arXiv subjects

Wei Kang

Publications and source records attributed to Wei Kang.

At least 73 records · Page 4Linked to original sources

arXiv2020

On how Cognitive Computing will plan your next Systematic Review

Systematic literature reviews (SLRs) are at the heart of evidence-based research, setting the foundation for future research and practice. However, producing good quality timely contributions is a challenging and highly cognitive endeavor, which has lately motivated the exploration of automation and support in the SLR process. In this paper we address an often overlooked phase in this process, that of planning literature reviews, and explore under the lenses of cognitive process augmentation how to overcome its most salient challenges. In doing so, we report on the insights from 24 SLR authors on planning practices, its challenges as well as feedback on support strategies inspired by recent advances in cognitive computing. We frame our findings under the cognitive augmentation framework, and report on a prototype implementation and evaluation focusing on further informing the technical feasibility.

cs.DL↗

arXiv2020

Neural Network Approximations of Compositional Functions With Applications to Dynamical Systems

As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many published results in recent years. Towards the goal of revealing the underlying reason why neural networks are capable of solving some high dimensional problems, we develop an algebraic framework and an approximation theory for compositional functions and their neural network approximations. The theoretical foundation is developed in a way so that it supports the error analysis for not only functions as input-output relations, but also numerical algorithms. This capability is critical because it enables the analysis of approximation errors for problems for which analytic solutions are not available, such as differential equations and optimal control. We identify a set of key features of compositional functions and the relationship between the features and the complexity of neural networks. In addition to function approximations, we prove several formulae of error upper bounds for neural networks that approximate the solutions to differential equations, optimization, and optimal control.

cs.LG↗

arXiv2020

QRnet: optimal regulator design with LQR-augmented neural networks

In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman equations arising in optimal feedback control. Concretely, we augment linear quadratic regulators with neural networks to handle nonlinearities. We train the augmented models on data generated without discretizing the state space, enabling application to high-dimensional problems. We use the proposed method to design a candidate optimal regulator for an unstable Burgers' equation, and through this example, demonstrate improved robustness and accuracy compared to existing neural network formulations.

math.OC↗

arXiv2020

The Capacity of Symmetric Private Information Retrieval under Arbitrary Collusion and Eavesdropping Patterns

We study the symmetric private information retrieval (SPIR) problem under arbitrary collusion and eavesdropping patterns for replicated databases. We find its capacity, which is the same as the capacity of the original SPIR problem with the number of databases $N$ replaced by a number $F^*$. The number $F^*$ is the optimal solution to a linear programming problem that is a function of the joint pattern, which is the union of the collusion and eavesdropping pattern. This is the first result that shows how two arbitrary patterns collectively affect the capacity of the PIR problem. We draw the conclusion that for SPIR problems, the collusion and eavesdropping constraints are interchangeable in terms of capacity. As special cases of our result, the capacity of the SPIR problem under arbitrary collusion patterns and the capacity of the PIR problem under arbitrary eavesdropping patterns are also found.

cs.IT↗

arXiv2020

Algorithms of Data Development For Deep Learning and Feedback Design

Recent research reveals that deep learning is an effective way of solving high dimensional Hamilton-Jacobi-Bellman equations. The resulting feedback control law in the form of a neural network is computationally efficient for real-time applications of optimal control. A critical part of this design method is to generate data for training the neural network and validating its accuracy. In this paper, we provide a survey of existing algorithms that can be used to generate data. All the algorithms surveyed in this paper are causality-free, i.e., the solution at a point is computed without using the value of the function at any other points. At the end of the paper, an illustrative example of optimal feedback design using deep learning is given.

math.DS↗

arXiv2020

The Capacity of Private Information Retrieval Under Arbitrary Collusion Patterns

We study the private information retrieval (PIR) problem under arbitrary collusion pattern for replicated databases. We find its capacity, which is the same as the capacity of the original PIR problem with the number of databases $N$ replaced by a number $S^*$. The number $S^*$ is the optimal solution to a linear programming problem that is a function of the collusion pattern. Hence, the collusion pattern affects the capacity of the PIR problem only through the number $S^*$.

cs.IT↗

arXiv2019

Density Propagation with Characteristics-based Deep Learning

Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few uncertain variables or require large amounts of simulation data. In this paper, we propose a data-driven method for approximating joint probability density functions (PDFs) of nonlinear dynamic systems with initial condition and parameter uncertainty. Our approach leverages on the power of deep learning to deal with high-dimensional inputs, but we overcome the need for huge quantities of training data by encoding PDF evolution equations directly into the optimization problem. We demonstrate the potential of the proposed method by applying it to evaluate the robustness of a feedback controller for a six-dimensional rigid body with parameter uncertainty.

math.DS↗

arXiv2019

The Capacity of Multi-round Private Information Retrieval from Byzantine Databases

In this work, we investigate the capacity of private information retrieval (PIR) from $N$ replicated databases, where a subset of the databases are untrustworthy (byzantine) in their answers to the query of the user. We allow for multi-round queries and demonstrate that the identities of the byzantine databases can be determined with a small additional download cost. As a result, the capacity of the multi-round PIR with byzantine databases (BPIR) reaches that of the robust PIR problem when the number of byzantine databases is less than the number of trustworthy databases.

cs.IT↗

arXiv2019

Coded Caching with Heterogeneous Cache Sizes and Link Qualities: The Two-User Case

Centralized coded caching problem is studied for the two-user scenario, considering heterogeneous cache capacities at the users and private channels from the server to the users, in addition to a shared channel. Optimal caching and delivery strategies that minimize the worst-case delivery latency are presented for an arbitrary number of files. The converse proof follows from the sufficiency of file-index-symmetric caching and delivery codes, while the achievability is obtained through memory-sharing among a number of special memory capacity pairs. The optimal scheme is shown to exploit the private link capacities by transmitting part of the corresponding user`s request in an uncoded fashion. When there are no private links, the results presented here improve upon the two known results in the literature, namely, i) equal cache capacities and arbitrary number of files; and ii) unequal cache capacities and $N=2$ files. The results are then extended to the caching problem with heterogeneous distortion requirements.

cs.IT↗

arXiv2018

Self-energy effects and energy band theory for warm dense matter

The energy band structures caused by self-energy shifting that results in bound energy levels broadening and merging in warm dense aluminum and beryllium are observed. An energy band theory for warm dense matter (WDM) is proposed and a new code based on the energy band theory is developed to improve the traditional density functional method. Massive data of the equation of state and transport coefficients for WDM in medium and low Z have been simulated. The transition from fully degenerate to partially degenerate (related to WDM) and finally to non-degenerate state is investigated using the Lorenz number varying with the degeneracy parameter, and the lower and upper parameter boundaries for WDM are achieved. It is shown that the pressure ionization results in the Wiedemann-Franz law no longer available for WDM.

physics.plasm-ph↗

arXiv2018

Sparsity-Based Kalman Filters for Data Assimilation

Several variations of the Kalman filter algorithm, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are widely used in science and engineering applications. In this paper, we introduce two algorithms of sparsity-based Kalman filters, namely the sparse UKF and the progressive EKF. The filters are designed specifically for problems with very high dimensions. Different from various types of ensemble Kalman filters (EnKFs) in which the error covariance is approximated using a set of dense ensemble vectors, the algorithms developed in this paper are based on sparse matrix approximations of error covariance. The new algorithms enjoy several advantages. The error covariance has full rank without being limited by a set of ensembles. In addition to the estimated states, the algorithms provide updated error covariance for the next assimilation cycle. The sparsity of error covariance significantly reduces the required memory size for the numerical computation. In addition, the granularity of the sparse error covariance can be adjusted to optimize the parallelization of the algorithms.

math.OC↗

arXiv2017

X-ray absorption of liquid water by advanced ab initio methods

Oxygen K-edge X-ray absorption spectra of liquid water are computed based on the configurations from advanced ab initio molecular dynamics simulations, as well as an electron excitation theory from the GW method. One one hand, the molecular structures of liquid water are accurately predicted by including both van der Waals interactions and hybrid functional (PBE0). On the other hand, the dynamic screening effects on electron excitation are approximately described by the recently developed enhanced static Coulomb hole and screened exchange approximation by Kang and Hybertsen [Phys. Rev. B 82, 195108 (2010)]. The resulting spectra of liquid water are in better quantitative agreement with the experimental spectra due to the softened hydrogen bonds and the slightly broadened spectra originating from the better screening model.

cond-mat.soft↗

arXiv2017

Relative and Mean Motions of Multi-Machine Power Systems in Classical Model

It is well-known that in an m-machine power system where each machine is represented by a second-order differential equation, the Jacobian of the system equation contains (m-1) pairs of conjugate eigenvalues and two real eigenvalues, including at least one zero. This letter proves that under the uniform damping condition, the dynamics associated with the two real eigenvalues do not have any impact on the dynamics associated with those complex eigenvalues. This conclusion is important to justify the use of the relative motions or center-of-inertia (COI) coordinate to analyze the rotor angle stability in a multi-machine power system.

eess.SY↗

arXiv2017

Secret Key Generation from Correlated Sources and Secure Link

In this paper, we study the problem of secret key generation from both correlated sources and a secure channel. We obtain the optimal secret key rate in this problem and show that the optimal scheme is to conduct secret key generation and key distribution jointly, where every bit in the secret channel will yield more than one bit of secret key rate. This joint scheme is better than the separation-based scheme, where the secure channel is used for key distribution, and as a result, every bit in the secure channel can only provide one bit of secret key rate.

cs.IT↗

arXiv2017

Solving 1D Conservation Laws Using Pontryagin's Minimum Principle

This paper discusses a connection between scalar convex conservation laws and Pontryagin's minimum principle. For flux functions for which an associated optimal control problem can be found, a minimum value solution of the conservation law is proposed. For scalar space-independent convex conservation laws such a control problem exists and the minimum value solution of the conservation law is equivalent to the entropy solution. This can be seen as a generalization of the Lax--Oleinik formula to convex (not necessarily uniformly convex) flux functions. Using Pontryagin's minimum principle, an algorithm for finding the minimum value solution pointwise of scalar convex conservation laws is given. Numerical examples of approximating the solution of both space-dependent and space-independent conservation laws are provided to demonstrate the accuracy and applicability of the proposed algorithm. Furthermore, a MATLAB routine using Chebfun is provided (along with demonstration code on how to use it) to approximately solve scalar convex conservation laws with space-independent flux functions.

math.NA↗

arXiv2016

Nonlinear Modal Decoupling of Multi-Oscillator Systems with Applications to Power Systems

Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such a system, we propose a nonlinear modal decoupling (NMD) approach inversely constructing as many decoupled nonlinear oscillators as the system oscillation modes so that individual decoupled oscillators can easily be analyzed to infer dynamics and stability of the original system. The NMD follows a similar idea to the normal form except that we eliminate inter-modal terms but allow intra-modal terms of desired nonlinearities in decoupled systems, so decoupled systems can flexibly be shaped into desired forms of nonlinear oscillators. The NMD is then applied to power systems towards two types of nonlinear oscillators, i.e. the single-machine-infinite-bus (SMIB) systems and a proposed non-SMIB oscillator. Numerical studies on a 3-machine 9-bus system and New England 10-machine 39-bus system show that (i) decoupled oscillators keep a majority of the original system modal nonlinearities and the NMD provides a bigger validity region than the normal form, and (ii) decoupled non-SMIB oscillators may keep more authentic dynamics of the original system than decoupled SMIB systems.

eess.SY↗

arXiv2016

Extended First-Principles Molecular Dynamics Method From Cold Materials to Hot Dense Plasmas

An extended first-principles molecular dynamics (FPMD) method based on Kohn-Sham scheme is proposed to elevate the temperature limit of the FPMD method in the calculation of dense plasmas. The extended method treats the wave functions of high energy electrons as plane waves analytically, and thus expands the application of the FPMD method to the region of hot dense plasmas without suffering from the formidable computational costs. In addition, the extended method inherits the high accuracy of the Kohn-Sham scheme and keeps the information of elec- tronic structures. This gives an edge to the extended method in the calculation of the lowering of ionization potential, X-ray absorption/emission spectra, opacity, and high-Z dense plasmas, which are of particular interest to astrophysics, inertial confinement fusion engineering, and laboratory astrophysics.

physics.plasm-ph↗

arXiv2016

Molecular Dynamics Simulation of Strong Shock Waves Propagating in Dense Deuterium With the Effect of Excited Electrons

We present a molecular dynamics simulation of shock waves propagating in dense deuterium with the electron force field method [J. T. Su and W. A. Goddard, Phys. Rev. Lett. 99, 185003 (2007)], which explicitly takes the excitation of electrons into consideration. Non-equilibrium features associated with the excitation of electrons are systematically investigated. We show that chemical bonds in D$_2$ molecules lead to a more complicated shock wave structure near the shock front, compared with the results of classical molecular dynamics simulation. Charge separation can bring about accumulation of net charges on the large scale, instead of the formation of a localized dipole layer, which might cause extra energy for the shock wave to propagate. In addition, the simulations also display that molecular dissociation at the shock front is the major factor corresponding to the "bump" structure in the principal Hugoniot. These results could help to build a more realistic picture of shock wave propagation in fuel materials commonly used in the inertial confinement fusion.

physics.plasm-ph↗