Related papers: Domain Overlapping Algorithm with Nonlinear Mappin…
In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm…
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…
The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…
This paper introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nystr\"om-collocation method using…
Most unsupervised image anomaly localization methods suffer from overgeneralization because of the high generalization abilities of convolutional neural networks, leading to unreliable predictions. To mitigate the overgeneralization, this…
Over-segmentation into superpixels is a very effective dimensionality reduction strategy, enabling fast dense image processing. The main issue of this approach is the inherent irregularity of the image decomposition compared to standard…
We present a domain decomposition-based deep learning method for solving elliptic and parabolic interface problems with discontinuous coefficients in two to ten dimensions. Our Multi-Activation Function (MAF) approach employs two…
We propose a new method to solve eigenvalue problems for linear and semilinear second order differential operators in high dimensions based on deep neural networks. The eigenvalue problem is reformulated as a fixed point problem of the…
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…
We use the Method of Difference Potentials (MDP) to solve a non-overlapping domain decomposition formulation of the Helmholtz equation. The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with…
In this paper, we propose a new feature selection method for unsupervised domain adaptation based on the emerging optimal transportation theory. We build upon a recent theoretical analysis of optimal transport in domain adaptation and show…
Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection…
Solving an optimization problem whose objective function is the sum of two convex functions has received considerable interests in the context of image processing recently. In particular, we are interested in the scenario when a…
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 ROBO (Riemannian Overlapping Block Optimization), a distributed and parallel approach to multi-robot pose graph optimization (PGO) based on the idea of overlapping domain decomposition. ROBO offers a middle ground between…
In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in $\mathbb{R}^n$. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
In this paper, a new framework for continuous-time maximum a posteriori estimation based on the Chebyshev polynomial optimization (ChevOpt) is proposed, which transforms the nonlinear continuous-time state estimation into a problem of…