Related papers: Exact and Parametric Dynamical System Representati…
The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions.…
This paper presents a Fourier integral pseudospectral (FIPS) method for a general class of nonlinear, periodic optimal control (OC) problems with equality and/or inequality constraints and sufficiently smooth solutions. In this scheme, the…
The present paper treats the identification of nonlinear dynamical systems using Koopman-based deep state-space encoders. Through this method, the usual drawback of needing to choose a dictionary of lifting functions a priori is…
The challenge of finding exact and finite-dimensional Koopman embeddings of nonlinear systems has been largely circumvented by employing data-driven techniques to learn models of different complexities (e.g., linear, bilinear, input…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian…
The Finite Elements with Switch Detection (FESD) method is a highly accurate direct transcription method for optimal control of several classes of nonsmooth dynamical systems. This paper extends the FESD method to Projected Dynamical…
The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of disciplines and remains a central focus of active scientific…
The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the instrument to describe the behavior of systems with the…
We present a mathematical model: dynamical systems over finite sets (DSF), and we show that Boolean and discrete genetic models are special cases of DFS. In this paper, we prove that a function defined over finite sets with different number…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
Let $\psi$ and $F$ be positive definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical representations of $\psi$ by $F$, provided $\psi$ is…
Function fitting/approximation plays a fundamental role in computer graphics and other engineering applications. While recent advances have explored neural networks to address this task, these methods often rely on architectures with many…
The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding and index coding, and in the context of hat games, such as the guessing game and…
It has been recognized that using time-varying initialization functions to solve the initial value problem of fractional-order systems (FOS) is both complex and essential in defining the dynamical behavior of the states of FOSs. In this…
This paper develops methods for analyzing periodic orbits of states of linear feedback shift registers with periodic coefficients and estimating their lengths. These shift registers are among the simplest nonlinear feedback shift registers…
This note describes the full approximation storage (FAS) multigrid scheme for an easy one-dimensional nonlinear boundary value problem. The problem is discretized by a simple finite element (FE) scheme. We apply both FAS V-cycles and…
The present article is devoted to functions from a certain subclass of non-differentiable functions. The arguments and values of considered functions represented by the s-adic representation or the nega-s-adic representation of real…
We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which represents a limit on the practical simulation time. The…
The transformation of a nondeterministic finite-state automaton into a deterministic finite-state automaton is an integral part of any course on formal languages and automata theory. For some students, understanding this transformation is…