相关论文: Dynamical System Inspired Adaptive Time Stepping C…

It has been found that residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODEs). In this paper, we explore a deeper relationship between Transformer and numerical methods of ODEs. We show that a…

We study stability issue of reset and impulsive switched systems. We find time constraints (dwell time and flee time) on switching signals which stabilize a given reset switched system. For a given collection of matrices, we find an…

The stiffness of the Hodgkin-Huxley (HH) equations during an action potential (spike) limits the use of large time steps. We observe that the neurons can be evolved independently between spikes, $i.e.,$ different neurons can be evolved with…

This paper considers the fixed-time control problem of a multi-agent system composed of a class of Euler-Lagrange dynamics with parametric uncertainty and a dynamic leader under a directed communication network. A distributed fixed-time…

In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…

Real-world network systems are inherently dynamic, with network topologies undergoing continuous changes over time. Previous works often focus on static networks or rely on complete prior knowledge of evolving topologies, whereas real-world…

Time integration of Fourier pseudo-spectral DNS is usually performed using the classical fourth-order accurate Runge--Kutta method, or other methods of second or third order, with a fixed step size. We investigate the use of higher-order…

We analyze the input-output behavior of residual networks from a dynamical system point of view by disentangling the residual dynamics from the output activities before the classification stage. For a network with simple skip connections…

The exponential time differencing (ETD) method allows using a large time step to efficiently evolve the stiff system such as Hodgkin-Huxley (HH) neural networks. For pulse-coupled HH networks, the synaptic spike times cannot be…

Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…

Deep neural networks have achieved state-of-the-art performance in a variety of fields. Recent works observe that a class of widely used neural networks can be viewed as the Euler method of numerical discretization. From the numerical…

Accurate forecasting of energy demand and supply is critical for optimizing sustainable energy systems, yet it is challenged by the variability of renewable sources and dynamic consumption patterns. This paper introduces a neural framework…

Recurrent Neural Networks excel at predicting and generating complex high-dimensional temporal patterns. Due to their inherent nonlinear dynamics and memory, they can learn unbounded temporal dependencies from data. In a Machine Learning…

Adaptive control is a classical control method for complex cyber-physical systems, including transportation networks. In this work, we analyze the convergence properties of such methods on exemplar graphs, both theoretically and…

The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work…

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation…

Gradient-based methods for the distributed training of residual networks (ResNets) typically require a forward pass of the input data, followed by back-propagating the error gradient to update model parameters, which becomes time-consuming…

This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…

The work deals with two major topics concerning the numerical analysis of Runge-Kutta-like (RK-like) methods, namely their stability and order of convergence. RK-like methods differ from additive RK methods in that their coefficients are…