DiffusionNet: Accelerating the solution of Time-Dependent partial differential equations using deep learning

Citation

@article{asem2020diffusionnet,
  title={DiffusionNet: Accelerating the solution of Time-Dependent partial differential equations using deep learning},
  author={Asem, Mahmoud},
  journal={arXiv preprint arXiv:2011.10015},
  year={2020}
}

Install requirements

pip install -r requirements.txt

I. Transient Heat transfer Section

Contents

Script	Description
solver.py	Alternate direction implicit scheme solver for transient heat transfer
DiffusionNet.py	Content Cell
generator.py	data generation utility functions for Transient heat transfer
visualize.py	Heat map comparison utility function
speedup_analysis.py	speedup analysis section utility functions

Notebook	Description
Reproduce models.ipynb	Reproduce trained models
Heatmaps figure.ipynb	Reproduce and visualize heat maps comparisons
Speedup figures.ipynb	Reproduce speedups plots for Iterations / Gridsize ( GPU+CPU specific )
Loss plots figures	Reproduce loss plots

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1) Reproduce trained models

To reproduce trained models, under Reproduce models notebook

1. Choose the appropriate parameters for grid size ,step,number of batches to be trained on.
2. Tick the train checkbox to start training, reproduced models will be saved under ReproducedModels and ReproducedLogs folders.

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2) Reproduce loss plots figures

Under Loss plots figures.ipynb notebook choose the desired log from drop down menu and check plot

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3) Reproduce Heat maps comparisons figure

Under visualization notebook, Choose the following parameters,

Parameter	Description
Step	step size
Content Cell	Content Cell
Grid size	Grid size NxN
bc1	Bottom boundary condition
bc2	Left boundary condition
bc3	Top boundary condition
bc4	Right boundary condition
ic	Initial condition
t00	Initial input step to model

1. Tick analyze to view Timing of numerical solution and deep learning solution, and Error metrics.
2. Ticks plot to view the heat maps of Numerical solution , Deep learning solution and the absolute difference between them, respectively.
3. Tick save to save the resultant heat maps (optional).
4. Make sure the loaded model Step[10,100] and gridsizes[12,24,48,96] matches that of selected heat maps parameters above

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4) Reproduce Speedup figures

Under Speedup Figures notebook, Choose the following parameters,

Parameter	Description
Speedup analysis	Iteration analysis / Gridsize analysis
P	Deep learning prediction step
Grid size	Grid size NxN

Tick Start to start analysis and then plot figures as in below

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II. Inviscid burgers Section

Contents

Script	Description
utils.py	Utility functions
DiffusionNet.py	Content Cell
generator.py	data generation utility functions for Transient heat transfer

Notebook	Description
Reproduce models.ipynb	Reproduce trained models
Reproduce Figures.ipynb	Reproduce Data representation,Error histogram and Sample plot figure
Reproduce Test data prediction.ipynb	Generate the prediction of DiffusionNet for the given test data