相关论文: Recovery by discretization corrected particle stre…

In this work, we propose a new stochastic domain decomposition method for solving steady-state partial differential equations (PDEs) with random inputs. Based on the efficiency of the Variable-separation (VS) method in simulating stochastic…

Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to…

Distribution system state estimation (DSSE) is an essential tool for operation of distribution networks, the results of which enables the operator to have a thorough observation of the system. Thus, most distribution management systems…

This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…

A discretization scheme for variable coefficient elliptic PDEs in the plane is presented. The scheme is based on high-order Gaussian quadratures and is designed for problems with smooth solutions, such as scattering problems involving soft…

In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on…

We present a novel method to fuse the power of deep networks with the computational efficiency of geometric and probabilistic localization algorithms. In contrast to other methods that completely replace a classical visual estimator with a…

Neural operator learning has emerged as a powerful approach for solving partial differential equations (PDEs) in a data-driven manner. However, applying principal component analysis (PCA) to high-dimensional solution fields incurs…

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…

Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…

Elliptic partial differential equations (PDEs) arise in many areas of computational sciences such as computational fluid dynamics, biophysics, engineering, geophysics and more. They are difficult to solve due to their global nature and…

This paper introduces a novel framework for physics-aware sparse signal recovery in measurement systems governed by partial differential equations (PDEs). Unlike conventional compressed sensing approaches that treat measurement systems as…

Data reconciliation (DR) and Principal Component Analysis (PCA) are two popular data analysis techniques in process industries. Data reconciliation is used to obtain accurate and consistent estimates of variables and parameters from…

We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…

This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…

This paper presents some applications of using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain…

Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…

This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…