Impedance-Based Estimation of Process Parameters in Electrolytic Systems via Circuit-Embedded Neural Networks (CENN) - DATA

The Data folder contains all data supporting the impedance-based estimation of electrolyte concentration and temperature in aqueous H₂SO₄ using nanoporous gold electrodes. It includes 260 electrochemical impedance spectroscopy (EIS) spectra measured across 20 concentrations (1–20 mM) and 13 temperatures (26–50 °C). Raw measurements are organized by concentration and temperature, together with equivalent-circuit fits (ZARC + transmission-line model) that yield parameters such as solution resistance, interfacial polarization, and porous transport. The folder also holds outputs from the Circuit-Embedded Neural Network (CENN) forward and inverse models, including impedance predictions, concentration and temperature estimates from full and reduced-frequency sets, and Jacobian-based sensitivity analysis that identifies informative frequency bands. Results for different frequency-selection strategies (single-band, multi-band, and full-spectrum) are provided, along with classical machine learning benchmarks (Ridge, SVR, GPR, MLP, etc.) for comparison. The data support the main findings of the paper: CENN achieves a forward RMSE of about 0.06 Ω, inverse estimation with mean absolute errors of roughly 0.10 mM for concentration and 1.0 °C for temperature on full spectra, and comparable accuracy (about 0.12 mM and 1.1 °C) using only three optimized frequency anchors, reducing acquisition time from minutes to about six seconds.