Related papers: Differential algebraic system nodes
Lie algebraic techniques are powerful and widely-used tools for studying dynamics and metrology in quantum optics. When the Hamiltonian generates a Lie algebra with finite dimension, the unitary evolution can be expressed as a finite…
Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…
We study a deflation method to reduce and to solve linear dfferential-algebraic equations (DAEs). It consists to define a sequence of DAEs with index reduction of one unit by step. This is simultaneously performed by substitution and…
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…
In this paper, we consider the spectral theory of linear differential-algebraic equations (DAEs) for periodic DAEs in canonical form, i.e., \begin{equation*} J \frac{df}{dt}+Hf=\lambda Wf, \end{equation*} where $J$ is a constant…
We consider initial value problems for differential-algebraic equations in a possibly infinite-dimensional Hilbert space. Assuming a growth condition for the associated operator pencil, we prove existence and uniqueness of solutions for…
Real-world phenomena can often be conveniently described by dynamical systems (that is, ODE systems in the state-space form). However, if one observes the state of the system only partially, the observed quantities (outputs) and the inputs…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces…
Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…
Deep Learning has emerged as one of the most significant innovations in machine learning. However, a notable limitation of this field lies in the ``black box" decision-making processes, which have led to skepticism within groups like…
This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules…
This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations…
As an algebraic study of differential equations, differential algebras have been studied for a century and and become an important area of mathematics. In recent years the area has been expended to the noncommutative associative and Lie…
Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…
We tersely review a recently introduced technique to identify systems of two nonlinearly-coupled Ordinary Di{\S}erential Equations (ODEs) solvable by algebraic operations; and we report some specifc examples of this kind, namely systems of…
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…
Differential-algebraic equations (DAEs) arise naturally in constrained dynamical systems, but their algebraic constraints and hidden compatibility conditions make them more subtle than standard ordinary differential equations. This paper…
We provide an introduction to infinite-dimensional port-Hamiltonian systems. As this research field is quite rich, we restrict ourselves to the class of infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial…
We are concerned with the arithmetic of solutions to ordinary or partial nonlinear differential equations which are algebraic in the indeterminates and their derivatives. We call these solutions D-algebraic functions, and their equations…