Learning the Mapping x→Σi=1^d xi^(2):the Cost of Finding the Needle in a Haystack

The task of using the machine learning to approximate the mapping x→Σi=1^d xi^(2)with Xi∈[-1,1]seems to be a trivial one.Given the knowledge of the separable structure of the function,one can design a sparse network to represent the function very accurately,or even exactly.When such structural information is not available,and we may only use a dense neural network,the optimization procedure to find the sparse network embedded in the dense network is similar to finding the needle in a haystack,using a given number of samples of the function.We demonstrate that the cost(measured by sample complexity)of finding the needle is directly related to the Barron norm of the function.While only a small number of samples are needed to train a sparse network,the dense network trained with the same number of samples exhibits large test loss and a large generalization gap.To control the size of the generalization gap,we find that the use of the explicit regularization becomes increasingly more important as d increases.The numerically observed sample complexity with explicit regularization scales as G(d^(2.5)),which is in fact better than the theoretically predicted sample complexity that scales as 0(d^(4)).Without the explicit regularization(also called the implicit regularization),the numerically observed sample complexity is significantly higher and is close to 0(d^(4.5)).

Detecting lithium plating dynamics in a solid-state battery with operando X-ray computed tomography using machine learning

Operando X-ray micro-computed tomography(µCT)provides an opportunity to observe the evolution of Li structures inside pouch cells.Segmentation is an essential step to quantitatively analyzingµCT datasets but is challenging to achieve on operando Li-metal battery datasets due to the low X-ray attenuation of the Li metal and the sheer size of the datasets.Herein,we report a computational approach,batteryNET,to train an Iterative Residual U-Net-based network to detect Li structures.The resulting semantic segmentation shows singular Li-related component changes,addressing diverse morphologies in the dataset.In addition,visualizations of the dead Li are provided,including calculations about the volume and effective thickness of electrodes,deposited Li,and redeposited Li.We also report discoveries about the spatial relationships between these components.The approach focuses on a method for analyzing battery performance,which brings insight that significantly benefits future Li-metal battery design and a semantic segmentation transferrable to other datasets.

Predicting defect behavior in B2 intermetallics by merging ab initio modeling and machine learning

We present a combination of machine learning and high throughput calculations to predict the points defects behavior in binary intermetallic(A–B)compounds,using as an example systems with the cubic B2 crystal structure(with equiatomic AB stoichiometry).To the best of our knowledge,this work is the first application of machine learning-models for point defect properties.High throughput first principles density functional calculations have been employed to compute intrinsic point defect energies in 100 B2 intermetallic compounds.The systems are classified into two groups:(i)those for which the intrinsic defects are antisites for both A and B rich compositions,and(ii)those for which vacancies are the dominant defect for either or both composition ranges.The data was analyzed by machine learning-techniques using decision tree,and full and reduced multiple additive regression tree(MART)models.Among these three schemes,a reduced MART(r-MART)model using six descriptors(formation energy,minimum and difference of electron densities at the Wigner–Seitz cell boundary,atomic radius difference,maximal atomic number and maximal electronegativity)presents the highest fit(98%)and predictive(75%)accuracy.This model is used to predict the defect behavior of other B2 compounds,and it is found that 45%of the compounds considered feature vacancies as dominant defects for either A or B rich compositions(or both).The ability to predict dominant defect types is important for the modeling of thermodynamic and kinetic properties of intermetallic compounds,and the present results illustrate how this information can be derived using modern tools combining high throughput calculations and data analytics.

Water on silicene： A hydrogen bond-autocatalyzed physisorption-chemisorption-dissociation transition

A single water molecule is nothing special. However, macroscopic water displays many anomalous properties at interfaces, such as hydrophobicity and hydrophilicity. Although the underlying mechanisms remain elusive, hydrogen bonds between water molecules are expected to play a major role in these interesting phenomena. An important question concerns whether water clusters containing few molecules are qualitatively different from a single molecule. Using the water adsorption behavior as an example and by carefully choosing two-dimensional silicene as the substrate material, we demonstrate that water monomers, dimers, and trimers show distinct adsorption properties at the substrate surface. On silicene, the additional water molecules in dimers and trimers induce a transition from physisorption to chemisorption and then to dissociation, arising from the enhancement of charge transfer and proton transfer processes induced by hydrogen bonding. Such a hydrogen bond autocatalytic effect is expected to have broad applications in metal-free catalysis for the oxygen reduction reaction and water dissociation.

A New Approach to Multivariate Network Traffic Analysis

Network traffic analysis is one of the core functions in network monitoring for effective network operations and management.While online traffic analysis has been widely studied,it is still intensively challenging due to several reasons.One of the primary challenges is the heavy volume of traffic to analyze within a finite amount of time due to the increasing network bandwidth.Another important challenge for effective traffic analysis is to support multivariate functions of traffic variables to help administrators identify unexpected network events intuitively.To this end,we propose a new approach with the multivariate analysis that offers a high-level summary of the online network traffic.With this approach,the current state of the network will display patterns compiled from a set of traffic variables,and the detection problems in network monitoring(e.g.,change detection and anomaly detection)can be reduced to a pattern identification and classification problem.In this paper,we introduce our preliminary work with clustered patterns for online,multivariate network traffic analysis with the challenges and limitations we observed.We then present a grid-based model that is designed to overcome the limitations of the clustered pattern-based technique.We will discuss the potential of the new model with respect to the technical challenges including streaming-based computation and robustness to outliers.

BLOCK ALGORITHMS WITH AUGMENTED RAYLEIGH-RITZ PROJECTIONS FOR LARGE-SCALE EIGENPAIR COMPUTATION

Most iterative algorithms for eigenpair computation consist of two main steps:a subspace update(SU)step that generates bases for approximate eigenspaces,followed by a Rayleigh-Ritz(RR)projection step that extracts approximate eigenpairs.So far the predominant methodology for the SU step is based on Krylov subspaces that builds orthonormal bases piece by piece in a sequential manner.In this work,we investigate block methods in the SU step that allow a higher level of concurrency than what is reachable by Krylov subspace methods.To achieve a competitive speed,we propose an augmented Rayleigh-Ritz(ARR)procedure.Combining this ARR procedure with a set of polynomial accelerators,as well as utilizing a few other techniques such as continuation and deflation,we construet a block algorithm designed to reduce the number of RR steps and elevate concurrency in the SU steps.Extensive computational experiments are conducted in C on a representative set of test problems to evaluate the performance of two variants of our algorithm.Numerical results,obtained on a many-core computer without explicit code parallelization,show that when computing a relatively large number of eigenpairs,the performance of our algorithms is competitive with that of several state-of-the-art eigensolvers.

Decay estimates of discretized Green's functions for Schrdinger type operators

For a sparse non-singular matrix A, generally A^(-1)is a dense matrix. However, for a class of matrices,A^(-1)can be a matrix with off-diagonal decay properties, i.e., |A_(ij)^(-1)| decays fast to 0 with respect to the increase of a properly defined distance between i and j. Here we consider the off-diagonal decay properties of discretized Green's functions for Schr¨odinger type operators. We provide decay estimates for discretized Green's functions obtained from the finite difference discretization, and from a variant of the pseudo-spectral discretization. The asymptotic decay rate in our estimate is independent of the domain size and of the discretization parameter.We verify the decay estimate with numerical results for one-dimensional Schr¨odinger type operators.

Low rank approximation in G0W0 calculations

The single particle energies obtained in a Kohn-Sham density functional theory(DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in transport,tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green's function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G_0W_0 approximation is a widely used technique in which the self energy is expressed as the convolution of a noninteracting Green's function(G_0) and a screened Coulomb interaction(W_0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W_0 at multiple frequencies. In this paper, we discuss how the cost of G_0W_0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W_0. In particular, we examine the effect of such a low rank approximation on the accuracy of the G_0W_0 approximation. We also discuss how the numerical convolution of G_0 and W_0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.