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Helper functions for NSE as LPV with Neural Networks

Project description

Neural Networks for NSE as low-dimensional LPV

Active workflow


# 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

# install this module and helper modules
pip install .

Generate the data

cd ../simulations-training-data
mkdir cached-data
mkdir train-data
# source

# python3
cd -

Check the NN


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. 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 ...'}
  1. (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]
  1. 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.

  2. 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




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


# 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.

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