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https://github.com/trixi-framework/smartshockfinder.jl

Create troubled cell indicators for Trixi.jl using artificial neural networks
https://github.com/trixi-framework/smartshockfinder.jl

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Create troubled cell indicators for Trixi.jl using artificial neural networks

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README 

        
# SmartShockFinder.jl



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[![License: MIT](https://img.shields.io/badge/License-MIT-success.svg)](https://opensource.org/licenses/MIT)



**Note: This package is in a pre-alpha stage: anything can (and will!) change at any time!**



**SmartShockFinder.jl** is used to create troubled cell indicators based on neural networks. The obtained neural networks can be used directly in [Trixi.jl](https://github.com/trixi-framework/Trixi.jl). For receiving the final networks, the process is separated into two parts. The creation of the training data and the subsequent training of the networks.



**Datasets:**



The datasets are created with the functions  `generate_traindataset1d(...)` and `generate_traindataset2d(...)`. The datatype is passed as first parameter. This specifies the input data X of the training datasets. A distinction is made between NNPP and NNRH (and CNN in 2d).



* `datatype = NeuralNetworkPerssonPeraire()`

  * Input: The energies in lower modes as well as nnodes(dg).



* `datatype = NeuralNetworkRayHesthaven()`

  * 1d Input: Cell average of the cell and its neighboring cells as well as the interface values.

  * 2d Input: Linear modal values of the cell and its neighboring cells.



    Ray, Hesthaven (2018)

    "An artificial neural network as a troubled-cell indicator"

    [doi:10.1016/j.jcp.2018.04.029](https://doi.org/10.1016/j.jcp.2018.04.029)

    

    Ray, Hesthaven (2019)

    "Detecting troubled-cells on two-dimensional unstructured grids using a neural network"

    [doi:10.1016/j.jcp.2019.07.043](https://doi.org/10.1016/j.jcp.2019.07.043)



* `datatype = CNN (Only in 2d)`

  Based on convolutional neural network.

  * 2d Input: Interpolation of the nodal values of the `indicator.variable` to the 4x4 LGL nodes.



As additional parameters the number of meshs and the polynomial degree are passed. In the [`examples/`](examples/) folder, all training datasets are created once (`traindata_datatyp.jl`). Similarly, the `generate_validdataset1d(...)` (`generate_validdataset2d(...)`) function can be used to generate the validation datasets.



**Networks:**



With the obtained training datasets the neural networks can be trained. This is done with the functions `train_network1d(...)` and `train_network2d(...)` and with [Flux.jl](https://github.com/FluxML/Flux.jl).

Various parameters can be determined:

* `η = learning rate`

* `β = regularization paramater`

* `number_epochs`

* `Sb = batch size`

* `L = early stopping parameter`



In addition, the number of units in each layer can be passed. In the [`examples/`](examples/) folder, all networks are trained once (`network_datatyp.jl`). 



With the trained networks the `IndicatorNeuralNetwork()` in [Trixi.jl](https://github.com/trixi-framework/Trixi.jl) can be used.



The references to the used networks and datasets for the indicator types are listed below:



* `datatype = NeuralNetworkPerssonPeraire()` in 1d

  * traindata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/traindata1dNNPP.h5

  * validdata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/validdata1dNNPP.h5

  * network: https://gist.github.com/JuliaOd/97728c2c15d6a7255ced6e46e3a605b6/raw/modelnnpp-0.97-0.0001.bson

* `datatype = NeuralNetworkRayHesthaven()` in 1d

  * traindata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/traindata1dNNRH.h5

  * validdata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/validdata1dNNRH.h5

  * network: https://gist.github.com/JuliaOd/97728c2c15d6a7255ced6e46e3a605b6/raw/modelnnrh-0.95-0.009.bson

* `datatype = NeuralNetworkPerssonPeraire()` in 2d

  * traindata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/traindata2dNNPP.h5

  * validdata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/validdata2dNNPP.h5

  * network: https://gist.github.com/JuliaOd/97728c2c15d6a7255ced6e46e3a605b6/raw/modelnnpp-0.904-0.0005.bson

* `datatype = NeuralNetworkRayHesthaven()` in 2d

  * traindata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/traindata2dNNRHs.h5

  * validdata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/validdata2dNNRH.h5

  * network: https://gist.github.com/JuliaOd/97728c2c15d6a7255ced6e46e3a605b6/raw/modelnnrhs-0.973-0.001.bson

* `datatype = CNN()` in 2d

  * traindata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/traindata2dCNN.h5

  * validdata: https://gist.github.com/JuliaOd/f4d10153e539c026daf7076f087dc937/raw/validdata2dCNN.h5

  * network: https://gist.github.com/JuliaOd/97728c2c15d6a7255ced6e46e3a605b6/raw/modelcnn-0.964-0.001.bson



## Authors

SmartShockFinder was initiated by

[Michael Schlottke-Lakemper](https://www.mi.uni-koeln.de/NumSim/schlottke-lakemper) and

Julia Odenthal (both University of Cologne, Germany).



## License and contributing

SmartShockFinder is licensed under the MIT license (see [LICENSE.md](LICENSE.md)).