Related papers: Mini-step Strategy for Transient Analysis

A new statistical model designed for regression analysis with a sparse design matrix is proposed. This new model utilizes the positions of the limited non-zero elements in the design matrix to decompose the regression model into…

Gradient descent is the method of choice for training large artificial intelligence systems. As these systems become larger, a better understanding of the mechanisms behind gradient training would allow us to alleviate compute costs and…

Inference scaling methods for LLMs often rely on decomposing problems into steps (or groups of tokens), followed by sampling and selecting the best next steps. However, these steps and their sizes are often predetermined or manually…

Sparse reduced-rank regression is an important tool to uncover meaningful dependence structure between large numbers of predictors and responses in many big data applications such as genome-wide association studies and social media…

Even in cases where quantum linear solvers provide significant speedup compared to their classical counterparts, their performance depends on some of the same parameters. In particular, the condition number of the matrix which is to be…

High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be…

In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…

Existing methods to determine the stability of a power system to small perturbations are based on eigenvalue analysis and focus on the asymptotic (long-term) behavior of the power grid. During the preasymptotic (short-term) transient,…

In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…

We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…

Autoencoding has achieved great empirical success as a framework for learning generative models for natural images. Autoencoders often use generic deep networks as the encoder or decoder, which are difficult to interpret, and the learned…

Migrating monolithic software systems into microservices requires the application of decomposition techniquesto find and select appropriate service boundaries. These techniques are often based on domain knowledge, static code analysis, and…

We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…

Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

This paper presents a three-scale computational strategy for the study of composite modeled at the mesoscale so that delamination can be reliably simulated. The solver is based on a LaTIn approach so that nonlinearities can be tackled at…

Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…

We present a simple, parallel and distributed algorithm for setting up and partitioning a sparse representation of a regular discretized simulation domain. This method is scalable for a large number of processes even for complex geometries…

Computed tomography (CT) has been used worldwide as a non-invasive test to assist in diagnosis. However, the ionizing nature of X-ray exposure raises concerns about potential health risks such as cancer. The desire for lower radiation doses…