To reduce the computational time, the DNN-DRT model developed herein includes a pretraining step. As shown in Figure , RR is used to obtain a coarse DRT estimate and pretrain the DNN . Then, the accuracy of the pretrained DNN is improved by minimizing a loss function generally without penalty (i.e., (2) without the 𝑃(𝜸) term). Second, postprocessing is used to analyze errors, and, if needed, the obtained model error is minimized by refining the grid over which the integral in (1) is computed. By removing the non-negativity constraint and introducing suitable penalty terms, the DNN-DRT model can recover DRTs with negative peaks. The consistency of the DNN-DRT method was evaluated using synthetic experiments, including EIS data with overlapping features, discontinuities, and negative peaks. Furthermore, the DNN-DRT method was validated against real EIS data from a lithium-ion battery , a solid oxide fuel cell , and a proton exchange membrane fuel cell .