arXiv subjects
Publications and source records attributed to Zhen Wu.
In this paper, we obtain the maximum principle for optimal controls of stochastic systems with jumps by introducing a new method of variation. The control is allowed to enter both diffusion and jump term and the control domain need not to be convex.
In this research, we investigate in-depth the nonlinear energy transmission phenomenon in a metastable modular metastructure and develop efficient tools for the design of such systems. Previous studies on a one-dimensional (1D) reconfigurable metastable modular chain uncover that when the driving frequency is within the stopband of the periodic structure, there exists a threshold input amplitude, beyond which sudden increase in the energy transmission can be observed. This onset of transmission is caused by nonlinear instability and is known as supratransmission. Due to spatial asymmetry of strategically configured constituents, such transmission thresholds could shift considerably when the structure is excited from different ends and therefore enabling the non-reciprocal energy transmission. This one-way propagation characteristic can be adaptable via reconfiguring the metastable modular system. In this new study, we build upon these findings and advance the state of the art by (a) exploring the different mechanisms that are able to activate the onset of supratransmission and their implications on wave energy transmission potential, and (b) developing an effective design tool - a localized nonlinear-linear model combined with harmonic balancing and transfer matrix analyses to analytically and efficiently predict the critical threshold amplitude of the metastable modular chain. These investigations provide important new understandings of the rich and intricate dynamics achievable by nonlinearity, asymmetry, and metastability, and create opportunities to accomplish adaptable non-reciprocal wave energy transmission
We consider a controlled linear-quadratic (LQ) large-population system with mixture of three types agents: major leader, minor leaders and minor followers. The Stackelberg-Nash-Cournot (SNC) approximate equilibrium is studied by a major-minor mean-field game (MFG) coupled with a leader-follower Stackelberg game. By variational method, the SNC approximate equilibrium strategy can be represented by some forward-backward-stochastic-differential-equations (FBSDEs) in the open-loop sense. And we pay great effort to give the feedback form of the open-loop strategy by some Riccati equations.
In this paper, we present a piezo-metastructure shunted with bistable circuits to achieve adaptive nonreciprocal elastic wave transmission. Static properties of the bistable circuit are first investigated, followed by numerical investigation of wave transmission characteristics on the nonlinear piezo-metastructure. Both the local-resonance bandgap and the bandgap transmission phenomenon, also known as supratransmission, are explored and investigated. By introducing circuit asymmetry, the supratransmission thresholds, critical excitation amplitudes to enable bandgap transmission, are found at different levels for the different wave transmission directions and hence creating an excitation amplitude range within which nonreciprocal wave transmission can be facilitated. Effect of the asymmetry factor on nonreciprocity properties is subsequently analyzed and the trade-offs between the forward transmission amplitude and the range of excitation with nonreciprocity are identified. Additionally, it is demonstrated that wave transmission characteristics of the proposed nonlinear piezo-metastructure can be adaptively tuned by conveniently adjusting stable equilibria of the bistable circuit. Lastly, the observed wave transmission properties are further corroborated by experimental investigations. Overall, the results illustrate a novel means to manipulate unidirectional elastic wave transmission using a nonlinear piezo-metastructure.
Neural network methods have achieved great success in reviews sentiment classification. Recently, some works achieved improvement by incorporating user and product information to generate a review representation. However, in reviews, we observe that some words or sentences show strong user's preference, and some others tend to indicate product's characteristic. The two kinds of information play different roles in determining the sentiment label of a review. Therefore, it is not reasonable to encode user and product information together into one representation. In this paper, we propose a novel framework to encode user and product information. Firstly, we apply two individual hierarchical neural networks to generate two representations, with user attention or with product attention. Then, we design a combined strategy to make full use of the two representations for training and final prediction. The experimental results show that our model obviously outperforms other state-of-the-art methods on IMDB and Yelp datasets. Through the visualization of attention over words related to user or product, we validate our observation mentioned above.
The optomechanics can generate fantastic effects of optics due to appropriate mechanical control. Here we theoretically study effects of slow and fast lights in a single-sided optomechanical cavity with an external force. The force-induced transparency of slow/fast light and the force-dependent conversion between the slow and fast lights are resulted from effects of the rotating-wave approximation (RWA) and the anti-RWA, which can be controlled by properly modifying the effective cavity frequency due to the external force. These force-induced phenomena can be applied to control of the light group velocity and detection of the force variation, which are feasible using current laboratory techniques.
This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum principle and the dynamic programming principle for such control problem without the assumption that the value is smooth enough, the set inclusions among the sub- and super-jets of the value function and the first-order and second-order adjoint processes as well as the generalized Hamiltonian function are established. Moreover, by comparing these results with the classical ones in Yong and Zhou [{\em Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999}], it is natural to obtain the first- and second-order adjoint equations of Hu [{\em Direct method on stochastic maximum principle for optimization with recursive utilities, arXiv:1507.03567v1 [math.OC], 13 Jul. 2015}].
The Auto-Importance Sampling (AIS) method is a Monte Carlo variance reduction technique proposed for deep penetration problems, which can significantly improve computational efficiency without pre-calculations for importance distribution. However, the AIS method is only validated with several simple examples, and cannot be used for coupled neutron-photon transport. This paper presents the improved algorithms for the AIS method, including particle transport, fictitious particles creation and adjustment, fictitious surface geometry, random number allocation and calculation of the estimated relative error. These improvements allow the AIS method to be applicable to complicated deep penetration problems with complex geometry and multiple materials. A coupled Neutron-Photon Auto-Importance Sampling (NP-AIS) method is proposed to solve the deep penetration problems of coupled neutron-photon transport using the improved algorithms. The NUREG/CR-6115 PWR benchmark was calculated by using the methods of NP-AIS, geometry splitting with Russian roulette and the analog Monte Carlo, respectively. The calculation results of NP-AIS were in good agreement with those of geometry splitting with Russian roulette and the benchmark solutions. The computational efficiency of NP-AIS for both neutron and photon was much better than that of geometry splitting with Russian roulette in most cases, and increased by several orders of magnitude compared with that of the analog Monte Carlo.
This paper deals with a nonsmooth version of the connection between the maximum principle and dynamic programming principle, for the stochastic recursive control problem when the control domain is convex. By employing the notions of sub- and super-jets, the set inclusions are derived among the value function and the adjoint processes. The general case for non-convex control domain is open.
In this paper, we study the well-posedness of the Forward-Backward Stochastic Differential Equations (FBSDE) in a general non-Markovian framework. The main purpose is to find a unified scheme which combines all existing methodology in the literature, and to address some fundamental longstanding problems for non-Markovian FBSDEs. An important device is a decoupling random field that is regular (uniformly Lipschitz in its spatial variable). We show that the regulariy of such decoupling field is closely related to the bounded solution to an associated characteristic BSDE, a backward stochastic Riccati-type equation with superlinear growth in both components $Y$ and $Z$. We establish various sufficient conditions for the well-posedness of an ODE that dominates the characteristic BSDE, which leads to the existence of the desired regular decoupling random field, whence the solvability of the original FBSDE. A synthetic analysis of the solvability is given, as a "User's Guide," for a large class of FBSDEs that are not covered by the existing methods. Some of them have important implications in applications.
In this article, we deal with a multiple dimensional coupled Markovian BSDEs system with stochastic linear growth generators with respect to volatility processes. An existence result is provided by using approximation techniques.
This paper is concerned with a backward-forward stochastic differential equation (BFSDE) system, in which a large number of negligible agents are coupled in their dynamics via state average. Here some BSDE is introduced as the dynamics of major player, while dynamics of minor players are described by SDEs. Some auxiliary mean-field SDEs (MFSDEs) and a $3\times2$ mixed forward-backward stochastic differential equation (FBSDE) system are considered and analyzed instead of involving the fixed-point analysis as in other mean-field games. We also derive the decentralized strategies which are shown to satisfy the $ε$-Nash equilibrium property.
Stemmed from the derivation of the optimal control to a stochastic linear-quadratic control problem with Markov jumps, we study one kind of backward stochastic differential equations (BSDEs) that the generator f is affected by a Markovian switching. Then, the case that the Markov chain is involved in a large state space is considered. Following the classical approach, a hierarchical approach is adopted to reduce the complexity and a singularly perturbed Markov chain is involved. We will study the asymptotic property of BSDE with the singularly perturbed Markov chain. At last, as an application of our theoretical result, we show the homogenization of one system of partial differential equations (PDEs) with a singularly perturbed Markov chain.
In this paper we study reflected backward stochastic differential equations with a continuous, linear growth coefficient and two barriers which belong to L^2. We prove that there exists at least by penalization method.
In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential equations. We will give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding Hamilton-Jacobi-Bellman equations.