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FlowPINN Model

This repository contains all code and data relevant for reproducing the results of our paper "Bridging the Gap for Sparse Observations: Data-Driven versus Physics-Informed Neural Networks for Hydrogeological Applications". This readme was tested under Manjaro Linux. It should work similarly under Windows/Mac.

1. Prerequisites: Download Anaconda and Setup Anaconda Environment

For creating the virtual environment, we use Miniconda which is a light version of Anaconda. Please make sure that you have one of them installed on your machine.

Open the terminal/command line and type the following commands:

#clone repository on your computer
git clone https://github.com/linuswalter/PINN-for-Subsurface-Flow

# Install from file
conda env create -f environment.yml
conda activate FlowPINN

We recommend to use our code in VSCode in combination with the IPython Extension which allows you to run code cells separately.

1. Data

The 01_data directory contains the csv-files ogs_output_a_1e0.csv and ogs_output_a_5e0.csv which contain the synthetic datasets for an equivalent fracture length of a=1m and a=5m. These are outputs from the numerical code OpenGeoSys. To make these outputs more reproducible, we also appended the directories model_a_1e0 and model_a_5e0 which contain the respective mesh files (See mesh-directory, the project file LiquidFlow.prj for running the OGS model and the OGS output files in the pvd and vtu format. The file LiquidFlow_.pvd can be viewed in the interactive GUI of ParaView.

2. Experiments

To reproduce the experimental results, just start initialize and run the Jupyter Notebook. The model can be parameterized in the section "Experimental Parameters".

2.1 Experiment ANN versus PINN

For reproducing the first experiment, you need to select the following options when setting up the experiment parameters:

Name Ground Truth Dataset = ogs_output_a_5e0
Load weights for kd? = False
Load weights for pd_pinn? = False
Number Epochs Training kd = 500
Number Epochs pd = 1000
Perform retraining for too high loss values? = False
Number of Iterations = 1
Nr observation points = 25
Standard Deviation of the Gaussian Noise = 0
PINN with observation loss term? = True
Learning Rate values = [0.001, 1e-05]
Learning Rate method = step
Adaptive Weighting = None
Safe Plots as PNG? = True
Create GIF of PNG? = True

In the second part of the first experiment, one can set the experiment parameter Standard Deviation of the Gaussian Noise to a higher value, like σ = 0.02 or σ=0.04.

Expected Results:

2.2 PINN with high Permeability Contrast and no Observation Points

The second experiment can be reproduced by choosing the following parameter settings.

Name Ground Truth Dataset = ogs_output_a_1e0
Load weights for kd? = False
Load weights for pd_pinn? = False
Number Epochs Training kd = 300
Number Epochs pd = 500
Perform retraining for too high loss values? = True
Error Treshold for Retraining PINN = 0.0001
Number of Iterations = 20
Nr observation points = 0
Standard Deviation of the Gaussian Noise = 0
PINN with observation loss term? = False
Learning Rate values = [0.001, 1e-05]
Learning Rate method = step
Adaptive Weighting = None
Safe Plots as PNG? = True
Create GIF of PNG? = True

Expected Result:

Model Output

The results will be saved in the directory 02_model_output -> model_DATE_TIME