Jagtap, A.D., Kharazmi, E. and Karniadakis, G.E. (2020) Conservative Physics-Informed Neural Networks on Discrete Domains for Conservation Laws: Applications to Forward and Inverse Problems. Computer Methods in Applied Mechanics and Engineering, 365, Article ID: 113028.
https://doi.org/10.1016/j.cma.2020.113028

has been cited by the following article:

• TITLE: Physics-Aware Deep Learning on Multiphase Flow Problems

  AUTHORS: Zipeng Lin

  KEYWORDS: Deep Learning, Neural Network, Multi-Phase, Oil Incompressible, Fluid Physics, Partial Differential Equation

  JOURNAL NAME: Communications and Network, Vol.13 No.1, December 18, 2020

  ABSTRACT: In this article, a physics aware deep learning model is introduced for multiphase flow problems. The deep learning model is shown to be capable of capturing complex physics phenomena such as saturation front, which is even challenging for numerical solvers due to the instability. We display the preciseness of the solution domain delivered by deep learning models and the low cost of deploying this model for complex physics problems, showing the versatile character of this method and bringing it to new areas. This will require more allocation points and more careful design of the deep learning model architectures and residual neural network can be a potential candidate.