PI-rCNN

An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator

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Arda Mavi ¹

Ali Can Bekar ¹

Ehsan Haghighat ²

Erdogan Madenci ¹

¹ University of Arizona, Tucson, AZ

² Massachusetts Institute of Technology, Cambridge, MA

Paper: arXiv:2210.12177

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Burgers’

Equation

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λ − ω Reaction-Diffusion

Equation

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Gray-Scott

Equation

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README Contents:

• Running the Code
• Modules -- Main Pipeline -- Pipeline options -- PDDO Kernels -- Model Procedures -- Training Procedure -- Plotting Procedure
• Data Generation
• Envoriment Versions
• Hardware
• Sample SLURM Job
• Cite as

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Running the Code

• Fulfill the environment requirements, see Envoriment Versions
• Download the Repository
• Create a Dataset/ folder under code.

Save the dataset (see Data Generation section) in it with name dataset.npy as Numpy file. - Change directory to code/Main_Pipeline - Run main pipeline using python main_pipeline.py or see Sample SLURM Job

Trained model parameters will be saved into code/Main_Pipeline/Checkpoints/Model

All the train and test figures will be saved into code/Main_Pipeline/Main_Outputs/Figures

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Modules

Detailed module documentations can be found in the module files, e.g. :

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code/Plotting/plotting_procedures.py

Main Pipeline:

File: code/Main_Pipeline/main_pipeline.py

Creating, training, and testing model and plotting the figures.

Pipeline options:

• python main_pipeline.py -m train creates and trains the model.
• python main_pipeline.py -m plot plots the figures using existed model.
• Use -m train plot arguments together or leave blank to run both pipeline.

PDDO Kernels:

Folder: code/PDDO_Kernels

Keeps Peridynamic kernel files as .mat format.

Model Procedures:

File: code/Model/model_procedure.py

Prepares model and loss functions.

Training Procedure:

File: code/Training/training_procedure.py

Model training procedure.

Plotting Procedure:

File: code/Plotting/plotting_procedure.py

Plotting of training loss, several comparison figures, and GIF animations of data during time.

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Data Generation

• Burgers’ Equation : Repo
• λ − ω Reaction-Diffusion Equation : Repo
• Gray-Scott Equation : Repo

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Envoriment Versions

• CentOS 7
• Anaconda 3
• Conda 4.9.2
• Python 3.6.13
• * CUDA 11.6
• * CuDNN 8.2.1.32
• * Cudatoolkit 10.2.89
• Necessary Python modules can be installed using pip install -r library_requirements.txt command.

* Optional for CPU usages. Required to take advantage of GPU and multi-GPU feature.

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Hardware

• Device Model: Penguin Altus XE2242

• CPU: AMD EPYC 7642 - 48 Cores - 2.4 GHz

• Memory: 4 GB

• * GPU: NVIDIA V100S - 32 GB

* Due to a bug we had with the TensorFlow library, only 22.4 GB out of 32 GB was allocated as the maximum GPU memory limit while testing GPU features.

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Sample SLURM Job

Sample SLURM Job script can be found with name slurm_job.sh under the Sample_Slurm_Job/ directory.

Caution: Change the <...> parts.

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Cite as

@misc{mavi2022unsupervised,
      title={An unsupervised latent/output physics-informed convolutional-LSTM network for solving partial differential equations using peridynamic differential operator},
      author={A. Mavi and A. C. Bekar and E. Haghighat and E. Madenci},
      year={2022},
      eprint={2210.12177},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}