init

LICENSE.rst

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+The MIT License (MIT)
+
+Copyright (c) 2019-2020 ATHENA contributors
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

README.md

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+## Table of contents
+- [Table of contents](#table-of-contents)
+- [Description](#description)
+- [Dependencies and installation](#dependencies-and-installation)
+- [Documentation DD-ROMs for Friedrichs' systems](#documentation-dd-roms-for-friedrichs-systems)
+  - [Procedure for DD-ROMs with repartitioning strategies](#procedure-for-dd-roms-with-repartitioning-strategies)
+  - [Procedure for vanishing viscosity solutions inference with GNNs](#procedure-for-vanishing-viscosity-solutions-inference-with-gnns)
+- [How to cite](#how-to-cite)
+- [Authors and contributors](#authors-and-contributors)
+- [License](#license)
+
+## Description
+This repository contains the code used to generate the results in the pre-print "**Friedrichs’ systems discretized with the Discontinuous Galerkin method:
+domain decomposable model order reduction and Graph Neural Networks
+approximating vanishing viscosity solutions**", https://arxiv.org/pdf/2308.03378.
+
+## Dependencies and installation
+The following packages are required `deal.II`, `PETSc`, `petsc4py`, `torch`, `torch_geometric`, `pytorch_lightning` among others.
+
+## Documentation DD-ROMs for Friedrichs' systems
+### Procedure for DD-ROMs with repartitioning strategies
+
+Compile the deal.II script. As first step we need to save the matrices needed for the affine decomposition:
+```bash
+> cd maxwellParallel
+> cmake .
+> make release
+> make 
+> mpirun -np 4 ./maxwell
+```
+we also need the positions of the support points of the dofs for our repartitioning strategies. Inside "parameters.prm" set "task to perform" from "affine" to "save_pos". Then run:
+```bash
+> mpirun -np 4 ./maxwell
+> cd affine_matrices
+> python3 postprocess.py 4
+> cd ..
+> cd ..
+```
+run offline and online stages in parallel with:
+```bash
+> mpirun -np 4 python3 run_FOM_ROM.py
+```
+
+**Additionally**: to see the partitioning of the computational domain do the following:
+```bash
+> cd maxwellParallel
+```
+inside "parameters.prm" set "task to perform" from "affine" to "labels"
+```bash
+> mpirun -np 4 ./maxwell
+```
+and open in paraview:
+```bash
+> paraview partition_0.pvtu
+```
+
+**Additionally**: to plot the FOM and ROM solutions do the following:
+```bash
+> cd maxwellParallel
+```
+inside "parameters.prm" set "task to perform" from "affine" to "plot"
+```bash
+> mpirun -np 4 ./maxwell
+```
+and open the fields in paraview: the FOM fields with
+```bash
+> paraview snapshots/reconstructed_[0-9].pvtu
+```
+and the DD-ROM predicted fields
+```bash
+> paraview snapshots/rreconstructed_[0-9].pvtu
+```
+
+### Procedure for vanishing viscosity solutions inference with GNNs
+The following procedure is used to infer the vanishing viscosity solutions through our multi-fidelity multi-resolution strategy that makes use of DD-ROMs and GNNs. Run the following to train a GNN with data already obtained from an advection-diffusion-reaction test case: download first the dataset with
+```bash
+> cd vv
+> wget https://zenodo.org/records/13946510/files/vv.tar.gz
+> tar -zxfv vv.tar.gz
+```
+then run the training with:
+```bash
+> python3 vvgraph_all.py
+```
+move the file that starts with "tb_logs/vv/version_0/checkpoints/epoch*" in "tb_logs/vv.ckpt" so that it can be loaded by the script "predict.py"
+```bash
+> python3 predict.py
+```
+
+## How to cite
+If you use this package in your publications please cite the package as follows:
+
+Romor, F., Torlo, D. and Rozza, G., 2023. Friedrichs' systems discretized with the Discontinuous Galerkin method: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions. arXiv preprint arXiv:2308.03378.
+
+Or if you use LaTeX:
+```tex
+@article{romor2023friedrichs,
+  title={Friedrichs' systems discretized with the Discontinuous Galerkin method: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions},
+  author={Romor, Francesco and Torlo, Davide and Rozza, Gianluigi},
+  journal={arXiv preprint arXiv:2308.03378},
+  year={2023}
+}
+```
+
+## Authors and contributors
+The authors of the reported results are
+* [Francesco Romor](mailto:francesco.romor@gmail.com)
+* [Davide Torlo](davidetorlo@gmail.com)
+
+under the supervision of [Prof. Gianluigi Rozza](mailto:gianluigi.rozza@sissa.it).
+
+Contact us by email for further information or questions, or suggest pull requests. Contributions improving either the code or the documentation are welcome!
+
+## License
+
+See the [LICENSE](LICENSE.rst) file for license rights and limitations (MIT).