Weiwei Hu

Weiwei Hu, Mariano Mateos, John R. Singler et al.

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.

Weiwei Hu, Jiguang Shen, John R. Singler et al.

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.

Weiwei Hu, Jiguang Shen, John R. Singler et al.

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.

Weiwei Hu, Jiguang Shen, John R. Singler et al.

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.

Weiwei Hu, Mariano Mateos, John R. Singler et al.

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.

Qiu Ran, Peng Li, Weiwei Hu et al.

Multiple-choice reading comprehension (MCRC) is the task of selecting the correct answer from multiple options given a question and an article. Existing MCRC models typically either read each option independently or compute a fixed-length representation for each option before comparing them. However, humans typically compare the options at multiple-granularity level before reading the article in detail to make reasoning more efficient. Mimicking humans, we propose an option comparison network (OCN) for MCRC which compares options at word-level to better identify their correlations to help reasoning. Specially, each option is encoded into a vector sequence using a skimmer to retain fine-grained information as much as possible. An attention mechanism is leveraged to compare these sequences vector-by-vector to identify more subtle correlations between options, which is potentially valuable for reasoning. Experimental results on the human English exam MCRC dataset RACE show that our model outperforms existing methods significantly. Moreover, it is also the first model that surpasses Amazon Mechanical Turker performance on the whole dataset.

Weiwei Hu, Ying Tan

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.

Weiwei Hu, Ying Tan

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.