Complex-valued neural networks for spectral induced polarization applications

SUMMARY Spectral induced polarization (SIP) aims to characterize geological materials by measuring the dispersion of their complex conductivity in the frequency domain. Despite the complex-valued nature of SIP data, most machine learning models used for its analysis rely on real-valued representations that discard phase information and may limit performance. This study investigates the benefits of complex-valued neural networks (CVNN) for SIP applications by comparing their performance against real-valued neural networks (RVNN) across three tasks: mineral classification, Cole–Cole parameter estimation, and mechanistic modelling of ionic and electric potential perturbations around polarizable minerals. To ensure fair comparisons and emphasize the effect of complex-valued representations, we design CVNN and RVNN models with matched capacity, aspect ratio and training duration. Our numerical experiments show that CVNNs consistently outperform RVNNs in the classification task, achieving lower validation loss and up to 5 per cent higher classification metrics ($p\text{-value}= 2.9\times 10^{-7}$). We test the Cole–Cole inversion networks on laboratory SIP measurements and validate the parameter estimation accuracy using synthetic data. Test results indicate that CVNNs produce curve fits that are $\approx 4\, \%$ more accurate for the imaginary part of resistivity ($p\text{-value}= 3.1\times 10^{-4}$), and validation results show accuracy improvements of up to 2 per cent for chargeability, relaxation time and the Cole–Cole exponent (p-value = $1.7 \times 10^{-7}$). CVNNs also yield more accurate approximations of mechanistic model variables, with error reductions of up to 1 per cent for ionic concentrations ($p\text{-value}= 1.6\times 10^{-4}$). Our experiments suggest that CVNNs provide modest but statistically significant benefits in SIP applications involving laboratory or synthetic data. While RVNNs may eventually reach comparable predictive accuracy if trained longer, we observe that CVNNs converge more rapidly under matched training conditions. This study provides a reproducible framework for benchmarking neural network architectures in SIP and supports the integration of CVNNs into geophysical workflows where phase responses encode physically meaningful information.

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