Related papers: Conservative approximation-based feedforward neura…
We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…
In this paper, we combine the nonlinear HWENO reconstruction in \cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilton-Jacobi equations in a novel HWENO framework recently…
In this work, we introduce a deep artificial neural network (ANN) that can detect locations of discontinuity and build a six-point ENO-type scheme based on a set of smooth and discontinuous training data. While a set of candidate stencils…
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…
Recently, the targeted ENO (TENO) schemes give a novel framework to keep optimal high-order spatial reconstruction wherever discontinuity is deemed to be vanished, including at smooth critical points, and to avoid oscillations by completely…
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces,…
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…
To address the order degradation at critical points in the WENO3-Z scheme, some improvements have been proposed , but these approaches generally fail to consider the occurrence of critical points at arbitrary positions within grid…
The weighted essentially non-oscillatory (WENO) schemes are widely used for hyperbolic conservation laws due to the ability to resolve discontinuities and maintain high-order accuracy in smooth regions at the same time. For hyperbolic…
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…
A deep neural network (DNN) model consisting of two hidden layers was proposed for predicting the immediate environments of specific atoms based on X-ray absorption near-edge spectra (XANES). The output layer of the DNN can be adjusted to…
Based on the solution formula method, a series of one-step fully-discrete schemes, such as FWENO/Full-WENO has been proposed. Storing the by-products conservative variables at the half points (grid center) and using them as interpolation…
The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to…
Convolutional Neural Networks (CNN) have recently seen tremendous success in various computer vision tasks. However, their application to problems with high dimensional input and output, such as high-resolution image and video segmentation…
This work examines the deep disconnect between existing theoretical analyses of gradient-based algorithms and the practice of training deep neural networks. Specifically, we provide numerical evidence that in large-scale neural network…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrich splitting, the WENO reconstruction, the…
Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsatisfactory accuracy…
This study aims to optimize Deep Feedforward Neural Networks (DFNNs) training using nature-inspired optimization algorithms, such as PSO, MTO, and its variant called MTOCL. We show how these algorithms efficiently update the weights of…
We describe a newly developed cosmological hydrodynamics code based on the weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. High order finite difference WENO schemes are designed for problems with…