Data-Driven Analysis of Electrochemical Processes

In this research area, we propose a novel data-driven analysis of electrochemical processes using the Loewner framework (LF) (see Figure 1). Our initial focus is on analyzing linear frequency response data, such as Electrochemical Impedance Spectroscopy (EIS) [1,2], a widely used method for examining various electrochemical systems, and Concentration Frequency Response Analysis (CFRA) [1], a new frequency response method that employs periodic concentration perturbations as input. Additionally, we have demonstrated that this analysis can be extended to nonlinear frequency response data [3].

Figure 1: A schematic representation showing application of Loewner framework based algorithm for determination of the distribution of relaxation times. Regularization or parameters adjustment is not necessary. Based on [2] — **Figure 1:** A schematic representation showing application of Loewner framework based algorithm for determination of the distribution of relaxation times. Regularization or parameters adjustment is not necessary. Based on [2]

**Figure 1:** A schematic representation showing application of Loewner framework based algorithm for determination of the distribution of relaxation times. Regularization or parameters adjustment is not necessary. Based on [2]

Figure 2: Experimental EIS spectra of ferrocyanide oxidation on a rotating disk electrode at different potentials. These spectrawere analyzed using a),b) a mechanistic model based on [R6], c) a LF data-driven model, and d) a LF distribution of relaxationtimes (DRT). While the mechanistic model shows some deviations, the data-driven model perfectly describes the experimentaldata. The LF DRT reveals additional features not present in the mechanistic model. This information can be used to improve the mechanistic model. Based on [2]. — **Figure 2:** Experimental EIS spectra of ferrocyanide oxidation on a rotating disk electrode at different potentials. These spectra were analyzed using a),b) a mechanistic model based on [R6], c) a LF data-driven model, and d) a LF distribution of relaxation times (DRT). While the mechanistic model shows some deviations, the data-driven model perfectly describes the experimental data. The LF DRT reveals additional features not present in the mechanistic model. This information can be used to improve the mechanistic model. Based on [2].

**Figure 2:** Experimental EIS spectra of ferrocyanide oxidation on a rotating disk electrode at different potentials. These spectra
were analyzed using a),b) a mechanistic model based on [R6], c) a LF data-driven model, and d) a LF distribution of relaxation
times (DRT). While the mechanistic model shows some deviations, the data-driven model perfectly describes the experimental
data. The LF DRT reveals additional features not present in the mechanistic model. This information can be used to improve the mechanistic model. Based on [2].

LF is a data-driven modeling methodology grounded in linear system theory. It provides a transfer function in the frequency domain in the form of a rational polynomial that interpolates the data, effectively offering a Voigt model that interpolates the impedance data set. This method was introduced in electrochemistry through collaboration with Prof. Antoulas (formerly of the MPI fellow group and currently at Rice University, Houston) and Dr. Gosea (CSC group), who are experts in LF and have demonstrated its application across various scientific fields over the years [2 and references therein]. LF enhances EIS data analysis by identifying unique distributions of relaxation times (DRT) for different systems, offering deeper insights into the underlying electrochemical processes. The effectiveness of this approach is validated through the analysis of both synthetic and experimental EIS data (Figure 2), highlighting its potential to revolutionize EIS data analysis and contribute to more accurate modeling of electrochemical systems. This work is relevant to researchers and practitioners in electrochemistry, materials science, and energy technology, enhancing the development and optimization of key technologies such as fuel cells, batteries, and electrolyzers.

Funding: IMPRS

Collaborations:

Prof. Antoulas Rice University Houston, USA & Dr. Gosea, MPI Magdeburg

Selected recent publications:

[1] Patel, B. (2021) Application of Loewner framework for data-driven modeling and diagnosis of polymer electrolyte membrane fuel cells, Master Thesis, Otto-von-Guerike Universität, doi:10.25673/101328.

[2] Sorrentino, A., Patel, B., Gosea, I. V., Antoulas, A. C., & Vidaković-Koch, T. (2023) Determination of the distribution of relaxation times through Loewner framework: A direct and versatile approach Journal of Power Sources, 585, 233575. doi:10.1016/j.jpowsour.2023.233575

[3] Gosea, I. V., Živković, L. A., Karachalios, D., Vidaković-Koch, T., & Antoulas, A. C. (2023) A data-driven nonlinear frequency response approach based on the Loewner framework: preliminary analysis In: IFAC-Papers OnLine, 234–239 doi:10.1016/j.
ifacol.2023.02.040