相关论文: Enhanced fifth order WENO Shock-Capturing Schemes …
Based on the understandings regarding linear upwind schemes with flux splitting to achieve free-stream preservation (Q. Li, etc. Commun. Comput. Phys., 22 (2017) 64-94), a series of WENO interpolation-based and upwind-biased nonlinear…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
The lack of smoothness is a common feature of weak solutions of nonlinear hyperbolic equations and is a crucial issue in their approximation. This has motivated several efforts to define appropriate indicators, based on the values of the…
In this paper, a positivity-preserving fifth-order finite volume compact-WENO scheme is proposed for solving compressible Euler equations. As we know conservative compact finite volume schemes have high resolution properties while WENO…
This work is dedicated to the development and comparison of WENO-type reconstructions for hyperbolic systems of balance laws. We are particularly interested in high order shock capturing non-oscillatory schemes with uniform accuracy within…
Pixel-wise prediction with deep neural network has become an effective paradigm for salient object detection (SOD) and achieved remarkable performance. However, very few SOD models are robust against adversarial attacks which are visually…
A new adaptive weighted essentially non-oscillatory WENO-$\theta$ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter…
Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order accuracy at a fraction of the cost of a finite volume WENO…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
Deep Learning shows very good performance when trained on large labeled data sets. The problem of training a deep net on a few or one sample per class requires a different learning approach which can generalize to unseen classes using only…
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). The computational cost of such schemes increases…
The state-of-the-art deep learning-based object recognition YOLO algorithm and object tracking DeepSORT algorithm are combined to analyze digital images from fluid dynamic simulations of multi-core emulsions and soft flowing crystals and to…
High order reconstruction in the finite volume (FV) approach is achieved by a more fundamental form of the fifth order WENO reconstruction in the framework of orthogonally-curvilinear coordinates, for solving the hyperbolic conservation…
High-order gas-kinetic scheme (HGKS) has been well-developed in the past years. Abundant numerical tests including hypersonic flow, turbulence, and aeroacoustic problems, have been used to validate its accuracy, efficiency, and robustness.…
Weighted compact nonlinear schemes (WCNS) [Deng and Zhang, JCP 165(2000): 22-44] were developed to improve the performance of the compact high-order nonlinear schemes (CNS) by utilizing the weighting technique originally designed for WENO…
In this work, we present the feedforward neural network based on the conservative approximation to the derivative from point values, for the weighted essentially non-oscillatory (WENO) schemes in solving hyperbolic conservation laws. The…
We introduce a new second-order inertial optimization method for machine learning called INNA. It exploits the geometry of the loss function while only requiring stochastic approximations of the function values and the generalized…
In typical machine learning tasks and applications, it is necessary to obtain or create large labeled datasets in order to to achieve high performance. Unfortunately, large labeled datasets are not always available and can be expensive to…
We propose a class of weighted compact central (WCC) schemes for solving hyperbolic conservation laws. The linear version can be considered as a high-order extension of the central Lax-Friedrichs (LxF) scheme and the central conservation…
Deep learning-based image compression has made great progresses recently. However, many leading schemes use serial context-adaptive entropy model to improve the rate-distortion (R-D) performance, which is very slow. In addition, the…