Related papers: Learning WENO for entropy stable schemes to solve …

This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast algebraic solvers. We present details for the second order…

The rapid proliferation of deep neural networks (DNNs) across several domains has led to increasing concerns regarding intellectual property (IP) protection and model misuse. Trained DNNs represent valuable assets, often developed through…

We propose a neural entropy-stable conservative flux form neural network (NESCFN) for learning hyperbolic conservation laws and their associated entropy functions directly from solution trajectories, without requiring any predefined…

In this paper, we develop high-order, conservative, non-splitting Eulerian-Lagrangian (EL) Runge-Kutta (RK) finite volume (FV) weighted essentially non-oscillatory (WENO) schemes for convection-diffusion equations. The proposed…

In an attempt to investigate the structures of ultra-relativistic jets injected into the intracluster medium (ICM) and the associated flow dynamics, such as shocks, velocity shear, and turbulence, we have developed a new special…

Objective: Ultrasound Shear Wave Elastography (SWE) demonstrates great potential in assessing soft-tissue pathology by mapping tissue stiffness, which is linked to malignancy. Traditional SWE methods have shown promise in estimating tissue…

Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…

Wide Area Networks (WAN) are a key infrastructure in today's society. During the last years, WANs have seen a considerable increase in network's traffic and network applications, imposing new requirements on existing network technologies…

Accurate and efficient solutions of spatiotemporal partial differential equations (PDEs), such as phase-field models, are fundamental for understanding interfacial dynamics and microstructural evolution in materials science and fluid…

We introduce structured prediction energy networks (SPENs), a flexible framework for structured prediction. A deep architecture is used to define an energy function of candidate labels, and then predictions are produced by using…

The compact scheme has high order accuracy and high resolution, but cannot be used to capture the shock. WENO is a great scheme for shock capturing, but is too dissipative for turbulence and small length scales. We developed a modified…

We introduce a WENO reconstruction based on Hermite interpolation both for semi-Lagrangian and finite difference methods. This WENO reconstruction technique allows to control spurious oscillations. We develop third and fifth order methods…

This paper presents an extension of the hybrid scheme proposed by Wang et al. (J. Comput. Phys. 229 (2010) 169-180) for numerical simulation of compressible isotropic turbulence to flows with higher turbulent Mach numbers. The scheme still…

We apply deep neural networks (DNN) to data from the EXO-200 experiment. In the studied cases, the DNN is able to reconstruct the relevant parameters - total energy and position - directly from raw digitized waveforms, with minimal…

The spectral volume(SV) method constructs a high-order polynomial for SV based on the average value of control volume(CV), but for discontinuous problems, a limiter is required to mitigate oscillations. This paper presents a novel CV-based…

A novel approach for selecting appropriate reconstructions is implemented to the hyperbolic conservation laws in the high-order local polynomial-based framework, e.g., the discontinuous Galerkin (DG) and flux reconstruction (FR) schemes.…

In this paper, we develop parametrized positivity satisfying flux limiters for the high order finite difference Runge-Kutta weighted essentially non-oscillatory (WENO) scheme solving compressible Euler equations to maintain positive density…

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…

We illustrate that numerical solutions of high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for some nonconvex conservation laws perform poorly or converge to the entropy solution in a slow speed. The…

In this paper, we propose a novel deep architecture tailored for 3D point cloud applications, named as SPE-Net. The embedded ``Selective Position Encoding (SPE)'' procedure relies on an attention mechanism that can effectively attend to the…