Related papers: Space-Time Nonlinear Upscaling Framework Using Non…
This paper treats comprehensively the construction of problems from nonlinear dynamics and constrained optimization amenable to parameter continuation techniques and with particular emphasis on multi-segment boundary-value problems with…
In this paper, a two-dimensional incompressible miscible displacement model is considered, and a novel decoupled and linearized high-order finite difference scheme is developed, by utilizing the multi-time-step strategy to treat the…
In multiscale modelling, multiple models are used simultaneously to describe scale-dependent phenomena in a system of interest. Here we introduce a machine learning (ML)-based multiscale modelling framework for modelling hierarchical…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
Recent works on deep non-linear spatially selective filters demonstrate exceptional enhancement performance with computationally lightweight architectures for stationary speakers of known directions. However, to maintain this performance in…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the…
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…
We propose a novel deep-learning framework for super-resolution ultrasound images and videos in terms of spatial resolution and line reconstruction. We up-sample the acquired low-resolution image through a vision-based interpolation method;…
Subspace clustering has become widely adopted for the unsupervised analysis of hyperspectral images (HSIs). Recent model-aware deep subspace clustering methods often use a two-stage framework, involving the calculation of a…
Deep models are designed to operate on huge volumes of high dimensional data such as images. In order to reduce the volume of data these models must process, we propose a set-based two-stage end-to-end neural subsampling model that is…
Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
Spatial time series forecasting problems arise in a broad range of applications, such as environmental and transportation problems. These problems are challenging because of the existence of specific spatial, short-term and long-term…
The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to…