Related papers: O(N) methods in electronic structure calculations
Ionic liquids are widely used as electrolytes in electrochemical devices. In this context, many experimental and theoretical approaches have been recently developed for characterizing their interface with electrodes. In this perspective…
Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries.…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
Optical neural networks (ONNs) have demonstrated record-breaking potential in high-performance neuromorphic computing due to their ultra-high execution speed and low energy consumption. However, current learning protocols fail to provide…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the…
In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles…
We report a development of a new fast surface-based method for numerical calculations of solvation energy of biomolecules with a large number of charged groups. The procedure scales linearly with the system size both in time and memory…
Change-point problems have appeared in a great many applications for example cancer genetics, econometrics and climate change. Modern multiscale type segmentation methods are considered to be a statistically efficient approach for multiple…
We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity in the model of Massively Parallel Computation, where $N$ is the input size. We show that if…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…
Many tools and techniques measure local structure in materials in contexts ranging from biology to geology. We provide a survey of those tools and metrics that are especially useful for analyzing particulate soft matter. The metrics we…
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…
We introduce an efficient neural network (NN) architecture for classifying wave functions in terms of their localization. Our approach integrates a versatile quantum phase space parametrization leading to a custom 'quantum' NN, with the…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
As deep neural network (DNN) models grow ever-larger, they can achieve higher accuracy and solve more complex problems. This trend has been enabled by an increase in available compute power; however, efforts to continue to scale electronic…
An early-stage version of simulation package is developed for electronic structure calculation and dynamics of atom process in large-scale systems, particularly, nm-scale or 10nm-scale systems. We adopted the Extensible Markup Language…
We introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach…