arXiv subjects

Yixuan Wang

Publications and source records attributed to Yixuan Wang.

170 records · Page 10Linked to original sources

arXiv2020

Energy-Efficient Control Adaptation with Safety Guarantees for Learning-Enabled Cyber-Physical Systems

Neural networks have been increasingly applied for control in learning-enabled cyber-physical systems (LE-CPSs) and demonstrated great promises in improving system performance and efficiency, as well as reducing the need for complex physical models. However, the lack of safety guarantees for such neural network based controllers has significantly impeded their adoption in safety-critical CPSs. In this work, we propose a controller adaptation approach that automatically switches among multiple controllers, including neural network controllers, to guarantee system safety and improve energy efficiency. Our approach includes two key components based on formal methods and machine learning. First, we approximate each controller with a Bernstein-polynomial based hybrid system model under bounded disturbance, and compute a safe invariant set for each controller based on its corresponding hybrid system. Intuitively, the invariant set of a controller defines the state space where the system can always remain safe under its control. The union of the controllers' invariants sets then define a safe adaptation space that is larger than (or equal to) that of each controller. Second, we develop a deep reinforcement learning method to learn a controller switching strategy for reducing the control/actuation energy cost, while with the help of a safety guard rule, ensuring that the system stays within the safe space. Experiments on a linear adaptive cruise control system and a non-linear Van der Pol's oscillator demonstrate the effectiveness of our approach on energy saving and safety enhancement.

eess.SY↗

arXiv2020

Martingale Solution for Stochastic Active Liquid Crystal System

The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in $\mathbb{R}^{3}$ with large initial data. The coupled structure makes the analysis challenging, and more delicate arguments are required in stochastic case compared to the deterministic one \cite{11}.

math.AP↗

arXiv2019

Influenza Modeling Based on Massive Feature Engineering and International Flow Deconvolution

In this article, we focus on the analysis of the potential factors driving the spread of influenza, and possible policies to mitigate the adverse effects of the disease. To be precise, we first invoke discrete Fourier transform (DFT) to conclude a yearly periodic regional structure in the influenza activity, thus safely restricting ourselves to the analysis of the yearly influenza behavior. Then we collect a massive number of possible region-wise indicators contributing to the influenza mortality, such as consumption, immunization, sanitation, water quality, and other indicators from external data, with $1170$ dimensions in total. We extract significant features from the high dimensional indicators using a combination of data analysis techniques, including matrix completion, support vector machines (SVM), autoencoders, and principal component analysis (PCA). Furthermore, we model the international flow of migration and trade as a convolution on regional influenza activity, and solve the deconvolution problem as higher-order perturbations to the linear regression, thus separating regional and international factors related to the influenza mortality. Finally, both the original model and the perturbed model are tested on regional examples, as validations of our models. Pertaining to the policy, we make a proposal based on the connectivity data along with the previously extracted significant features to alleviate the impact of influenza, as well as efficiently propagate and carry out the policies. We conclude that environmental features and economic features are of significance to the influenza mortality. The model can be easily adapted to model other types of infectious diseases.

cs.LG↗

arXiv2018

An Analytical Analogue of Morse's Lemma

The Morse function $f$ near a non-degenerate critical point $p$ is understood topologically, in the light of Morse's lemma. However, Morse's lemma standardizes the function $f$ itself, providing little information of how the gradient $\nabla f$ behaves. In this paper, we prove an analytical analogue of Morse's lemma, showing that there exist smooth local coordinates on which a generic Morse gradient field $\nabla f$ near the critical point exhibits a unique linear vector field. We show that on a small neighbourhood of the critical point, the gradient field $\nabla f$ has a natural choice of standard form $V_0(\mathbb{x})=\sum_{i=1}^n λ_ix_i\frac{\partial}{\partial x_i}$, and this form only depend on the local behaviour of the Morse function and the Riemannian metric near the critical point. Then we present a constructive proof of the fact that given a generic Morse function $f$, for every critical point, there is a local coordinate on which the gradient field reduces to its standard form.

math.DG↗

arXiv2018

Approximation to Singular Quadratic Collision Model in Fokker-Planck-Landau Equation

We propose a Hermite-Galerkin spectral method to numerically solve the spatially homogeneous Fokker-Planck-Landau equation with singular quadratic collision model. To compute the collision model, we adopt a novel approximation formulated by a combination of a simple linear term and a quadratic term very expensive to evaluate. Using the Hermite expansion, the quadratic term is evaluated exactly by calculating the spectral coefficients. To deal with singularities, we make use of Burnett polynomials so that even very singular collision model can be handled smoothly. Numerical examples demonstrate that our method can capture low-order moments with satisfactory accuracy and performance.

math.NA↗

arXiv2018

Global Well-Posedness and Large-Time Behavior of 1D Compressible Navier-Stokes System with Density-Depending Viscosity and Vacuum in Unbounded Domains

We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-dependent viscosity and large external force. Under a general assumption on the density-dependent viscosity, we prove that the Cauchy problem admits a unique global strong (classical) solution for the large initial data with vacuum. Moreover, the density is proved to be bounded from above time-independently. As a consequence, we obtain the large time behavior of the solution without external forces.

math.AP↗

arXiv2018

On Global Classical Solutions to 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Vacuum

For the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global classical solution with large initial data containing vacuum. Furthermore, we show that the density is bounded from above independently of time which in particular yields the large time behavior of the solution as time tends to infinity: the density and the velocity converge to the steady states in $L^p$ and in $W^{1,p}$ ($1\le p<+\infty$) respectively. Moreover, the decay rate in time of the solution is shown to be exponential. Finally, we also prove that the spatial gradient of the density will blow up as time tends to infinity when vacuum states appear initially even at one point.

math.AP↗

arXiv2017

Adaptive Algebraic Multiscale Solver for Compressible Flow in Heterogeneous Porous Media

This paper presents the development of an Adaptive Algebraic Multiscale Solver for Compressible flow (C-AMS) in heterogeneous porous media. Similar to the recently developed AMS for incompressible (linear) flows [Wang et al., JCP, 2014], C-AMS operates by defining primal and dual-coarse blocks on top of the fine-scale grid. These coarse grids facilitate the construction of a conservative (finite volume) coarse-scale system and the computation of local basis functions, respectively. However, unlike the incompressible (elliptic) case, the choice of equations to solve for basis functions in compressible problems is not trivial. Therefore, several basis function formulations (incompressible and compressible, with and without accumulation) are considered in order to construct an efficient multiscale prolongation operator. As for the restriction operator, C-AMS allows for both multiscale finite volume (MSFV) and finite element (MSFE) methods. Finally, in order to resolve high-frequency errors, fine-scale (pre- and post-) smoother stages are employed. In order to reduce computational expense, the C-AMS operators (prolongation, restriction, and smoothers) are updated adaptively. In addition to this, the linear system in the Newton-Raphson loop is infrequently updated. Systematic numerical experiments are performed to determine the effect of the various options, outlined above, on the C-AMS convergence behaviour. An efficient C-AMS strategy for heterogeneous 3D compressible problems is developed based on overall CPU times. Finally, C-AMS is compared against an industrial-grade Algebraic MultiGrid (AMG) solver. Results of this comparison illustrate that the C-AMS is quite efficient as a nonlinear solver, even when iterated to machine accuracy.

math.NA↗