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Many large-scale optimization problems arising in science and engineering are naturally defined at multiple levels of discretization or model fidelity. Multilevel methods exploit this hierarchy to accelerate convergence by combining coarse-…
Extracting and fusing part features have become the key of fined-grained image recognition. Recently, Non-local (NL) module has shown excellent improvement in image recognition. However, it lacks the mechanism to model the interactions…
Motivated by problems from neuroimaging in which existing approaches make use of "mass univariate" analysis which neglects spatial structure entirely, but the full joint modelling of all quantities of interest is computationally infeasible,…
This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…
This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…
In this paper, we develop a Bayesian multiscale approach based on a multiscale finite element method. Because of scale disparity in many multiscale applications, computational models can not resolve all scales. Various subgrid models are…
As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle…
There is a rich literature on clustering functional data with applications to time-series modeling, trajectory data, and even spatio-temporal applications. However, existing methods routinely perform global clustering that enforces…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
We develop a mixed finite element domain decomposition method on non-matching grids for the Biot system of poroelasticity. A displacement-pressure vector mortar function is introduced on the interfaces and utilized as a Lagrange multiplier…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
We present a progressive image decomposition method based on a novel non-linear filter named Sub-window Variance filter. Our method is specifically designed for image detail enhancement purpose; this application requires extraction of image…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
Stationary subspace analysis (SSA) is a blind source separation framework that decomposes linearly mixed multivariate data into stationary and nonstationary components. We extend SSA to spatially indexed data by introducing spatial…
Recent semi-dense image matching methods have achieved remarkable success, but two long-standing issues still impair their performance. At the coarse stage, the over-exclusion issue of their mutual nearest neighbor (MNN) matching layer…
This is a study of a class of nonlocal nonlinear diffusion equations. We present a strong maximum principle for nonlocal time-dependent Dirichlet problems. Results are for bounded functions of space, rather than (semi)-continuous functions.…
High resolution depth-maps, obtained by upsampling sparse range data from a 3D-LIDAR, find applications in many fields ranging from sensory perception to semantic segmentation and object detection. Upsampling is often based on combining…