Related papers: Structural Analysis by Modified Signature Matrix f…
To find consistent initial data points for a system of differential-algebraic equations, requires the identification of its missing constraints. An efficient class of structural methods exploiting a dependency graph for this task was…
Systems of differential-algebraic equations (DAEs) are generated routinely by simulation and modeling environments such as Modelica and MapleSim. Before a simulation starts and a numerical solution method is applied, some kind of structural…
Differential-algebraic equation systems (DAEs) are generated routinely by simulation and modeling environments. Before a simulation starts and a numerical method is applied, some kind of structural analysis (SA) is used to determine which…
Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAEs), i.e., constraints of the form f(\dot{x},x,u)=0. This drastically facilitates modeling from first…
Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. In numerical analysis of DAEs, consistent initialization and index reduction are important preprocessing prior to numerical integration. Existing DAE…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
A key step in mechanistic modelling of dynamical systems is to conduct a structural identifiability analysis. This entails deducing which parameter combinations can be estimated from a given set of observed outputs. The standard…
Differential-algebraic equations (DAEs) have been used in modeling various dynamical systems in science and engineering. Several preprocessing methods for DAEs, such as consistent initialization and index reduction, use structural…
Motivated by Pryce's structural index reduction method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm and propose a fixed-point iteration method with parameters. It leads to a…
Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. The difficulty in solving numerically a DAE is measured by its differentiation index. For highly accurate simulation of dynamical systems, it is…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
In a previous article, the authors developed two conversion methods to improve the $\Sigma$-method for structural analysis (SA) of differential-algebraic equations (DAEs). These methods reformulate a DAE on which the $\Sigma$-method fails…
In this manuscript we consider Intrinsic Stochastic Differential Equations on manifolds and constrain it to a level set of a smooth function. Such type of constraints are known as explicit algebraic constraints. The system of differential…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
Abstract differential-algebraic equations (ADAEs) of a semilinear type are studied. Theorems on the existence and uniqueness of solutions and the maximal interval of existence, on the global solvability of the ADAEs, the boundedness of…
The $\Sigma$-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the…
Structural entropy is a metric that measures the amount of information embedded in graph structure data under a strategy of hierarchical abstracting. To measure the structural entropy of a dynamic graph, we need to decode the optimal…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
Structural analysis is a method for verifying equation-oriented models in the design of industrial systems. Existing structural analysis methods need flattening of the hierarchical models into an equation system for analysis. However, the…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…