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Finding valuable training data points for deep neural networks has been a core research challenge with many applications. In recent years, various techniques for calculating the "value" of individual training datapoints have been proposed…

Machine Learning · Computer Science 2021-04-29 Soumi Das , Arshdeep Singh , Saptarshi Chatterjee , Suparna Bhattacharya , Sourangshu Bhattacharya

We consider the problem of the construction of the acoustic structure of arbitrary geometry with prescribed desired properties. We use optimization approach for the solution of this problem and minimize the Tikhonov functional on adaptively…

Numerical Analysis · Mathematics 2017-10-06 Larisa Beilina , Eugene Smolkin

This paper presents the development and analysis of an asymptotically compatible (AC) unfitted finite element method for one-dimensional nonlocal elliptic interface problems. The proposed method achieves optimal error estimates through…

Numerical Analysis · Mathematics 2025-12-23 Haixia Dong , Ziqing Xie , Jiwei Zhang

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive…

Optimization and Control · Mathematics 2024-04-18 Bangti Jin , Jing Li , Yifeng Xu , Shengfeng Zhu

This paper is concerned with a priori error estimates for the local incremental minimization scheme, which is an implicit time discretization method for the approximation of rate-independent systems with non-convex energies. We first show…

Numerical Analysis · Mathematics 2021-05-03 Christian Meyer , Michael Sievers

In the algorithm selection research, the discussion surrounding algorithm features has been significantly overshadowed by the emphasis on problem features. Although a few empirical studies have yielded evidence regarding the effectiveness…

Machine Learning · Computer Science 2024-06-04 Xingyu Wu , Yan Zhong , Jibin Wu , Yuxiao Huang , Sheng-hao Wu , Kay Chen Tan

Certain Petrov-Galerkin schemes are inherently stable formulations of variational problems on a given mesh. This stability is primarily obtained by computing an optimal test basis for a given approximation space. Furthermore, these…

Computational Engineering, Finance, and Science · Computer Science 2020-12-24 Ankit Chakraborty , Ajay Rangarajan , Georg May

The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…

Machine Learning · Statistics 2025-03-04 Hee-Geon Kang , Sunggon Kim

We present an algorithm that enables one to perform locally adaptive block thresholding, while maintaining image continuity. Images are divided into sub-images based some standard image attributes and thresholding technique is employed over…

Computer Vision and Pattern Recognition · Computer Science 2007-05-23 S. Hemachander , Amit Verma , Siddharth Arora , Prasanta K. Panigrahi

A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate…

Numerical Analysis · Mathematics 2012-10-11 Lennard Kamenski

Neural networks and deep learning are changing the way that artificial intelligence is being done. Efficiently choosing a suitable network architecture and fine-tune its hyper-parameters for a specific dataset is a time-consuming task given…

Machine Learning · Computer Science 2019-05-16 David Laredo , Yulin Qin , Oliver Schütze , Jian-Qiao Sun

We introduce a new $hp$-adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approach is based on a generally applicable prediction strategy…

Numerical Analysis · Mathematics 2023-11-23 Patrick Bammer , Andreas Schröder , Thomas P. Wihler

We present a neural technique for learning to select a local sub-region around a point which can be used for mesh parameterization. The motivation for our framework is driven by interactive workflows used for decaling, texturing, or…

Computer Vision and Pattern Recognition · Computer Science 2023-03-28 Richard Liu , Noam Aigerman , Vladimir G. Kim , Rana Hanocka

This paper considers a time-varying optimization problem associated with a network of systems, with each of the systems shared by (and affecting) a number of individuals. The objective is to minimize cost functions associated with the…

Optimization and Control · Mathematics 2022-03-15 Ana M. Ospina , Andrea Simonetto , Emiliano Dall'Anese

We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…

Numerical Analysis · Mathematics 2022-10-21 Ángel J. Omella , David Pardo

Optimization is ubiquitous in our daily lives. In the past, (sub-)optimal solutions to any problem have been derived by trial and error, sheer luck, or the expertise of knowledgeable individuals. In our contemporary age, there thankfully…

Neural and Evolutionary Computing · Computer Science 2023-12-07 Raphael Patrick Prager

Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…

Machine Learning · Computer Science 2025-04-25 Changyu Gao , Andrew Lowy , Xingyu Zhou , Stephen J. Wright

We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an…

Optimization and Control · Mathematics 2024-03-13 Eduardo M. G. Vila , Eric C. Kerrigan , Paul Bruce

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

Optimization and Control · Mathematics 2026-02-17 Xiaozhe Hu , Sara Pollock , Zhongqin Xue , Yunrong Zhu

We consider the problem of open-goal planning for robotic cloth manipulation. Core of our system is a neural network trained as a forward model of cloth behaviour under manipulation, with planning performed through backpropagation. We…

Robotics · Computer Science 2021-11-15 Solvi Arnold , Daisuke Tanaka , Kimitoshi Yamazaki