Related papers: An algorithm for distributed time delay identifica…
We address in this paper the approximation problem of distributed delays. Such elements are convolution operators with kernel having bounded support, and appear in the control of time-delay systems. From the rich literature on this topic,…
In this paper, we propose a new algorithm for the estimation of multiple time delays (TDs). Since a TD is a fundamental spatial cue for sensor array signal processing techniques, many methods for estimating it have been studied. Most of…
We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
Distributed optimization finds applications in large-scale machine learning, data processing and classification over multi-agent networks. In real-world scenarios, the communication network of agents may encounter latency that may affect…
In the paper an efficient semi-analytical approach based on the method of steps and differential transformation is proposed for numerical approximation of solutions of retarded logistic models of delayed and neutral type, including models…
We present a graph-theoretical approach that can detect which equations of a delay differential-algebraic equation (DDAE) need to be differentiated or shifted to construct a solution of the DDAE. Our approach exploits the observation that…
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…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This…
A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…
Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…
By integrating edge computing with parallel computing, distributed edge computing (DEC) makes use of distributed devices in edge networks to perform computing in parallel, which can substantially reduce service delays. In this paper, we…
Deploying reinforcement learning (RL) in safety-critical settings is constrained by brittleness under distribution shift. We study out-of-distribution (OOD) detection for RL time series and introduce DEEDEE, a two-statistic detector that…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral…
We establish a discrete operator--theoretic framework for the analysis of implicit Euler and Lie--Trotter splitting schemes for delay differential equations (DDEs). Both schemes are formulated in terms of discrete resolvent operators acting…
We analyze convergence of decentralized cooperative online estimation algorithms by a network of multiple nodes via information exchanging in an uncertain environment. Each node has a linear observation of an unknown parameter with randomly…
We design a Linear Chain Trick (LCT)-algorithm for dynamical systems with distributed time delay where the time histories contain temporal oscillations. The methodology is illustrated by means of an example in population dynamics.
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…