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We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…

Methodology · Statistics 2026-03-30 Kayhan Behdin , Riade Benbaki , Peter Radchenko , Rahul Mazumder

This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology - a flexible mathematical tool from algebraic…

Machine Learning · Statistics 2019-10-28 Umar Islambekov , Yulia Gel

In this paper, we introduce a Homogeneous Second-Order Descent Method (HSODM) using the homogenized quadratic approximation to the original function. The merit of homogenization is that only the leftmost eigenvector of a gradient-Hessian…

Optimization and Control · Mathematics 2025-04-08 Chuwen Zhang , Dongdong Ge , Chang He , Bo Jiang , Yuntian Jiang , Chenyu Xue , Yinyu Ye

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…

Numerical Analysis · Mathematics 2016-01-20 Kosala Bandara , Thomas Rüberg , Fehmi Cirak

We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…

Numerical Analysis · Mathematics 2025-10-14 Maria Vasilyeva , James Brannick , Ben S. Southworth

We introduce a novel computational framework for the multiscale simulation of higher-order continua that allows for the consideration of first-, second- and third- order effects at both micro- and macro-level. In line with classical…

Computational Engineering, Finance, and Science · Computer Science 2022-03-08 Felix Schmidt , Melanie Krüger , Marc-Andre Keip , Christian Hesch

We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we…

Methodology · Statistics 2024-11-21 Biao Cai , Jingfei Zhang , Will Wei Sun

The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic…

Analysis of PDEs · Mathematics 2023-01-18 Eduard Rohan , Jan Heczko

A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational…

Machine Learning · Computer Science 2022-10-11 Jiawei Huang , Ruomin Huang , Wenjie Liu , Nikolaos M. Freris , Hu Ding

This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…

Optimization and Control · Mathematics 2020-03-10 Xiaodong Cheng , Lanlin Yu , Dingchao Ren , Jacquelien M. A. Scherpen

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its…

Machine Learning · Computer Science 2019-04-12 Mireille El Gheche , Giovanni Chierchia , Pascal Frossard

The image classification machine learning model was trained with the intention to predict the category of the input image. While multiple state-of-the-art ensemble model methodologies are openly available, this paper evaluates the…

Machine Learning · Computer Science 2020-10-19 W. H. Huang

Engineers manually optimizing a structure using Finite Element based simulation software often employ an iterative approach where in each iteration they change the structure slightly and resimulate. Standard Finite Element based simulation…

Numerical Analysis · Mathematics 2018-03-09 Andreas Buhr , Christian Engwer , Mario Ohlberger , Stephan Rave

This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The…

Numerical Analysis · Computer Science 2014-10-23 Daniel Aubram

Common techniques for the spatial discretisation of PDEs on a macroscale grid include finite difference, finite elements and finite volume methods. Such methods typically impose assumed microscale structures on the subgrid fields, so…

Dynamical Systems · Mathematics 2022-04-15 J. E. Bunder , A. J. Roberts

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…

Numerical Analysis · Mathematics 2024-09-30 Cecilia Pagliantini , Federico Vismara

We present a decentralized model for autonomous reconfiguration of homogeneous pivoting cube modular robots in two dimensions. Each cube in the ensemble is controlled by a neural network that only gains information from other cubes in its…

Neural and Evolutionary Computing · Computer Science 2025-09-04 Nadezhda Dobreva , Emmanuel Blazquez , Jai Grover , Dario Izzo , Yuzhen Qin , Dominik Dold

High-fidelity physics simulations are powerful tools in the design and optimization of charged particle accelerators. However, the computational burden of these simulations often limits their use in practice for design optimization and…

Accelerator Physics · Physics 2020-04-15 Auralee Edelen , Nicole Neveu , Yannick Huber , Mattias Frey , Christopher Mayes , Andreas Adelmann

We introduce a new concept of sparsity for the stochastic elliptic operator $-{\rm div}\left(a(x,\omega)\nabla(\cdot)\right)$, which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially…

Numerical Analysis · Mathematics 2015-06-22 Thomas Y. Hou , Pengfei Liu

Confocal microscopy of fluorescent labeled particles has been used to study the dynamical and structural properties of colloidal and granular matter in real space. Localization algorithms allow for a fully automatized determination of the…

Soft Condensed Matter · Physics 2011-12-08 Marcel Roth , Michael Franzmann , Maria D'Acunzi , Max Kreiter , Günter K. Auernhammer