Related papers: A Dynamical Model for Spatio-Temporal Processes Mo…
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…
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…
We study the general dynamics of the spherically symmetric gravitational collapse of a massless scalar field. We apply the Galerkin projection method to transform a system of partial differential equations into a set of ordinary…
Recent improvements in the expressive power of spatio-temporal models have led to performance gains in many real-world applications, such as traffic forecasting and social network modelling. However, understanding the predictions from a…
Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier--Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilised using a…
Moment estimation for stochastic differential equations (SDEs) is fundamental to the formal reasoning and verification of stochastic dynamical systems, yet remains challenging and is rarely available in closed form. In this paper, we study…
Explicit, unconditionally stable, high-order schemes for the approximation of some first- andsecond-order linear, time-dependent partial differential equations (PDEs) are proposed.The schemes are based on a weak formulation of a…
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…
Spatiotemporal prediction is important in solving natural problems and processing video frames, especially in weather forecasting and human action recognition. Recent advances attempt to incorporate prior physical knowledge into the deep…
High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…
System dynamics (SD) is an effective approach for helping reveal the temporal behavior of complex systems. Although there have been recent developments in expanding SD to include systems' spatial dependencies, most applications have been…
Formulated is a new systematic method for obtaining higher order corrections in numerical simulation of stochastic differential equations (SDEs), i.e., Langevin equations. Random walk step algorithms within a given order of finite $\Delta…
System identification in scenarios where the observed number of variables is less than the degrees of freedom in the dynamics is an important challenge. In this work we tackle this problem by using a recognition network to increase the…
This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…
Most practical engineering design problems involve nonlinear spatio-temporal dynamical systems. Multi-physics simulations are often performed to capture the fine spatio-temporal scales which govern the evolution of these systems. However,…
We analyse a second-order SPDE model in multiple space dimensions and develop estimators for the parameters of this model based on discrete observations of a solution in time and space on a bounded domain. While parameter estimation for one…
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…
This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics of weakly compressible fluids. The mathematical model is…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We develop a spatio-temporal model to forecast sensor output at five locations in North East England. The signal is described using coupled dynamic linear models, with spatial effects specified by a Gaussian process. Data streams are…