Search · four archives
Search · four archives
21 papers · ranked by Valyu relevance
T. W. Anderson, Jamie Haddock, Jackie Lok
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications, and thus it is imperative to have a thorough theoretical understanding of their…
Katherine J. Pearce, Per‐Gunnar Martinsson
This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimension reduction, such as the singular value decomposition (SVD) or interpolative (ID) and CUR…
Monika Eisenmann, Marvin Jans, Raphael Kruse, Helmut Podhaisky
A randomized Singly Diagonally Implicit Runge-Kutta (SDIRK) method, based on the randomized trapezoidal rule as the underlying quadrature scheme, is proposed. Every realization of the scheme is an algebraically stable SDIRK method of at least second order. The main result is the proof that the randomized scheme…
Haochen Jiang, Dongdong Liu, Xianping Wu, Yang Xu
Motivated by the randomized sketch to solve a variety of problems in scientific computation, we improve both the maximal weighted residual Kaczmarz method and the randomized block average Kaczmarz method using two new randomized sketch techniques. Besides, convergence analyses of the proposed methods are provided.…
Michał Dereziński, Ethan N. Epperly, Deanna Needell, Alexander Xue
The randomized Kaczmarz method and its accelerated variants are a powerful class of iterative methods for solving large-scale linear systems, offering guaranteed convergence with low per-iteration cost. However, their numerical stability remains poorly understood. In this work, we investigate the stability properties…
Meng-Long Xiao, Tao Li, Deanna Needell
The projected linear system solver (PLSS), by incrementally appending columns to a random or deterministic sketching matrix, provides an attractive finite termination property for consistent linear systems. Nevertheless, a critical computational bottleneck of PLSS is accessing the whole coefficient matrix per…
Raphael Kruse, Nick Polydorides, Yue Wu
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be approximated by quadrature rules. If the coefficient functions of the differential…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Authors not listed
The reliability of the random phase approximation (RPA) and σ-functional methods in conjunction with the mixed Gaussian and plane wave (GPW) basis set scheme as implemented in the CP2K package is investigated. First, based on results for thermochemical properties of molecules and structural properties of crystalline…
Authors not listed
Metastable states and the conformational transitions in between them are key to understanding dynamical behaviour and function of large-scale molecular systems. By combining basic dimensionality reduction techniques with a state-of-the art approximation of the Koopman operator associated to molecular dynamics…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Mengqi Zhang, Guangqiang Teng, Xiaoyu Lei, Boris Ryabko
Lei proposed an algorithm Algorithm $A_{3}$ in 2023 to generate an exact discrete uniform distribution from an unknown biased Bernoulli source. The present paper does not claim a new extraction algorithm. Its contributions are analytical: first, we provide a Fourier-analytic proof of the uniformity mechanism based on…
Haidy A. Newer
Statistical inference for cluster randomized trials often involves complex derived endpoints, such as biomarker ratios or cumulative products, which significantly complicate the application of standard asymptotic theory. When the number of clusters is limited or intra-cluster dependence is pronounced, conventional…
Olga Kuznetsova, Jennifer Ross, Daniel Bodden, Freda Cooner + 10 more
While platform trials have several benefits with their adaptive features, randomization challenges become of central relevance to the design and execution of a platform trial. This paper intends to address these challenges and explore some potential solutions. A platform type of clinical trial is a clinical trial…
Eliane Rached, Jihan Allaw, Joy Khayat, Hassan Karaki + 7 more
Background: Numerical cognition and motor performance rely on overlapping brain systems, yet the extent of their reciprocal interaction remains unclear. This systematic review explores how number processing influences motor execution and how motor activity shapes numerical cognition, emphasizing the neural mechanisms…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and adaptability needed for emerging imaging technologies and clinical insights. We…
Jinwei Qiao, Yuanyang Qiao, Yinnian He, Miguel Rubi
It is well known that the Cahn-Hilliard equation satisfies the energy dissipation law and the mass conservation property. Recently, the radial basis function-finite difference (RBF-FD) approach and its numerous variants have garnered significant attention for the numerical solution of surface-related problems, owing to…
Rudra Prakash, Shaunak Sen
The paper addresses the critical challenge of accurately characterising steady states in biomolecular systems, which are often complex, nonlinear, multistable and subject to significant uncertainties. Traditional numerical methods often fail to provide complete or guaranteed solutions under these conditions. To…
Authors not listed
Collective variables (CVs) are essential for interpreting and accelerating rare events in molecular simulations. However, their design remains limited by the requirement of differentiability with respect to atomic coordinates. This constraint excludes many powerful structural descriptors that are routinely used for…
Sumedh S Nagrale, Alik S Widge
The use of Deep Brain Stimulation (DBS) on the ventral capsule/ventral striatum (VCVS) has therapeutic potential for patients with refractory psychiatric disorders, but clinical success is impeded by the need for a time-consuming and trial-and-error process when setting the parameters, this process relying on…
Authors not listed
Knowledge of the reaction rate constants can be vital in understanding electrochemical reaction mechanisms and their rate-determining processes. Although first-principles methods, such as density functional theory (DFT), provide valuable insight into reaction free energies and rate constants, they commonly use…