In addition, we compared the DNN-DRT and deep-DRT models for 𝑁 = 𝑀 (the parameters are reported in Table ) for the fractal and PWC models. The DNN-DRT model outperformed the deep-DRT model for the DRT recovery of the fractal (𝜀 , = 73.30% and 89.47% for the DNN-DRT and deep DRT models, respectively, see Table ) and PWC (𝜀 , = 7.50% and 10.45%) models. We also found that the DNN-DRT and deep-DRT models performed similarly for the impedance recovery (𝜀̅ , = 6.91% and 6.00% for the fractal model, 𝜀̅ , = 7.30% and 7.83% for the PWC model). The comparisons between the DNN-DRT and deep-DRT models were validated with ten synthetic spectra for each impedance model investigated (Table ). Next, we focused on the ability of the DNN-DRT model to handle DRTs with negative peaks, which we described with the hook model (the parameters are reported in Table S24 ). After RR, we observed oscillations at the bottom of each peak, and both peaks were underestimated (Figure (a)). This explains the high value of the DRT error for RR (𝜀 , = 41.30%, see Table ). Then, the DRT recovery was greatly improved after DNN training because of the two additional penalty terms 𝑃 (𝜽) and 𝑃 (𝜽) in ℒ (𝜽) (see ( )), which led to 𝜀 , ≤ 34.24%. The specific role of each penalty term will be further investigated in the next section.