Related papers: Distributed Delay Differential Equation Representa…
We propose a physical analogy between finding the solution of an ordinary differential equation (ODE) and a $N$ particle problem in statistical mechanics. It uses the fact that the solution of an ODE is equivalent to obtain the minimum of a…
Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
Integrating dynamical systems models with time series data is a central part of contemporary mathematical biology. With the rich variety of available models and data, numerous methods and computational tools have been developed for these…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
Mathematical modelers have long known of a "rule of thumb" referred to as the Linear Chain Trick (LCT; aka the Gamma Chain Trick): a technique used to construct mean field ODE models from continuous-time stochastic state transition models…
In this study, a species-clustered ordinary differential equations (ODE) solver for chemical kinetics with large detailed mechanisms based on operator-splitting is presented. The ODE system is split into clusters of species by using graph…
The existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
Ordinary differential equations (ODE) are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the flow from one infection state to another. However, scientific…
Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…
This papers studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs). It presents a new framework using discrete ODEs as a central tool for computation and provides several implicit characterizations…
We study a class of linear ordinary differential equations (ODE)s with distributional coefficients. These equations are defined using an {\it intrinsic} multiplicative product of Schwartz distributions which is an extension of the…
This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and…
Discrete-event (DE) systems are concurrent programs where components communicate via tagged events, where tags are drawn from a totally ordered set. Reactors are an emerging model of computation based on DE and realized in the open-source…