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Weiwei Hu

Publications and source records attributed to Weiwei Hu.

27 records · Page 2Linked to original sources
arXiv2018

A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs I: High Regularity

We propose a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a Dirichlet boundary control problem governed by an elliptic convection diffusion PDE. Even without a convection term, Dirichlet boundary control problems are well-known to be very challenging theoretically and numerically. Although there are many works in the literature on Dirichlet boundary control problems for the Poisson equation, the authors are not aware of any existing theoretical or numerical analysis works for convection diffusion Dirichlet control problems. We make two contributions. First, we obtain well-posedness and regularity results for the Dirichlet control problem. Second, under certain assumptions on the domain and the target state, we obtain optimal a priori error estimates in 2D for the control for the new HDG method. As far as the authors are aware, there are no existing comparable results in the literature. We present numerical experiments to demonstrate the performance of the HDG method.

math.NA↗
arXiv2018

A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity

In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D polygonal domain, we also proved an optimal superlinear convergence rate for the control under certain assumptions on the domain and on the target state. In this work, we revisit the convergence analysis without these assumptions; in this case, the solution can have low regularity and we use a different analysis approach. We again prove an optimal convergence rate for the control, and present numerical results to illustrate the convergence theory.

math.NA↗
arXiv2017

An HDG Method for Distributed Control of Convection Diffusion PDEs

We propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a distributed optimal control problem governed by an elliptic convection diffusion PDE. We derive optimal a priori error estimates for the state, adjoint state, their fluxes, and the optimal control. We present 2D and 3D numerical experiments to illustrate our theoretical results.

math.NA↗
arXiv2017

A Superconvergent Hybridizable Discontinuous Galerkin Method for Dirichlet Boundary Control of Elliptic PDEs

We begin an investigation of hybridizable discontinuous Galerkin (HDG) methods for approximating the solution of Dirichlet boundary control problems governed by elliptic PDEs. These problems can involve atypical variational formulations, and often have solutions with low regularity on polyhedral domains. These issues can provide challenges for numerical methods and the associated numerical analysis. We propose an HDG method for a Dirichlet boundary control problem for the Poisson equation, and obtain optimal a priori error estimates for the control. Specifically, under certain assumptions, for a 2D convex polygonal domain we show the control converges at a superlinear rate. We present 2D and 3D numerical experiments to demonstrate our theoretical results.

math.NA↗
arXiv2017

A Superconvergent HDG Method for Distributed Control of Convection Diffusion PDEs

We consider a distributed optimal control problem governed by an elliptic convection diffusion PDE, and propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution. We use polynomials of degree $k+1$ and $k \ge 0$ to approximate the state, dual state, and their fluxes, respectively. Moreover, we use polynomials of degree $k$ to approximate the numerical traces of the state and dual state on the faces, which are the only globally coupled unknowns. We prove optimal a priori error estimates for all variables when $ k > 0 $. Furthermore, from the point of view of the number of degrees of freedom of the globally coupled unknowns, this method achieves superconvergence for the state, dual state, and control when $k\geq 1$. We illustrate our convergence results with numerical experiments.

math.NA↗
arXiv2017

Black-Box Attacks against RNN based Malware Detection Algorithms

Recent researches have shown that machine learning based malware detection algorithms are very vulnerable under the attacks of adversarial examples. These works mainly focused on the detection algorithms which use features with fixed dimension, while some researchers have begun to use recurrent neural networks (RNN) to detect malware based on sequential API features. This paper proposes a novel algorithm to generate sequential adversarial examples, which are used to attack a RNN based malware detection system. It is usually hard for malicious attackers to know the exact structures and weights of the victim RNN. A substitute RNN is trained to approximate the victim RNN. Then we propose a generative RNN to output sequential adversarial examples from the original sequential malware inputs. Experimental results showed that RNN based malware detection algorithms fail to detect most of the generated malicious adversarial examples, which means the proposed model is able to effectively bypass the detection algorithms.

cs.LG↗
arXiv2017

Optimal Impulse Control of a Simple Reparable System in a Nonreflexive Banach Space

We discuss the problem of optimal impulse control representing the preventive maintenance of a simple reparable system. The system model is governed by coupled transport and integro-differential equations in a nonreflexive Banach space. The objective of this paper is to construct nonnegative impulse control inputs at given system running times that minimize the probability of the system in failure mode. To guarantee the nonnegativity of the controlled system, we consider the control inputs to depend on the system state. This essentially leads to a bilinear control problem. We first present a rigorous proof of existence of an optimal controller and then apply the variational inequality to derive the first-order necessary conditions of optimality.

math.OC↗
arXiv2017

Generating Adversarial Malware Examples for Black-Box Attacks Based on GAN

Machine learning has been used to detect new malware in recent years, while malware authors have strong motivation to attack such algorithms. Malware authors usually have no access to the detailed structures and parameters of the machine learning models used by malware detection systems, and therefore they can only perform black-box attacks. This paper proposes a generative adversarial network (GAN) based algorithm named MalGAN to generate adversarial malware examples, which are able to bypass black-box machine learning based detection models. MalGAN uses a substitute detector to fit the black-box malware detection system. A generative network is trained to minimize the generated adversarial examples' malicious probabilities predicted by the substitute detector. The superiority of MalGAN over traditional gradient based adversarial example generation algorithms is that MalGAN is able to decrease the detection rate to nearly zero and make the retraining based defensive method against adversarial examples hard to work.

cs.LG↗