In this work, the authors introduce a Circuit-Embedded Neural Network (CENN), a physics-aware machine learning framework for real-time estimation of electrolyte concentration and temperature from Electrochemical Impedance Spectroscopy (EIS) measurements. Using nanoporous gold electrodes in aqueous sulfuric acid as a model system, impedance spectra were acquired across concentrations of 1-20 mM and temperatures of 26-50 °C, and interpreted using an equivalent-circuit model fitted over the full concentration and temperature domain.
The resulting parameter maps were embedded into a circuit-informed neural network, enabling high-fidelity prediction of full impedance spectra directly from state variables with a root-mean-square error of 0.06 Ω. Inverting the model allowed electrolyte properties to be estimated from measured spectra with mean absolute errors of 0.10 mM in concentration and 1.0 °C in temperature. A Jacobian-based sensitivity analysis then identified three informative frequencies that preserved the essential spectral information, reducing acquisition time by more than 95 %, from minutes to under six seconds, while maintaining high accuracy.
The framework offers an interpretable and transferable workflow for rapid multi-parameter sensing, bringing the field closer to smart and autonomous process systems, provided that the equivalent-circuit structure and calibration domain are adapted to the target system. The study was carried out at the Institute of Chemical Reaction Engineering at Hamburg University of Technology within the CRC 1615 SMART Reactors.
Hossein Ostovar, Marine Bossert, Zahra Sharafian, Oliver Korup, Raimund Horn (2026). Impedance-Based Estimation of Process Parameters in Electrolytic Systems via Circuit-Embedded Neural Network (CENN). Ind. Eng. Chem. Res. 65 (28), 15039-15059.
