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We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its convergence analysis. We discuss the…
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the…
Motion by weighted mean curvature is a geometric evolution law for surfaces and represents steepest descent with respect to anisotropic surface energy. It has been proposed that this motion could be computed numerically by using a…
Clustering is an important part of many modern data analysis pipelines, including network analysis and data retrieval. There are many different clustering algorithms developed by various communities, and it is often not clear which…
Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In…
Molecular and lattice vibrations are able to couple to the spin of electrons and lead to their relaxation and decoherence. Ab initio simulations have played a fundamental role in shaping our understanding of this process but further…
A fully adaptive methodology is developed for reducing the complexity of large dissipative systems. This represents a significant step towards extracting essential physical knowledge from complex systems, by addressing the challenging…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
The classical line search for learning rate (LR) tuning in the stochastic gradient descent (SGD) algorithm can tame the convergence slowdown due to data-sampling noise. In a federated setting, wherein the client heterogeneity introduces a…
Integrating topology optimization and additive manufacturing (AM) technology can facilitate innovative product development. However, laser powder bed fusion, which is the predominant method in metal AM, can lead to issues such as residual…
Two new relaxation schemes are proposed for the smoothing step in the geometric multigrid solution of PDEs on 2D and 3D stretched structured grids. The new schemes are characterized by efficient line relaxation on branched sets of lines of…
This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based…
Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting…
We present a new adiabatic quantum algorithm for searching over structured databases. The new algorithm is optimized using a simplified complexity analysis.
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
The linked cell list algorithm is an essential part of molecular simulation software, both molecular dynamics and Monte Carlo. Though it scales linearly with the number of particles, there has been a constant interest in increasing its…
Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…