. Building upon the previously developed Optimized Mean Trajectory (OMT) approximation that has been used to compute linear and…

This paper presents a Carleman-Fourier linearization method for nonlinear dynamical systems with periodic vector fields involving multiple fundamental frequencies. By employing Fourier basis functions, the nonlinear dynamical system is…

Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding…

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…

We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called spin-PLDM. Within a classical trajectory picture, partially linearized…

We consider the problem of estimating missing values in trajectories of linear parameter-varying (LPV) systems. We solve this interpolation problem for the class of shifted-affine LPV systems. Conditions for the existence and uniqueness of…

We show that the standard discrete update rule of transformer layers can be naturally interpreted as a forward Euler discretization of a continuous dynamical system. Our Transformer Flow Approximation Theorem demonstrates that, under…

Control invariant set is critical for guaranteeing safe control and the problem of computing control invariant set for linear discrete-time system is revisited in this paper by using a data-driven approach. Specifically, sample points on…

We introduce the parafermionic truncated Wigner approximation ($p$TWA), a semiclassical phase-space framework for simulating the nonequilibrium dynamics of lattice systems with fractional exchange statistics. The method extends truncated…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

We present a mathematical and numerical analysis on a control model for the time evolution of a multi-layered piezoelectric cantilever with tip mass and moment of inertia, as developed by Kugi and Thull [31]. This closed-loop control system…

This work aims at tackling the problem of learning surrogate models from noisy time-domain data by means of matrix pencil-based techniques, namely the Hankel and Loewner frameworks. A data-driven approach to obtain reduced-order state-space…