Related papers: Mass-Matrix Differential-Algebraic Equation Formul…
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…
These lecture notes are a concise introduction of recent techniques to prove local spectral universality for a large class of random matrices. The general strategy is presented following the recent book with H.T. Yau. We extend the scope of…
In this paper, the stability of $\theta$-methods for delay differential equations is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay and $A$ is a positive definite matrix. It is mainly…
This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…
The problem of late time instability in time domain integral equations for electromagnetics is longstanding. While several techniques have been suggested for addressing this problem, they either require impractically high degrees of freedom…
Existing dynamics prediction frameworks for transient stability analysis (TSA) fail to achieve multi-scenario "universality": the inherent ability of a single, pre-trained architecture to generalize across diverse operating conditions,…
We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of…
Power system dynamic modeling involves nonlinear differential and algebraic equations (DAEs). Solving DAEs for large power grid networks by direct implicit numerical methods could be inefficient in terms of solution time; thus, such methods…
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…
The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can…
System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
In this paper, we study jumps of nonlinear DAEs caused by inconsistent initial values. First, we propose a simple normal form called the index-1 nonlinear Weierstrass form (INWF) for nonlinear DAEs. Then we generalize the notion of…
Variational autoencoder is a powerful deep generative model with variational inference. The practice of modeling latent variables in the VAE's original formulation as normal distributions with a diagonal covariance matrix limits the…
This paper proposes a new semi-analytical approach for online time-domain power system simulation. The approach applies the differential transformation method (DTM) to the power system differential equation model to offline derive a…
Multirate behavior of ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) is characterized by widely separated time constants in different components of the solution or different additive terms of the…
This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…
Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…
Time domain simulation is the basis of dynamic security assessment for power systems. Traditionally, numerical integration methods are adopted by simulation software to solve nonlinear power system differential-algebraic equations about any…
We analyze the convergence of the harmonic balance method for computing isolated periodic solutions of a large class of continuously differentiable Hilbert space valued differential-algebraic equations (DAEs). We establish asymptotic…