Related papers: Carleman Linearization of Differential-Algebraic E…
Carleman linearization is a technique that embeds systems of ordinary differential equations with polynomial nonlinearities into infinite dimensional linear systems in a procedural way. In this paper we generalize the method for systems of…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate the well-posedness and convergence of the truncated Carleman…
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…
The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fixed points. We propose and test three different versions of a…
Nonlinear dynamical systems are widely encountered in various scientific and engineering fields. Despite significant advances in theoretical understanding, developing complete and integrated frameworks for analyzing and designing these…
The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman…
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…
The Carleman linearization is one of the mainstream approaches to lift a finite-dimensional nonlinear dynamical system into an infinite-dimensional linear system with the promise of providing accurate approximations of the original…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introduced bi-level variational quantum PDE constrained…
Nonlinearity presents a significant challenge in problems involving dynamical systems, prompting the exploration of various linearization techniques, including the well-known Carleman Linearization. In this paper, we introduce the Koopman…
Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…
In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that we employ a particular embedding (Carleman linearization) to…
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a…
The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must…
Infinite-dimensional differential algebraic equations (short DAEs) with input and output are studied. The concepts of operator nodes and system nodes are extended to systems which additionally may include algebraic constraints.…
Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup…