The Deep-Prior Distribution of Relaxation Times

Electrochemical impedance spectroscopy (EIS) is the established tool for the study of many electrochemical experiments. While the analysis of EIS data is challenging, this can be assisted by the distribution of relaxation time (DRT) method. However, obtaining the DRT is difficult as the underlying problem is ill-posed. Inspired by recent advances in image analysis, we develop a completely new approach, named the deep prior distribution of relaxation time (DP-DRT), for the deconvolution of the EIS to obtain the DRT. The DP-DRT uses a deep neural network fed with a single random input to deconvolve the DRT and fit the EIS data. The DP-DRT has the peculiarity of having a number of parameters much larger than the number of observations. Further, unlike most supervised deep learning models, large datasets are not needed as the DP-DRT is trained against a single available EIS spectrum. The DP-DRT was successfully tested against both synthetic and real experiments displaying considerable promise and opportunities for extensions.