Adaptive Bit Rate (ABR) decision plays a crucial role for ensuring satisfactory Quality of Experience (QoE) in video streaming applications, in which past network statistics are mainly leveraged for future network bandwidth prediction. However, most
algorithms, either rules-based or learning-driven approaches, feed throughput traces or classified traces based on traditional statistics (i.e., mean/standard deviation) to drive ABR decision, leading to compromised performances in specific scenarios. Given the diverse network connections (e.g., WiFi, cellular and wired link) from time to time, this paper thus proposes to learn the ANT (a.k.a., Accurate Network Throughput) model to characterize the full spectrum of network throughput dynamics in the past for deriving the proper network condition associated with a specific cluster of network throughput segments (NTS). Each cluster of NTS is then used to generate a dedicated ABR model, by which we wish to better capture the network dynamics for diverse connections. We have integrated the ANT model with existing reinforcement learning (RL)-based ABR decision engine, where different ABR models are applied to respond to the accurate network sensing for better rate decision. Extensive experiment results show that our approach can significantly improve the user QoE by 65.5% and 31.3% respectively, compared with the state-of-the-art Pensive and Oboe, across a wide range of network scenarios.
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable solids. Due t
o the inertia effect, the dynamic equilibrium cannot be established without evaluating the second-order derivatives of the deep autoencoder network. This is beyond the capability of off-the-shelf automatic differentiation packages and algorithms, which mainly focus on the gradient evaluation. Solving the nonlinear force equilibrium is even more challenging if the standard Newtons method is to be used. This is because we need to compute a third-order derivative of the network to obtain the variational Hessian. We attack those difficulties by exploiting complex-step finite difference, coupled with reverse automatic differentiation. This strategy allows us to enjoy the convenience and accuracy of complex-step finite difference and in the meantime, to deploy complex-value perturbations as collectively as possible to save excessive network passes. With a GPU-based implementation, we are able to wield deep autoencoders (e.g., $10+$ layers) with a relatively high-dimension latent space in real-time. Along this pipeline, we also design a sampling network and a weighting network to enable emph{weight-varying} Cubature integration in order to incorporate nonlinearity in the model reduction. We believe this work will inspire and benefit future research efforts in nonlinearly reduced physical simulation problems.
This paper is devoted to the study of the existence and uniqueness of global admissible conservative weak solutions for the periodic single-cycle pulse equation. We first transform the equation into an equivalent semilinear system by introducing a ne
w set of variables. Using the standard ordinary differential equation theory, we then obtain the global solution to the semilinear system. Next, returning to the original coordinates, we get the global admissible conservative weak solution for the periodic single-cycle pulse equation. Finally, given an admissible conservative weak solution, we find a equation to single out a unique characteristic curve through each initial point and prove the uniqueness of global admissible conservative weak solution without any additional assumptions.
In this paper, we mainly investigate the Cauchy problem of the non-resistive MHD equation. We first establish the local existence in the homogeneous Besov space $dot{B}^{frac{d}{p}-1}_{p,1}times dot{B}^{frac{d}{p}}_{p,1}$ with $p<infty$, and give a l
ifespan $T$ of the solution which depends on the norm of the Littlewood-Paley decomposition of the initial data. Then, we prove that if the initial data $(u^n_0,b^n_0)rightarrow (u_0,b_0)$ in $dot{B}^{frac{d}{p}-1}_{p,1}times dot{B}^{frac{d}{p}}_{p,1}$, then the corresponding existence times $T_nrightarrow T$, which implies that they have a common lower bound of the lifespan. Finally, we prove that the data-to-solutions map depends continuously on the initial data when $pleq 2d$. Therefore the non-resistive MHD equation is local well-posedness in the homogeneous Besov space in the Hadamard sense. Our obtained result improves considerably the recent results in cite{Li1,chemin1,Feffer2}.
In this paper we mainly study large time behavior for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. There is a lot results about the $L^2$ decay rate of the co-rotation model. In this paper, we consider the ge
neral case. We prove that the optimal $L^2$ decay rate of the velocity is $(1+t)^{-frac{d}{4}}$ with $dgeq 2$. This result improves the previous result in cite{Luo-Yin}.
This paper is concerned with a class of nonlocal dispersive models -- the $theta$-equation proposed by H. Liu [ On discreteness of the Hopf equation, {it Acta Math. Appl. Sin.} Engl. Ser. {bf 24}(3)(2008)423--440]: $$ (1-partial_x^2)u_t+(1-thetaparti
al_x^2)(frac{u^2}{2})_x =(1-4theta)(frac{u_x^2}{2})_x, $$ including integrable equations such as the Camassa-Holm equation, $theta=1/3$, and the Degasperis-Procesi equation, $theta=1/4$, as special models. We investigate both global regularity of solutions and wave breaking phenomena for $theta in mathbb{R}$. It is shown that as $theta$ increases regularity of solutions improves: (i) $0 <theta < 1/4$, the solution will blow up when the momentum of initial data satisfies certain sign conditions; (ii) $1/4 leq theta < 1/2$, the solution will blow up when the slope of initial data is negative at one point; (iii) ${1/2} leq theta leq 1$ and $theta=frac{2n}{2n-1}, nin mathbb{N}$, global existence of strong solutions is ensured. Moreover, if the momentum of initial data has a definite sign, then for any $thetain mathbb{R}$ global smoothness of the corresponding solution is proved. Proofs are either based on the use of some global invariants or based on exploration of favorable sign conditions of quantities involving solution derivatives. Existence and uniqueness results of global weak solutions for any $theta in mathbb{R}$ are also presented. For some restricted range of parameters results here are equivalent to those known for the $b-$equations [e.g. J. Escher and Z. Yin, Well-posedness, blow-up phenomena, and global solutions for the b-equation, {it J. reine angew. Math.}, {bf 624} (2008)51--80.]
