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Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
This work presents a supervised learning based approach to the computer vision problem of frame interpolation. The presented technique could also be used in the cartoon animations since drawing each individual frame consumes a noticeable…
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
Particulate flows have been largely studied under the simplifying assumptions of one-way coupling regime where the disperse phase do not react-back on the carrier fluid. In the context of turbulent flows, many non trivial phenomena such as…
Traditional approaches to interpolate/extrapolate frames in a video sequence require accurate pixel correspondences between images, e.g., using optical flow. Their results stem on the accuracy of optical flow estimation, and could generate…
This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…
Deep learning based methods have penetrated many image processing problems and become dominant solutions to these problems. A natural question raised here is "Is there any space for conventional methods on these problems?" In this paper,…
In this paper we present a novel method to overcome membrane locking of thin shells. An interpolation operator into the so-called Regge finite element space is inserted in the membrane energy term to weaken the implicitly given kernel…
Singular Value Decomposition (SVD) is a well studied research topic in many fields and applications from data mining to image processing. Data arising from these applications can be represented as a matrix where it is large and sparse. Most…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to…
This paper addresses enforcing non-vanishing constraints for solutions to a second order elliptic partial differential equation by appropriate choices of boundary conditions. We show that, in dimension $d\geq2$, under suitable regularity…
Image resizing is a basic tool in image processing and in literature we have many methods, based on different approaches, which are often specialized in only upscaling or downscaling. In this paper, independently of the (reduced or…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
We develop here a computationally effective approach for producing high-quality $\mathcal{H}_\infty$-approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an approach for…
Modern machine learning paradigms, such as deep learning, occur in or close to the interpolation regime, wherein the number of model parameters is much larger than the number of data samples. In this work, we propose a regularity condition…
In this article, we derive fast and robust parallel-in-time preconditioned iterative methods for the all-at-once linear systems arising upon discretization of time-dependent PDEs. The discretization we employ is based on a Runge--Kutta…