Related papers: Adaptive multiresolution analysis based on anisotr…
We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement…
Multiresolution topology optimization (MTO) methods involve decoupling of the design and analysis discretizations, such that a high-resolution design can be obtained at relatively low analysis costs. Recent studies have shown that the MTO…
Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
This paper introduces a new computational methodology for determining a-posteriori multi-objective error estimates for finite-element approximations, and for constructing corresponding (quasi-)optimal adaptive refinements of finite-element…
Hierarchical learning algorithms that gradually approximate a solution to a data-driven optimization problem are essential to decision-making systems, especially under limitations on time and computational resources. In this study, we…
A method is created to automatically increase the threshold projection parameter in three-field density-based topology optimization to achieve a near binary design. The parameter increase each iteration is based on an exponential growth…
We investigate the problem of fitting piecewise affine functions (PWA) to data. Our algorithm divides the input domain into finitely many polyhedral regions whose shapes are specified using a user-defined template such that the data points…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
We present a Reinforcement Learning (RL) solution to the view planning problem (VPP), which generates a sequence of view points that are capable of sensing all accessible area of a given object represented as a 3D model. In doing so, the…
Mesh adaptation for finite element approximation is a procedure used in numerous applications. The use of thin and long anisotropic triangles improves the efficiency of the procedure. When piecewise linear finite elements are used, the…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…