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NNC: Neural Network Control

The nnc module aims to offer neural network controllers in pytorch, such as neural PIDs, Model Predictive control and other baselines.

NODEC: Neural Ordinary Differential Equation Control

NODEC is a novel method that controls dynamical systems that describe the evolution and interactions of networked components. We refer to these components as state variables on a graph. A graph consists of nodes that are connected with edges. Each node is assigned a state variable value, and this value evolves through time according to some interaction rules that are described in the form of an ordinary differential equation. External control signals may be applied to a subset of nodes to guide the evolution of the system towards a target state. The main idea is to use neural networks, and more specifically Neural ODEs to learn the aforementioned control signals in a non-supervised manner.


For now NNC and NODEC work only with pytorch, and we offer a very simple yet descriptive example on continuous time time-invariant dynamics, which can be found in:

  • examples/ct_lti_small/small_example.ipynb or examples/ct_lti_small/small_example.ipynb
  • Google Collab

A comparison between adjoint-gradient-method (AGM) and NODEC for Kuramoto dynamics control can be found in nodec_experiments/multiplicative_kuramoto.

The repository will be updated regularly with latest research work and applications. Our aim is to showcase the capabilities of NODEC, especially for high-dimensional non-linear dynamics.


Requirements to run nnc and its examples.


Module dependencies (nnc/*):

  • Python 3.6+
  • torch 1.4+
  • torchdiffeq
  • numpy 1.17.2+
  • scipy =1.3.1+

Example dependencies (examples/*):

  • plotly 4+
  • tqdm
  • pandas


We tested most our experiments on both CUDA and CPU. We advise using CUDA with more than 8GB of VRAM for training of NODEC.

Project structure

In code you may find 4 folders, and their contents are described as:

  • nnc the main neural network control module with utilities and baselines for neural network control.
  • nodec_experiments the folder containing the scripts that train and evaluate NODEC vs other baselines.
  • test: a folder with unit tests on some methods, which in the future will expand to achieve full coverage.
  • examples: a folder with small-scale examples, which aid in understanding how NODEC works.
  • ../data: a folder that contains the parameter and result data used by the scripts in the experiments folder to generate plots, train or evaluate.
  • ../results: a folder that contains the output of the scripts from nodec_experiments folder. In case you need to use data from the results folder please copy paste the date in the corresponding data folder or change the paths in the provided scripts.

Further Notes

As neural networks rely on stochastic initialization, results may vary compared to those described in our paper if a different weight initialization is used. Our current seed settings do not replicate exact results on different machines, but with a few runs it is possible to generate similar results to the paper. The seed setting will be further examined in the future.

For an overview of NODEC and its application to various dynamical systems, see our arXiv preprint arXiv:2006.09773 (soon to appear in Physical Review Research) and our work on AI Pontryagin.

Data of the numerical experiments can be found at IEEEDataPort.

These data contain pretrained models and evaluation results.

Please cite our work if this repository is useful for your research.

  title={Neural Ordinary Differential Equation Control of Dynamics on Graphs},
  author={Asikis, Thomas and B{\"o}ttcher, Lucas and Antulov-Fantulin, Nino},
  journal={Physical Review Research},
  url = {}
  title={AI Pontryagin or how neural networks learn to control dynamical systems},
  author={B{\"o}ttcher, Lucas and Antulov-Fantulin, Nino and Asikis, Thomas},
  journal={Nature Communications},


A framework for neural network control of dynamical systems over graphs.







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