Goal & Context: Increase the degree of automation in polymeric membrane characterization by equivalent circuits
While solving the Machine learning problem outlined here (see the second paragraph) enriches the toolbox of scientists and engineers in many fields, we consider it to speed up the search for more suitable polymeric membranes. Polymeric membranes are at the heart of many devices that perform electrocatalytic processes such as devices for solar water splitting and CO2 reduction reaction. In those devices, the membranes serve two important functions: They allow to keep the two compartments of the cell ("positive" and "negative" sides) separated, so that it becomes possible to accumulate the reaction products on each side. At the same time, membranes support ion transfer between the two sides of the cell, closing the circuit within the liquid electrolyte and allowing the application of electrical biases.
To investigate how the physical/chemical properties of a polymeric membrane evolve over time (thus influencing the overall performance of the electrochemical device), scientists need a way to characterize the membranes while under operating conditions. One such way is to observe how the membrane reacts to AC voltage sources with different frequencies and to search an electrical equivalent circuit (EEC), that is a circuit (consisting of elementary electronic elements such as resistors and capacitors) that produces the same reactions as the membrane [1,2]. The parameters of the found EEC are associated to processes that occur in the electrochemical device and on the membrane. Changes in the EEC architecture and in the values of the circuital elements over time hence reveal information about changes in those processes. In the search for an EEC, the first step is an architectural choice, namely the arrangement (parallel, serial) of the circuit elements, the second step concerns the parameters of the elements. Currently, both steps relay, to a large part, on human intuition [3],[4],[5]. The goal of this thesis is to increase the degree of automation in both steps.
Machine Learning: Inverse problems for multiple forward models
The second step of the problem of finding an EEC can be framed as an inverse problem ([6],[7]), since the map from the parameters of the circuit to the answer of this circuit to the AC sources, the so called forward map, is known, while the backward map from this AC answer to an equivalent parametrization is searched. Furthermore, the combination of step one and two leads to a special problem structure: There are multiple possible architectures for the EEC, or in other words, there are multiple possible forward models. One approach could be to assume that there is an 'universal'/abstract parametrization and that for each architecture there are maps from the universal parametrization to the equivalent parametrization of the architecture. The main goal of the thesis is to extend an existing machine learning based inverse problem solver (examples are [8], [9],[10]) such that it supports the multiple forward model and to empirically study this extension. Interesting questions are: Does the training profit from the multiple forward models? How hard is it to extend a trained model such that it can support a new architecture? What information can we deduce from the universal parameter set? How does it compare to a benchmark model such as a minimally adopted 'traditional' auto-encoder based architecture?
In fact, the membrane use-case is only one instance of the general machine learning problem to learn a universal parameter set in situations where there are multiple possible forward models.
Qualifications
- Bachelor degree in computer science, physics or mathematics
- Experience in implementing machine learning models
- Ability to work scientifically independently
- Interest in interdisciplinary work
- Suited for teamwork
- Good knowledge of the English language
Contact
Dr. Alexander Kister
P: +49 (0)30 8104-4826
E: Alexander.Kister@bam.de
[1] Electrochemical Impedance Spectroscopy (ntnu.edu)
[2] Physical Interpretations of Nyquist Plots for EDLC Electrodes and Devices | The Journal of Physical Chemistry C (acs.org)
[3] Applying Machine Learning Techniques to Lithium-ion Cell Research (dal.ca)
[4] Equivalent Circuits Applied in Electrochemical Impedance Spectroscopy and Fractional Derivatives with and without Singular Kernel (hindawi.com)
[5] A Study on Battery Model Parametrisation Problem - Application-Oriented Trade-offs between Accuracy and Simplicity - ScienceDirect
[6] Inverse Problems: The American Mathematical Monthly: Vol 83, No 2 (tandfonline.com)
[7] Deep Learning and Inverse Problems | NeurIPS Workshop on Deep Learning and Inverse Problems (deep-inverse.org)
[8] [1912.04212] Solving Bayesian Inverse Problems via Variational Autoencoders (arxiv.org)
[9] [1808.04730] Analyzing Inverse Problems with Invertible Neural Networks (arxiv.org)
[10] Variational Autoencoder with Learned Latent Structure (mlr.press)