SparseEIS-Bench: Benchmarking Three- and Five-Point EIS Reconstruction with Measurement-Conditioned Operator-Homotopy Flow Matching

Electrochemical impedance spectroscopy (EIS) provides rich frequency-domain information for battery management, but the time required for multifrequency scans limits its online use. We study ultra-sparse EIS reconstruction: recovering a complete impedance spectrum from only three to five complex-valued measurements. To support standardized research on this problem, we introduce SparseEIS-Bench, a large-scale benchmark comprising 25,090 measured spectra from 406 batteries across diverse chemistries, capacities, states of charge, states of health, and temperatures. SparseEIS-Bench provides a unified spectral representation, strictly disjoint Battery ID splits, and standardized three- and five-point reconstruction protocols for jointly evaluating reconstruction accuracy, physical consistency, probabilistic quality, and downstream utility. As a strong generative reference baseline, we further propose Measurement-Conditioned Operator-Homotopy Flow Matching (MOH-FM), which combines deterministic prediction with conditional residual generation and restores measured impedance values at the registered input positions. MOH-FM achieves aggregate complex root mean squared errors of 0.0465±0.0032 Ω and 0.0359±0.0025 Ω in the three- and five-point settings, respectively, yielding the lowest mean among the eight evaluated methods in both settings. Compared with linear residual flow matching, it reduces the mean aggregate error by 16.1% and 14.9%, respectively. The total scan-plus-inference time of both three- and five-point schemes is approximately 95% shorter than full-frequency scan time. Together, SparseEIS-Bench and MOH-FM establish a benchmark and modeling framework for rapid, measurement-efficient EIS reconstruction for practical battery management.