Incorporating physical constraints in a (deep) probabilistic machine learning framework for coarse-graining dynamical systems

Highlights:

A generative model for the automated discovery of CG dynamics.
The target density is augmented by virtual observables which reflect physical constraints.
The incorporation of physical constraints leads to a reduction of the training data.
A probabilistic formulation that is capable of quantifying predictive uncertainty.
Full reconstruction of futures of the entire FG state vector as well as any FG observable.

Content:

The folder Particle contains some of the training data, code and results for the Advection-Diffusion and Burgers' example from the paper. The folder Pendulum contains some of the training data, code and results for the pendulum example from the paper.

Dependencies

For the particle example:

Tensorflow 1.13.1
mpi4py

For the pendulum example:

Tensorflow 2.0

Particle example

The proposed framework is applied to a system of moving particle. We are able to extract meaningful CG dynamics as well as to do interpolative and extrapolative predictions.

To visualize the results, please use the file Prediction.ipynb

To start the training process, please run mpi_train.py using mpirun

Pendulum example

The proposed framework is applied to a series of images of a nonlinear pendulum. We are able to extract the two-dimensional dynamics as well as a coarse-to-fine mapping.

To visualize the results, please use the file Prediction.ipynb

To start the training process, please run training.py

Citation

If this code is relevant for your research, please consider citing:

@article{kaltenbach2020incorporating,
  title={Incorporating physical constraints in a deep probabilistic machine learning framework for coarse-graining dynamical systems},
  author={Kaltenbach, Sebastian and Koutsourelakis, Phaedon-Stelios},
  journal={Journal of Computational Physics},
  year={2020},
  publisher={Elsevier},
  doi = "https://doi.org/10.1016/j.jcp.2020.109673",
  url = "https://www.sciencedirect.com/science/article/pii/S0021999120304472"
}

pkmtum/IncorporatingPhysicalConstraints