相关论文: A hybrid SIAC -- data-driven post-processing filte…

State estimation (SE) of water distribution networks (WDNs) is difficult to solve due to nonlinearity/nonconvexity of water flow models, uncertainties from parameters and demands, lack of redundancy of measurements, and inaccurate flow and…

Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious…

Matching sonar images with high accuracy has been a problem for a long time, as sonar images are inherently hard to model due to reflections, noise and viewpoint dependence. Autonomous Underwater Vehicles require good sonar image matching…

In this paper we present a formally fourth-order accurate hybrid-variable method for the Euler equations in the context of method of lines. The hybrid-variable (HV) method seeks numerical approximations to both cell-averages and nodal…

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

In this paper, we investigate an optimal control problem with terminal stochastic linear complementarity constraints (SLCC), and its discrete approximation using the relaxation, the sample average approximation (SAA) and the implicit Euler…

Transformer based models are increasingly being used in various domains including recommender systems (RS). Pretrained transformer models such as BERT have shown good performance at language modelling. With the greater ability to model…

With the recent wave of digitalization, specifically in the context of safety-critical applications, there has been a growing need for computationally efficient, accurate, generalizable, and trustworthy models. Physics-based models have…

Approaches based on viscous hydrodynamics for the hot and dense stage and hadronic transport for the final dilute rescattering stage are successfully applied to the dynamic description of heavy ion reactions at high beam energies. One…

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration…

This paper develops a high-order selective discontinuous Galerkin (SDG) method for solving elliptic interface problems on interface-unfitted Cartesian meshes. This method applies the discontinuous Galerkin (DG) formulation on interface…

In order to solve the problem of the difficult direct measurement of temperature field in fluid machinery under high-speed compressible conditions, this study combines high-order finite difference numerical format, Weighted Essentially…

Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while, with the aid of limiters, still resolving strong shocks. These and other properties make DG methods…

Deep convolutional neural networks have become a key element in the recent breakthrough of salient object detection. However, existing CNN-based methods are based on either patch-wise (region-wise) training and inference or fully…

A previously-developed hybrid particle-continuum method [J. B. Bell, A. Garcia and S. A. Williams, SIAM Multiscale Modeling and Simulation, 6:1256-1280, 2008] is generalized to dense fluids and two and three dimensional flows. The scheme…

In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…

A least-squares neural network (LSNN) method was introduced for solving scalar linear and nonlinear hyperbolic conservation laws (HCLs) in [7, 6]. This method is based on an equivalent least-squares (LS) formulation and uses ReLU neural…

This article studies the intimate relationship between two filtering algorithms for continuous data assimilation, the synchronization filter and the nudging filter, in the paradigmatic context of the two-dimensional (2D) Navier-Stokes…

Linear wave equations sourced by a Dirac delta distribution $\delta(x)$ and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with…

We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several…