Automated Estimation of Equivalent Circuit Model from Impedances with Long Short-Term Memory

Electrochemical Impedance Spectroscopy (EIS) is a widely used, non-destructive technique for characterizing electrochemical systems, and its analysis typically relies on fitting the measured spectra to an Equivalent Circuit Model (ECM). Selecting an appropriate ECM, however, remains a major bottleneck: knowledge-based selection requires expert judgment and is difficult to reproduce, while existing automated approaches either choose from a fixed set of candidate circuits or, in the case of Gene Expression Programming, require repeated equivalent-circuit fitting and a predetermined circuit scale. Here, we propose a machine learning method that estimates an ECM directly from an impedance spectrum by representing the circuit as a serialized string of symbols and generating this string with a Long Short-Term Memory (LSTM) network coupled to a convolutional feature extractor. Because the LSTM inherently handles variable-length sequences, the method produces the circuit topology directly, without any fitting during estimation nor prior assumption for the number of elements. A fourth-root transformation of the impedance is introduced to emphasize the mid-frequency features essential for distinguishing circuits, and an adaptive beam search yields multiple ranked candidates. Evaluated on 100,000 synthetic datasets generated from 119 circuit topologies with 1% added noise on impedances, the method identified the correct topology as the most probable ECM in 77.8% of cases and among the top five candidates in 98.8% of cases, with an average estimation time of 17.8 milliseconds per dataset - several orders of magnitude faster than reported fitting-based approaches. These results indicate that direct topology generation with a neural network is a promising route toward fully automated, expert-independent ECM estimation.