Lijin Wang

Ziqi Yang, Lijin Wang, Da Yang et al.

Neural networks are susceptible to data inference attacks such as the membership inference attack, the adversarial model inversion attack and the attribute inference attack, where the attacker could infer useful information such as the membership, the reconstruction or the sensitive attributes of a data sample from the confidence scores predicted by the target classifier. In this paper, we propose a method, namely PURIFIER, to defend against membership inference attacks. It transforms the confidence score vectors predicted by the target classifier and makes purified confidence scores indistinguishable in individual shape, statistical distribution and prediction label between members and non-members. The experimental results show that PURIFIER helps defend membership inference attacks with high effectiveness and efficiency, outperforming previous defense methods, and also incurs negligible utility loss. Besides, our further experiments show that PURIFIER is also effective in defending adversarial model inversion attacks and attribute inference attacks. For example, the inversion error is raised about 4+ times on the Facescrub530 classifier, and the attribute inference accuracy drops significantly when PURIFIER is deployed in our experiment.

Liying Sun, Lijin Wang

In this article, we introduce a kind of numerical schemes, based on Pad$\acute{e}$ approximation, for two stochastic Hamiltonian systems which are treated separately. For the linear stochastic Hamiltonian systems, it is shown that the applied Pad$\acute e$ approximations $P_{(k,k)}$ give numerical solutions that inherit the symplecticity and the proposed numerical schemes based on $P_{(r,s)}$ are of mean-square order $\frac{r+s}{2}$ under appropriate conditions. In case of the special stochastic Hamiltonian systems with additive noises, the numerical method using two kinds of Pad$\acute e$ approximation $P_{(\hat r,\hat s)}$ and $P_{(\check r,\check s)}$ has mean-square order $\check r+\check s+1$ when $\hat r+\hat s=\check r+\check s+2$. Moreover, the numerical solution is symplectic if $\hat r=\hat s$.

Jialin Ruan, Lijin Wang

In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving properties of the schemes for SDEs with special structures are investigated. Numerical tests are performed to verify the theoretical results and illustrate the numerical behavior of the proposed methods.

Chen Chen, Lijin Wang, Yanzhao Cao et al.

In this paper we propose a novel neural network model for learning stochastic Hamiltonian systems (SHSs) from observational data, termed the stochastic generating function neural network (SGFNN). SGFNN preserves symplectic structure of the underlying stochastic Hamiltonian system and produces symplectic predictions. Our model utilizes the autoencoder framework to identify the randomness of the latent system by the encoder network, and detects the stochastic generating function of the system through the decoder network based on the random variables extracted from the encoder. Symplectic predictions can then be generated by the stochastic generating function. Numerical experiments are performed on several stochastic Hamiltonian systems, varying from additive to multiplicative, and from separable to non-separable SHSs with single or multiple noises. Compared with the benchmark stochastic flow map learning (sFML) neural network, our SGFNN model exhibits higher accuracy across various prediction metrics, especially in long-term predictions, with the property of maintaining the symplectic structure of the underlying SHSs.

Lijin Wang

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.

Lijin Wang, Jialin Hong

In this paper, a systematic approach of constructing modified equations for weak stochastic symplectic methods of stochastic Hamiltonian systems is given via using the generating functions of the stochastic symplectic methods. This approach is valid for stochastic Hamiltonian systems with either additive noises or half-multiplicative noises, and we prove that the modified equation of the weak stochastic symplectic methods are perturbed stochastic Hamiltonian systems of the original systems, which reveals in certain sense the reason for the good long time numerical behavior of stochastic symplectic methods.

Jialin Hong, Lijin Wang, Dongsheng Xu et al.

Based on the combinatory theory of rooted colored trees, we investigate the conditions for the explicit stochastic Runge-Kutta (SRK) methods to preserve quadratic invariants (QI) up to certain orders of accuracy. These conditions can supply a practical approach of constructing explicit nearly conservative SRK methods. Meanwhile, we estimate errors in the preservation of QI resulting from iterative implementation of implicit conservative SRK methods with fixed-point and Newton's iterations. Finally, numerical experiments are performed to test the behavior of the methods in preserving QI.