Physics-Informed Deep Operator Control (PIDOC), a deep learning method for controlling nonlinear chaos.

PIDOC is based on PINNs, is a general framework can be used for control nonlinear dynamics, achieved by the encoded control trajectory in the losses. Right now, PIDOC has only been used for control the van der Pol systems (Zhai & Sands, 2022). However, if carefully tuned, it can be applied to more complex systems.

To play with our simple example cases, you need to first download and convert your tensorflow to version 1.x; (Google Colab is a great platform for it) or directly download it through

pip install tensorflow==1.15.0

Then download our repo:

git clone https://github.com/hanfengzhai/PIDOC.git

Open the simple case of the van der Pol dynamics:

cd vanderPol

Run the basic example case with the benchmark case of 10% added noise:

python main.py

Or run with MPI using multiple cores:

mpirun -np 20 python benchmark_main.py

If the model start to train, you are ready to go! Try tunning the hyperparameters and change the training data (explore data) to play it around!

Based on the general framework of PINNs, PIDOC can be used for control all based on the signal-encoded (physics-informed) loss

L = MSE_NN + MSE_I + λ MSE_D

• where MSE_NN = MSE(x_prediction, x_training) is the neural network error given the training data.

• where MSE_I = MSE(x_prediction(0), x_control(0)) is the control error given the training data.

• where MSE_D = MSE(x_prediction, x_control) is the neural network error given the training data.

and λ is the Lagrangian multiplier to enforce control (proved in our paper that enlarging which doesn't work for better control).

It is clearly stated in our paper that PIDOC has an evident drawback: enlarging the systems nonlinearity will cause the reduced control quality.

If you use our package please considering cite:

@Article{math10030453,
AUTHOR = {Zhai, Hanfeng and Sands, Timothy},
TITLE = {Controlling Chaos in Van Der Pol Dynamics Using Signal-Encoded Deep Learning},
JOURNAL = {Mathematics},
VOLUME = {10},
YEAR = {2022},
NUMBER = {3},
ARTICLE-NUMBER = {453},
URL = {https://doi.org/10.3390/math10030453},
ISSN = {2227-7390},
DOI = {10.3390/math10030453}
}