nse-nn-lpv 0.1.1

Helper functions for NSE as LPV with Neural Networks

Neural Networks for NSE as low-dimensional LPV

Active workflow

Installation

# package for sparse cholesky factorizations 
# not needed but speed up with FEM norms and POD
apt install libsuitesparse-dev
pip install scikit-sparse==0.4.5

# fenics -- for the FEM part
apt install fenics  # see https://fenicsproject.org/download/

# install this module and helper modules
pip install .

Generate the data

cd ../simulations-training-data
mkdir cached-data
mkdir train-data
source single-cylinder-tdp-sim.sh
# source double-cylinder-tdp-sim.sh

# python3 time_dep_nse_generic.py
cd -

Check the NN

python3 data_fem_checks.py
python3 CNN_AE.py

Data and Handling

Generally, the data is

1. generated by the simulation
2. interpolated to the pictures
3. imported to PyTorch as tensors

The relevant formats and routines are as follows:

import nse_nn_lpv.nse_data_helpers as ndh

1. time_dep_nse_generic.py computes the trajectories with snapshots vvec and interpolates them to the two pictures vmatx and vmaty at all time instances ti. The data is stored as a json file, say, data.json like

{ti: {'vvec': vvec, 'vmatx': vmatx, 'vmaty': vmaty},
 'femdata': 'information of the simulation ...'}

2. (datal, vvecl) = ndh.get_nse_img_data('data.json') takes the data file data.json and returns the data as a list (of tuples) of numpy arrays:

datal = [(vmatx, vmaty, t_0), ..., (vmatx, vmaty, t_end)]
vvecl = [vvec_0, ..., ..., ..., ..., vvec_end]

3. trn_nse_data = ndh.NSEDataset(nsedatal, vvecl) takes the data lists and makes it available as a pytorch data set. In particular, the two pictures vmatx, vmaty are merged into a tensor.

4. stst_dataloader = pytorch.DataLoader(trn_nse_data, batch_size=1, shuffle=True) then defines a way to access the data. E.g.,

(ttstset, tstvec) = next(iter(stst_dataloader))

returns a data point via

• ttstset: the tensor of size (batch_size, 2, width, height), where (width, height) are the dimensions of the pictures
• tstvec: the corresponding vvecs (needed, e.g., for the loss function later)

Python Machine-Learning Resources

• an overview
  1. Tensorflow -- see below
  2. Pytorch -- see below
  3. NeuroLab
  4. ffnet
  5. Scikit-Neural Network
  6. Lasagne
  7. pyrenn

Tensorflow

• website
• Article for understanding NN using TensorFlow
• Previous experience with building NN
• Visualization feature TensorBoard
• Based on keras

PyTorch

• website
• Tutorial for simple NN
• Recommended by colleagues (Lessig, Richter)

Scikit-Learn

• website
• looks well maintained
• many routines for data processing
• a few on neural network

Install

# not needed anymore
# pip install -e .  # Python3 needed here! install the module (and one dependency)

pip install -e installs the module nse_nn_lpv to be used in the tests/... but keeps track of all changes made in nse_nn_lpv.