Developed at TU Dortmund University

Author: Felix Kratz (felix.kratz@tu-dortmund.de)
Supervisor: Jan Kierfeld (jan.kierfeld@tu-dortmund.de)

Citation and use

If you use this work in your research department or company and you publish data obtained with this, please cite the following article:

• Pendant Drop Tensiometry: A Machine Learning Approach,
  Felix Kratz and Jan Kierfeld,
  The Journal of Chemical Physics 153.9 (2020), DOI: 10.1063/5.0018814

@article{kratz2020,
author = {Kratz, Felix S.  and Kierfeld, Jan },
title = {Pendant drop tensiometry: A machine learning approach},
journal = {The Journal of Chemical Physics},
volume = {153},
number = {9},
year = {2020},
doi = {10.1063/5.0018814}
}

Use of the provided neural nets

Prerequisites:

The provided neural nets need Tensorflow 2 to be installed on the machine. Keras is now part of Tensorflow such that no additional installation is needed.

An example of the instructions below is provided in the form of the jupyter notebook "example.ipynb". Also provided are some example shapes generated numerically from the Young-Laplace equation.

Loading the neural net

The neural net can be loaded by using the provided AIMan module by performing the command while exchanging "model_xy.h5" for the name of the desired network

aiMan = AIMan("models/model_xy.h5")

Format of the data

The provided DataHandler can be used to save an load the data in an optimized and efficient way. To save data using the DataHandler following code can be used

dataHandler = DataHandler()
dataHandler.data = coordinates
dataHandler.saveData("path/to/file")

where coordinates is an array of the evenly sampled shape coorinates with an arclength step of 1e-2.

To load data from the preprocessed file the following code can be used when initializing a new DataHandler object

dataHandler = DataHandler("path/to/preprocessed/file")

or alternatively, if a DataHandler object dataHandler is already present:

dataHandler.loadDataFromPreprocessedFile("path/to/preprocessed/file",
                                          readDataPercentage=1.,
                                          readDataPercentMode="front")

where additional arguments can be used, as from which end ("front", "back") the data is read and which percentage of the data should be read (1: all, 0: none).

Networks sampled uniformly in p_L - Δ ρ space

This applies to the networks model_uniform_rho.h5 and model_uniform_rho_noise.h5.

The input is a vector of 452 elements per batch, hence the input to the network has shape (batches, 452) which consists of 226 dimensionless coordinate pairs that are spaced evenly with an arclength step of 1e-2, when given the zero padded coordinate data zeroPaddedCoordinates in shape zeroPaddedCoordinates.shape = (batches, 226, 2), can be formated by using the reshape function from numpy

inputData = zeroPaddedCoordinates.reshape(len(zeroPaddedCoordinates),
                                          len(zeroPaddedCoordinates[0]) * len(zeroPaddedCoordinates[0][0]))

or alternatively, using the provided DataHandler

dataHandler = DataHandler()
dataHandler.data = coordinates
dataHandler.zeroPadData(newLength=226)
dataHandler.reshapeData()

Network sampled uniformly in p_L - Wo space

This applies to the network model_uniform_Wo.h5.

The input is a vector that consists of 1025 elements per batch, hence the input to the network has the shape (batches, 1025). The input vector is build up by 512 coordinate pairs and the dimensionless volume of the drop. If the data is present in the shape coorinates.shape = (batches, 512, 2); volume.shape = (batches) the input vector can be constructed by using following command using numpy as np:

inputData = coorinates.reshape(len(zeroPaddedCoordinates), len(zeroPaddedCoordinates[0]) * len(zeroPaddedCoordinates[0][0]))

appendedData = []
for i in range(len(zeroPaddedCoordinates)):
    appendedData.append(np.append(zeroPaddedCoordinates[i], volume[i]))
inputData = np.stack(appendedData)

or alternatively, using the provided DataHandler

dataHandler = DataHandler()
dataHandler.data = coordinates
dataHandler.calculateVolume()
dataHandler.zeroPadData(newLength=512)
dataHandler.reshapeData()
dataHandler.appendVolumeToData()

Predict material parameters

To predict the dimensionless control parameters of the Young-Laplace equation with the loaded neural net following command can be used:

parameters = aiMan.predict(inputData)

or, when using a DataHandler object dataHandler

parameters = aiMan.predict(dataHandler.data)

where parameters has shape (batches, 2). For shape i the control parameters can then be accessed via

p = parameters[i][0]
rho = parameters[i][0]

Outlook

An image preprocessing frontend has been developed, but is still in an experimental phase. It will be added to this repo as soon as it has been tested extensively.