Prediction of impedance responses of protonic ceramic cells using artificial neural network tuned with the distribution of relaxation times

A deep-learning-based framework is proposed to predict the impedance response and underlying electrochemical behavior of the reversible protonic ceramic cell (PCC) across a wide variety of different operating conditions. Electrochemical impedance spectra (EIS) of PCCs were first acquired under a variety of operating conditions to provide a dataset containing 36 sets of EIS spectra for the model. An artificial neural network (ANN) was then trained to model the relationship between the cell operating condition and EIS response. Finally, ANN model-predicted EIS spectra were analyzed by the distribution of relaxation times (DRT) and compared to DRT spectra obtained from the experimental EIS data, enabling an assessment of the accumulative errors from the predicted EIS data vs the predicted DRT. We show that in certain cases, although the R² of the predicted EIS curve may be > 0.98, the R² of the predicted DRT may be as low as ∼ 0.3. This can lead to an inaccurate ANN prediction of the underlying time-resolved electrochemical response, although the apparent accuracy as evaluated from the EIS prediction may seem acceptable. After adjustment of the parameters of the ANN framework, the average R² of the DRTs derived from the predicted EIS can be improved to 0.9667. Thus, we demonstrate that a properly tuned ANN model can be used as an effective tool to predict not only the EIS, but also the DRT of complex electrochemical systems.