Related papers: A variational-level-set based partitioning method …
We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…
In this paper, we consider numerical approximations for the optimal partition problem using Lagrange multipliers. By rewriting it into constrained gradient flows, three and four steps numerical schemes based on the Lagrange multiplier…
The segmentation of plant roots from soil and other growing media in X-ray computed tomography images is needed to effectively study the root system architecture without excavation. However, segmentation is a challenging problem in this…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
Deep Neural Network (DNN) models are usually trained sequentially from one layer to another, which causes forward, backward and update locking's problems, leading to poor performance in terms of training time. The existing parallel…
This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…
Group convolution has been widely used in order to reduce the computation time of convolution, which takes most of the training time of convolutional neural networks. However, it is well known that a large number of groups significantly…
In this paper, the traditional model based variational method and learning based algorithms are naturally integrated to address mixed noise removal problem. To be different from single type noise (e.g. Gaussian) removal, it is a challenge…
We consider the solution of a stochastic convex optimization problem $\mathbb{E}[f(x;\theta^*,\xi)]$ over a closed and convex set $X$ in a regime where $\theta^*$ is unavailable and $\xi$ is a suitably defined random variable. Instead,…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the…
Level set methods are widely used for image segmentation because of their capability to handle topological changes. In this paper, we propose a novel parametric level set method called Disjunctive Normal Level Set (DNLS), and apply it to…
Various traditional numerical methods for solving initial value problems of differential equations often produce local solutions near the initial value point, despite the problems having larger interval solutions. Even current popular…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations. The convergence rate of the block Cimmino algorithm depends on…
We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to $\mathbb{R}^3$ of our two-dimensional strategy in [DOI: 10.1007/s10915-022-01952-2][1] and the hybrid inference system of [DOI:…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…