PFNN-2: A Domain Decomposed Penalty-Free Neural Network Method for Solving Partial Differential Equations

05/02/2022
by   Hailong Sheng, et al.
0

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the smoothness constraints and essential boundary conditions of self-adjoint problems with complex geometries, and extends the application to a broader range of non-self-adjoint time-dependent differential equations. In addition, PFNN-2 introduces an overlapping domain decomposition strategy to substantially improve the training efficiency without sacrificing accuracy. Experiments results on a series of partial differential equations are reported, which demonstrate that PFNN-2 can outperform state-of-the-art neural network methods in various aspects such as numerical accuracy, convergence speed, and parallel scalability.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/23/2021

Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics

In recent years a large literature on deep learning based methods for th...
research
03/02/2021

Parallel Machine Learning of Partial Differential Equations

In this work, we present a parallel scheme for machine learning of parti...
research
02/18/2022

FinNet: Solving Time-Independent Differential Equations with Finite Difference Neural Network

In recent years, deep learning approaches for partial differential equat...
research
07/08/2020

The Multivariate Theory of Functional Connections: Theory, Proofs, and Application in Partial Differential Equations

This article presents a reformulation of the Theory of Functional Connec...
research
02/21/2022

Communication-Efficient Algorithms for Solving Pressure Poisson Equation for Multiphase Flows using Parallel Computers

Numerical solution of partial differential equations on parallel compute...
research
01/21/2020

Understanding the stochastic partial differential equation approach to smoothing

Correlation and smoothness are terms used to describe a wide variety of ...
research
01/31/2022

Deep Petrov-Galerkin Method for Solving Partial Differential Equations

Deep neural networks are powerful tools for approximating functions, and...

Please sign up or login with your details

Forgot password? Click here to reset