Probabilistic deconvolution of the distribution of relaxation times from multiple electrochemical impedance spectra

Electrochemical impedance spectroscopy (EIS) is widely used to study the properties of electrochemical materials and systems. However, analyzing EIS data remains challenging. Among various analysis methods, the distribution of relaxation times (DRT) has emerged as a novel non-parametric approach capable of providing timescale information. Among the various DRT inversion methods, those based on Gaussian processes (GP) are particularly promising because they provide uncertainty estimates for both EIS and DRT. However, current GP-based DRT implementations can only handle one spectrum at a time. This work extends these models to allow concurrent analysis of multiple impedance spectra as a function of experimental conditions. The new method, called the quasi-Gaussian process distribution of relaxation times, treats the DRT as a GP with respect to the experimental state and as a finite approximation of a positively constrained GP with respect to timescales. This new DRT inversion approach is validated against noise-corrupted artificial EIS data and applied to experimental data, allowing us to expedite EIS data analysis of multiple EIS data from a probabilistic perspective.