DeePyMoD is a modular framework for model discovery of PDEs and ODEs from noise data. The framework is comprised of four components, that can separately be altered: i) A function approximator to construct a surrogate of the data, ii) a function to construct the library of features, iii) a sparse regression algorithm to select the active components from the feature library and iv) a constraint on the function approximator, based on the active components.

More information can be found in the following two papers: , arXiv:2011.04336, arXiv:1904.09406 and the full documentation is available on phimal.github.io/DeePyMoD/.

What's the use case? Classical Model Discovery methods struggle with elevated noise levels and sparse datasets due the low accuracy of numerical differentiation. DeepMoD can handle high noise and sparse datasets, making it well suited for model discovery on actual experimental data.

What types of models can you discover? DeepMoD can discover non-linear, multi-dimensional and/or coupled ODEs and PDEs. See our paper and the examples folder for a demonstration of each.

How to install

Dependencies and CUDA

We support Python 3.6, 3.7 and 3.8. We rely on the following packages, they will be installed in the pip installation procces for you: numpy, torch, sklearn, pysindy, natsort, tensorboard, matplotlib

We also make use of the PyTorch library, which can be installed with CPU and/or GPU support. Please refer to the PyTorch "Get Started" guide to get the version that is optimal for your system.

Install

To install DeePyMoD, pip can be used

pip install deepymod

in the main directory.

Development

If you wish to alter the code you can clone the package using:

git clone git@github.com:PhIMaL/DeePyMoD.git

and then install it from the cloned DeePyMoD directory using

pip install -e ./

Features

• Many example notebooks We have implemented a variety of examples ranging from 2D Advection Diffusion, Burgers' equation to non-linear, higher order ODE's If you miss any example, don't hesitate to give us a heads-up.

• Extendable DeePyMoD is designed to be easily extendable and modifiable. You can simply plug in your own cost function, library or training regime.

• Automatic library The library and coefficient vectors are automatically constructed from the maximum order of polynomial and differentiation. If that doesn't cut it for your use case, it's easy to plug in your own library function.

• Extensive logging We provide a simple command line logger to see how training is going and an extensive custom Tensorboard logger.

• Fast Depending on the size of the data-set DeepMoD, running a model search with DeepMoD takes of the order of minutes/ tens of minutes on a standard CPU. Running the code on GPU's drastically improves performance.