Sparse Identification of Nonlinear Dynamics (SINDy)

Overview

'Notebooks' Folder contains the Jupyter Notebooks.

1. Lorenz System

   1a. ODE modeling

   1b. Implementing PySINDy for discovery w/ and w/out noise

   1c. Implementing physics informed neural network for spatial/temporal simulation

2. Korteweg - De Vries & Burgers Equations

   2a. PDE modeling

   2b. Implementing PySINDy/PDE-FIND for discovery

   2c. Implementing physics informed neural network for spatial/temporal simulation

3. Waves

   3a. Modeling

   3b. PySINDy/PDE-FIND governing equation discovery

   3c. Implementing neural network for spatial/temporal simulation - maybe

4. Concluding remarks & analysis/presentation

This work is guided by the book Data Driven Science and Engineering by Brunton and Kutz.

Dependencies:

matplotlib widget and interactive plots requires Jupyter Lab with nodejs installed. Otherwise, switch to %matplotlib inline or %matplotlib notebook if using Jupyter Notebook. inline will not render animations. nodejs backend is useful.