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Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We propose a novel quantum algorithm for solving linear autonomous ordinary differential equations (ODEs) using the Pad\'e approximation. For linear autonomous ODEs, the discretized solution can be represented by a product of matrix…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns…
Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…
A novel implementation of the coupled-cluster singles and doubles (CCSD) approach is presented that is specifically tailored for the treatment of large, symmetric systems. It fully exploits Abelian point-group symmetry and the use of the…
While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual…
Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
If a tensor with various symmetries is properly unfolded, then the resulting matrix inherits those symmetries. As tensor computations become increasingly important it is imperative that we develop efficient structure preserving methods for…
Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
In this paper, we consider a class of generalized difference-of-convex functions (DC) programming, whose objective is the difference of two convex (not necessarily smooth) functions plus a decomposable (possibly nonconvex) function with…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
In this article we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical…
The Dynamical Cluster Approximation (DCA) is modified to include disorder. The DCA incorporates non-local corrections to local approximations such as the Coherent Potential Approximation (CPA) by mapping the lattice problem with disorder,…