Weak Form Generalized Hamiltonian Learning

This library provides a PyTorch implementation for performing Weak Form Generalized Hamiltonian Learning. This code accompanies this Neurips2020 paper [1] by Kevin L. Course, Trefor W. Evans, and Prasanth B. Nair.

As everything is written in PyTorch, all algorithms provide full GPU support.

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Please cite our paper if you find this code useful in your research. The bibliographic information for the paper is,

@inproceedings{course_wfghnn_2020,
 author = {Course, Kevin and Evans, Trefor and Nair, Prasanth},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {H. Larochelle and M. Ranzato and R. Hadsell and M. F. Balcan and H. Lin},
 pages = {18716--18726},
 publisher = {Curran Associates, Inc.},
 title = {Weak Form Generalized Hamiltonian Learning},
 url = {https://proceedings.neurips.cc/paper/2020/file/d93c96e6a23fff65b91b900aaa541998-Paper.pdf},
 volume = {33},
 year = {2020}
}

Our experiments make heavy use of Chen et. al's torchdiffeq package [2] and we use the rectified Huber unit from Kolter et. al [3].

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Installation

pip install git+https://github.com/coursekevin/weakformghnn#egg=weakformghnn

Library Overview

This library provides three main components:

• GHNN class: The class provides a convenient interface for specifying strong priors on the form of the generalized Hamiltonian. This module inherits from the torch nn.Module class. This allows GHNNs to be trained in the usual ways one can train a model for a continuous time ODE (ie. see [1,2]). See the ghnn_tutorial for an example of how to use this class in context.

• GHNNwHPrior class: This class has a similar structure to the main GHNN class except it should only be used when the generalized Hamiltonian is known. It can be trained in the same way as a standard GHNN.

• weak_form_loss: Use this loss function to perform "weak form regression" with any model for a continuous time ODE. See the weakform_tutorial for an example.

References

[1] Kevin L. Course, Trefor W. Evans, Prasanth B. Nair. "Weak Form Generalized Hamiltonian Learning." Advances in Neural Information Processing Systems. 2020.

[2] Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, David Duvenaud. "Neural Ordinary Differential Equations." Advances in Neural Information Processing Systems. 2018.

[3] J. Z. Kolter and G. Manek. “Learning Stable Deep Dynamics Models”. In: Advances in Neural Information Processing Systems 32. Ed. by H. Wallach, H. Larochelle, A. Beygelzimer, F. d. Alché-Buc, E. Fox, and R. Garnett. Curran Associates, Inc., 2019, pp. 11126–11134.