Related papers: A new methodology to decompose a parametric domain…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the need for global triangulations or grids on the manifolds.…
Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction…
This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…
In this paper we study a new approach in optimization that aims to search a large domain D where a given function takes large, small or specific values via an iterative optimization algorithm based on the gradient. We show that the…
The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering…
Solving large scale entropic optimal transport problems with the Sinkhorn algorithm remains challenging, and domain decomposition has been shown to be an efficient strategy for problems on large grids. Unbalanced optimal transport is a…
We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…
We consider parameter identification problems in parametrized partial differential equations (PDE). This leads to nonlinear ill-posed inverse problems. One way to solve them are iterative regularization methods, which typically require…
We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus…
Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…
We propose a novel model for nonlinear dimension reduction motivated by the probabilistic formulation of principal component analysis. Nonlinearity is achieved by specifying different transformation matrices at different locations of the…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…
We present new methods for solving a broad class of bound-constrained nonsmooth composite minimization problems. These methods are specially designed for objectives that are some known mapping of outputs from a computationally expensive…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
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, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The new method is an iterative two-scale method that uses a parareal-like update scheme in combination with…