Related papers: Holistic discretisation ensures fidelity to dynami…
Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
Systems of reaction-diffusion partial differential equations (RD-PDEs) are widely applied for modelling life science and physico-chemical phenomena. In particular, the coupling between diffusion and nonlinear kinetics can lead to the…
This paper proposes a new hybrid high-order discretization for the biharmonic problem and the corresponding eigenvalue problem. The discrete ansatz space includes degrees of freedom in $n-2$ dimensional submanifolds (e.g., nodal values in…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…
Solving the reactive low-Mach Navier-Stokes equations with high-order adaptive methods in time is still a challenging problem, in particular due to the handling of the algebraic variables involved in the mass constraint. We focus on the…
We introduce a simplified technique for incorporating diffusive phenomena into lattice-gas molecular dynamics models. In this method, spatial interactions take place one dimension at a time, with a separate fractional timestep devoted to…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
Consider the macroscale modelling of microscale spatiotemporal dynamics. Here we develop a new approach to ensure coarse scale discrete models preserve important self-adjoint properties of the fine scale dynamics. The first part explores…
We study whether fine discretization (i.e., terracing) of continuous pair interactions, when used in combination with first-order mean-spherical approximation theory, can lead to a simple and general analytical strategy for predicting the…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
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 address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we discretize the spatial variable and obtain a lattice dynamical system with a hysteretic…
Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…