hybrid-drt is a Python package for probabilistic analysis of electrochemical data.

The philosophy underpinning hybrid-drt is that distribution of relaxation times (DRT) analysis should fulfill two objectives: (1) determine the relaxation magnitude as a function of timescale and (2) identify the distinct processes that comprise the total distribution. The first objective is a regression task that is fulfilled by conventional DRT algorithms, while the second objective is a pseudo-classification task that is ignored by most DRT algorithms. hybrid-drt unites the regression and classification views of DRT inversion to clarify DRT interpretation and meaningfully express uncertainty, following the framework developed in this paper. The package currently provides several methods for analyzing electrochemical impedance spectroscopy (EIS) data:

• Conventional DRT estimation via a self-tuning hierarchical Bayesian model
• Probabilistic EIS deconvolution using the probability function of relaxation times (PFRT)
• A "dual inversion" algorithm for autonomous discrete model generation, comparison, and selection
• Methods for scoring the accuracy of DRT estimates using regression, classification, and hybrid metrics

Additional tutorials and new functionality will be added soon.

Disclaimer: hybrid-drt is experimental and under active development. The code is provided to demonstrate several conceptual approaches to electrochemical analysis, but the details of the implementation may change in the future.

hybrid-drt requires the mittag-leffler package, which is available at https://github.com/jdhuang-csm/mittag-leffler. hybrid-drt also requires the following packages:

• numpy
• matplotlib
• scipy
• pandas
• cvxopt
• scikit-learn

Install hybrid-drt from the repository files using either conda or pip. See installation.txt for step-by-step instructions.

If you use hybrid-drt in published work, please consider citing the following paper:

Huang, J. D., Sullivan, N. P., Zakutayev, A., & O’Hayre, R. (2023). How reliable is distribution of relaxation times (DRT) analysis? A dual regression-classification perspective on DRT estimation, interpretation, and accuracy. Electrochimica Acta, 443, 141879. https://doi.org/10.1016/j.electacta.2023.141879