hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition

by   Ehsan Kharazmi, et al.

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space of high-order polynomials. The trial space is the space of neural network, which is defined globally over the whole computational domain, while the test space contains the piecewise polynomials. Specifically in this study, the hp-refinement corresponds to a global approximation with local learning algorithm that can efficiently localize the network parameter optimization. We demonstrate the advantages of hp-VPINNs in accuracy and training cost for several numerical examples of function approximation and solving differential equations.


page 14

page 18

page 19

page 20

page 21


Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Physics-informed neural networks (PINNs) [31] use automatic differentiat...

Physics informed neural networks for continuum micromechanics

Recently, physics informed neural networks have successfully been applie...

Parallel Physics-Informed Neural Networks via Domain Decomposition

We develop a distributed framework for the physics-informed neural netwo...

Variational energy based XPINNs for phase field analysis in brittle fracture

Modeling fracture is computationally expensive even in computational sim...

Variational Physics Informed Neural Networks: the role of quadratures and test functions

In this work we analyze how Gaussian or Newton-Cotes quadrature rules of...

Discontinuity Computing with Physics-Informed Neural Network

How to simulate shock waves and other discontinuities is a long history ...

Numerical Approximation in CFD Problems Using Physics Informed Machine Learning

The thesis focuses on various techniques to find an alternate approximat...

Code Repositories


hp-VPINNs: variational physics-informed neural network with domain decomposition is a general framework to solve differential equations

view repo