Related papers: Matrix Structure Exploitation in Generalized Eigen…
Large scale Density Functional Theory (DFT) based electronic structure calculations are highly time consuming and scale poorly with system size. While semi-empirical approximations to DFT result in a reduction in computational time versus…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…
Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at…
First-principles density functional theory (DFT) with plane wave (PW) basis set is the most widely used method in quantum mechanical material simulations due to its advantages in accuracy and universality. However, a perceived drawback of…
The last decade has witnessed growth in the computational requirements for training deep neural networks. Current approaches (e.g., data/model parallelism, pipeline parallelism) parallelize training tasks onto multiple devices. However,…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
A critical challenge for density functional theory (DFT) in practice is its limited ability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. Recently, we combined…
In this paper, we study the problem of speeding up a type of optimization algorithms called Frank-Wolfe, a conditional gradient method. We develop and employ two novel inner product search data structures, improving the prior fastest…
Space-time adaptive processing (STAP) is one of the most effective approaches to suppressing ground clutters in airborne radar systems. It basically takes two forms, i.e., full-dimension STAP (FD-STAP) and reduced-dimension STAP (RD-STAP).…
We decompose the energy error of any variational DFT calculation into a contribution due to the approximate functional and that due to the approximate density. Typically, the functional error dominates, but in many interesting situations,…
The presence of interharmonics in power systems can lead to asynchronous sampling, a phenomenon further aggravated by shifts in the fundamental frequency, which significantly degrades the accuracy of power measurements. Under such…
Feature Transformation (FT) crafts new features from original ones via mathematical operations to enhance dataset expressiveness for downstream models. However, existing FT methods exhibit critical limitations: discrete search struggles…
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil $(A,B)$. Based on Zolotarev's best rational function approximations of the signum function and conformal…
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
Linear-response time-dependent Density Functional Theory (LR-TDDFT) is a widely used method for accurately predicting the excited-state properties of physical systems. Previous works have attempted to accelerate LR-TDDFT using heterogeneous…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…
Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn-Sham density matrix (DM). This causes a problem…
We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that…