lpde 0.0.4

Learning Partial Differential Equations

Learning Partial Differential Equations

INSTALLATION

By way of pip:

pip install lpde

By way of source

git clone https://github.com/fkemeth/lpde
cd lpde
pip install .

USAGE

This python package contains functions to learn partial differential equations (PDE) from data.

• The main components consists of a neural network PDE class Network(torch.nn.Module). To create an instance of this class, one needs to pass a config dictionary that specifies

  • kernel_size: The width of the finite difference stencil used to calculate input spatial derivatives
  • n_derivs: The number of derivatives used in the PDE model
  • device: Either 'cpu' or 'cuda
  • use_param: Boolean that specifies
  • num_params: If use_param is True, then here the number of parameters that change have to be specified.
  • n_filters: The number of neurons in each layer of the PDE model.
  • n_layers: The number of layers of the PDE model.

  In addition, the number of system variables n_var has to be provided

• Furthermore, a model wrapper to train and evaluate the neural network PDE is provided as a Model class. To create an instance of this class, one needs to provide

  • dataloader_train: A pytorch dataloader with the training data
  • dataloader_val: A pytorch dataloader with the validation data
  • network: A Network instance, as described above
  • config: A config dictionary containing
    • lr: The initial learning rate
    • patience: The patience used for the learning rate scheduler
    • reduce_factor: - The factor by which the learning rate is reduced when loss does not decrease
    • weight_decay: - Weight decay factor for regularization
  • path: String to the directory where the trained model shall be saved

See this GitHub repository for example usages.

ISSUES

For questions, please contact ([e-mail]), or visit the GitHub repository.

LICENCE

This work is licenced under MIT License. Please cite

"Learning emergent partial differential equations in a learned emergent space" F.P. Kemeth et al. (https://arxiv.org/abs/2012.12738)

if you use this package for publications.