Multigoal-oriented dual-weighted-residual error estimation using deep neural networks

12/21/2021
by   Ayan Chakraborty, et al.
0

Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. Deep learning is also considered as a powerful tool with high flexibility to approximate functions. In the present work, functions with desired properties are devised to approximate the solutions of PDEs. Our approach is based on a posteriori error estimation in which the adjoint problem is solved for the error localization to formulate an error estimator within the framework of neural network. An efficient and easy to implement algorithm is developed to obtain a posteriori error estimate for multiple goal functionals by employing the dual-weighted residual approach, which is followed by the computation of both primal and adjoint solutions using the neural network. The present study shows that such a data-driven model based learning has superior approximation of quantities of interest even with relatively less training data. The novel algorithmic developments are substantiated with numerical test examples. The advantages of using deep neural network over the shallow neural network are demonstrated and the convergence enhancing techniques are also presented

READ FULL TEXT

page 14

page 18

page 19

research
02/24/2021

Neural network guided adjoint computations in dual weighted residual error estimation

In this work, we are concerned with neural network guided goal-oriented ...
research
08/12/2021

Multigoal-oriented error estimation and mesh adaptivity for fluid-structure interaction

In this work, we consider multigoal-oriented error estimation for statio...
research
07/23/2021

Error Estimates for Neural Network Solutions of Partial Differential Equations

We develop an error estimator for neural network approximations of PDEs....
research
12/23/2021

Space-time error control using a partition-of-unity dual-weighted residual method applied to low mach number combustion

In this work, a space-time scheme for goal-oriented a posteriori error e...
research
10/25/2022

A Deep Fourier Residual Method for solving PDEs using Neural Networks

When using Neural Networks as trial functions to numerically solve PDEs,...
research
12/31/2017

Using Deep Neural Network Approximate Bayesian Network

We present a new method to approximate posterior probabilities of Bayesi...
research
06/15/2020

Deep-CAPTCHA: a deep learning based CAPTCHA solver for vulnerability assessment

CAPTCHA is a human-centred test to distinguish a human operator from bot...

Please sign up or login with your details

Forgot password? Click here to reset