This is a reproduction of the EQL machine learning model and its variations [1, 2] using Keras and Tensorflow.
It's worth noting that the resources in this repository are not perfectly documented and also highly customized to my research. Use at your own risk.
That being said, this repository can be used via a cloning to either your working directory or the folder housing your downloaded Python packages. models.py houses the EQL and EQLDIV classes, the two ML models developed in this project. These classes depend upon Keras and Tensorflow, along with custom Keras Layer/Constraint/Regularizer classes which can be found in the keras_classes.py file. Example code for creating and training the EQLDIV model shown in the image above is as follows.
import equation_learner as eql
my_eql_model = eql.models.EQLDIV(inputSize=3, outputSize=3, numLayers=3)
my_eql_model.build()
my_eql_model.fit(predictors, labels, numEpoch=1000)
Both EQL and EQLDIV classes have utility methods which allow users to do things like print the equation which the model has learned (getEquation()), plot 2-D slices of that equation (plotSlice()), and obtain the number of active nodes in the model architecture (sparsity()).
The user can use the functions in the data.py file to generate .npy files for use as training/testing datasets.
If the user is training their model to learn systems of ODEs, they can use functions in the ode.py file to evaluate and visualize the accuracy of their trained models, along with various other attributes depending on the system (conservation of energy, etc).
vpy.py contains functions which utilize VPython to create animations of double pendulums, controlled by their true equations of motion and/or equations of motion learned by an EQL/EQL-div model.
[1] Martius, Georg, and Christoph H. Lampert. "Extrapolation and learning equations." arXiv preprint arXiv:1610.02995 (2016).
[2] Sahoo, Subham S., Christoph H. Lampert, and Georg Martius. "Learning equations for extrapolation and control." arXiv preprint arXiv:1806.07259 (2018).