Physics-informed Artificial Neural Network
Author: Helon Ayala, October 2020
Based on: https://github.com/maziarraissi/DeepVIV
(translated to Keras layer subclassing and tf 2.0)
In this notebook we reproduce the results of the paper
- Raissi, Maziar, Zhicheng Wang, Michael S. Triantafyllou, and George Em Karniadakis."Deep learning of vortex-induced vibrations." Journal of Fluid Mechanics 861 (2019): 119-137.
in particular Section 2.1. Please refer to the paper for a detailed description of the method and case study. In the following we restrict to the information needed for the notebook to be self-contained.
https://www.youtube.com/watch?v=W1V14HBtSPE
Extend it to x,y,t independent variables (for e.g. NS-eqs.). Step-by-step:
- add more outputs to
class tToXandF(tf.keras.layers.Layer):, specifically in the lineself.denseList.append(tf.keras.layers.Dense(1)) # output layer - add more gradients to the environment
with tf.GradientTape( - change input-output data and loss function