Assessment of different loss functions for fitting equivalent circuit models to electrochemical impedance spectroscopy data

Electrochemical impedance spectroscopy (EIS) data is typically modeled using an equivalent circuit model (ECM), with parameters obtained by minimizing a loss function via nonlinear least squares fitting. This paper introduces two new loss functions, log-B and log-BW, derived from the Bode representation of EIS. Using a large dataset of generated EIS data, the performance of proposed loss functions was evaluated alongside existing ones in terms of R 2 scores, chi-squared, computational efficiency, and the mean absolute percentage error (MAPE) between the predicted component values and the original values. Statistical comparisons revealed that the choice of loss function impacts convergence, computational efficiency, quality of fit, and MAPE. Our analysis showed that X2 loss function (squared sum of residuals with proportional weighting) achieved the highest performance across multiple quality of fit metrics, making it the preferred choice when the quality of fit is the primary goal. On the other hand, log-B offered a slightly lower quality of fit while being approximately 1.4 times faster and producing lower MAPE for most circuit components, making log-B a strong alternative. This is a critical factor for large-scale least squares fitting in data-driven applications, such as training machine learning models on extensive datasets or iterations. This trade-off is particularly relevant for self-driving laboratories (SDLs), where EIS measurements and ECM fitting are performed autonomously in closed-loop workflows. In such settings, a computationally efficient and robust loss function is essential to prevent error accumulation across iterations and to enable scalable, reliable electrochemical SDLs. • Different loss fucntions produced varying fit quality when fitting EIS data to equivalent circuit models. • New loss fucntions based on Bode representation (named log-B and log-BW) were proposed. • log-B achieved similar fit quality while being 50% faster and yielding lower MAPE for most circuits. • Multiple performance metrics are needed to assess fit quality between true and ECM-predicted impedance data.