A deep learning based nonlinear upscaling method for transport equations

07/07/2020
by   Tak Shing Au Yeung, et al.
0

We will develop a nonlinear upscaling method for nonlinear transport equation. The proposed scheme gives a coarse scale equation for the cell average of the solution. In order to compute the parameters in the coarse scale equation, a local downscaling operator is constructed. This downscaling operation recovers fine scale properties using cell averages. This is achieved by solving the equation on an oversampling region with the given cell average as constraint. Due to the nonlinearity, one needs to compute these downscaling operations on the fly and cannot pre-compute these quantities. In order to give an efficient downscaling operation, we apply a deep learning approach. We will use a deep neural network to approximate the downscaling operation. Our numerical results show that the proposed scheme can achieve a good accuracy and efficiency.

READ FULL TEXT

Authors

page 8

page 9

page 11

page 12

page 14

page 15

04/08/2021

High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state S_N transport equation

In this paper, we propose to combine the fifth order Hermite weighted es...
10/03/2020

Deep Learning algorithms for solving high dimensional nonlinear Backward Stochastic Differential Equations

We study deep learning-based schemes for solving high dimensional nonlin...
12/14/2021

Learn bifurcations of nonlinear parametric systems via equation-driven neural networks

Nonlinear parametric systems have been widely used in modeling nonlinear...
03/19/2019

Deep Eikonal Solvers

A deep learning approach to numerically approximate the solution to the ...
03/06/2021

Enhanced fifth order WENO Shock-Capturing Schemes with Deep Learning

In this paper we enhance the well-known fifth order WENO shock-capturing...
01/04/2021

Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity

Nonlinear multi-scale problems are ubiquitous in materials science and b...
06/19/2021

Learning Rays via Deep Neural Network in a Ray-based IPDG Method for High-Frequency Helmholtz Equations in Inhomogeneous Media

We develop a deep learning approach to extract ray directions at discret...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.