Related papers: Formalising the Continuous/Discrete Modeling Step

Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…

We give an overview of time-continuous pedestrian models with a focus on data-driven modelling. Starting from pioneer, reactive force-based models we move forward to modern, active pedestrian models with sophisticated collision-avoidance…

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme which treat the nonlinear term explicitly (backward differentiation formula with a one-leg method). Uniform bounds on…

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated…

Image animation is the task of transferring the motion of a driving video to a given object in a source image. While great progress has recently been made in unsupervised motion transfer, requiring no labeled data or domain priors, many…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…

The slow iterative sampling nature remains a major bottleneck for the practical deployment of diffusion and flow-based generative models. While consistency models (CMs) represent a state-of-the-art distillation-based approach for efficient…

Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…

Behavioral models play an essential role in Model-driven engineering (MDE). Keeping inter-related behavioral models consistent is critical to use them successfully in MDE. However, consistency checking for behavioral models, especially in a…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Mechanical systems are most often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs) of a particular structure governed by the covariant derivative. The digital implementation of controllers for…

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…

We present a novel approach that redefines the traditional interpretation of explicit and implicit discretization methods for solving a general class of advection-diffusion equations (ADEs) featuring nonlinear advection, diffusion…

Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback…

We begin by reviewing a technique to approximate the dynamics of stochastic programs --written in a stochastic process algebra-- by a hybrid system, suitable to capture a mixed discrete/continuous evolution. In a nutshell, the discrete…

Learning models of dynamical systems with external inputs, which may be, for example, nonsmooth or piecewise, is crucial for studying complex phenomena and predicting future state evolution, which is essential for applications such as…

Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are…

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…