Related papers: Index Reduction for Differential-Algebraic Equatio…
Digital Image Correlation (DIC) is a powerful tool used to evaluate displacements and deformations in a non-intrusive manner. By comparing two images, one of the undeformed reference state of a specimen and another of the deformed target…
A fast metasurface optimization strategy for finite-size metasurfaces modeled using integral equations is presented. The metasurfaces considered are constructed from finite patterned metallic claddings supported by grounded dielectric…
Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…
In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across…
The Pantelides algorithm for delay differential-algebraic equations (DDAEs) is a method to structurally analyse such systems with the goal to detect which equations have to be differentiated or shifted to construct a solution. In this…
Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential…
In this work, we propose a novel backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations (BSDEs), where the deep neural network (DNN) models are trained not only…
Matrix differential-difference Lax pairs play an essential role in the theory of integrable nonlinear differential-difference equations. We present sufficient conditions which allow one to simplify such a Lax pair by matrix gauge…
In this study, perturbation-iteration algorithm, namely PIA, is applied to solve some types of system of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are…
Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…
This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…
We consider fast deterministic algorithms to identify the "best" linearly independent terms in multivariate mixtures and use them to compute, up to a user-selected accuracy, an equivalent representation with fewer terms. One algorithm…
The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying…
Data envelopment analysis (DEA) is a linear program (LP)-based method used to determine the efficiency of a decision making unit (DMU), which transforms inputs to outputs, by peer comparison. This paper presents a new computation algorithm…
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…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
Different representations of dissipative Hamiltonian and port-Hamiltonian differential-algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between the different…
Missing data is a widespread problem in many domains, creating challenges in data analysis and decision making. Traditional techniques for dealing with missing data, such as excluding incomplete records or imputing simple estimates (e.g.,…