Related papers: Distributed Delay Differential Equation Representa…
Natural laws are often described through differential equations yet finding a differential equation that describes the governing law underlying observed data is a challenging and still mostly manual task. In this paper we make a step…
Neural ordinary differential equations describe how values change in time. This is the reason why they gained importance in modeling sequential data, especially when the observations are made at irregular intervals. In this paper we propose…
We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…
The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…
This paper deals with the numerical integration of well-posed multiscale systems of ODEs or evolutionary PDEs. As these systems appear naturally in engineering problems, time-subcycling techniques are widely used every day to improve…
We consider delay differential equations with a polynomially distributed delay. We derive an equivalent system of delay differential equations, which includes just two discrete delays. The stability of the equivalent system and its…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
Predicting counterfactual distributions in complex dynamical systems is essential for scientific modeling and decision-making in domains such as public health and medicine. However, existing methods often rely on point estimates or purely…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…
Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient continuous-time way to model functions of potentially…
Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…
We consider the model of economic growth with time delayed investment function. Assuming the investment is time distributed we can use the linear chain trick technique to transform delay differential equation system to equivalent system of…
Many physical systems are governed by ordinary or partial differential equations (see, for example, Chapter ''Differential equations'', ''System of Differential Equations''). Typically the solution of such systems are functions of time or…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of…