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REVIEW 4 major objections 6 minor 9 references

Accelerating Electrochemical Impedance Spectroscopy Measurements by Reducing Reliance on Noisy Low-Frequency Data

T0 review · 4 major / 6 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Densifying high-frequency EIS sampling lets Bayesian equivalent-circuit fits recover the low-frequency impedance that was never measured, shifting the reliable cutoff frequency upward and cutting modeled measurement time by up to 98%.

desk verdict Useful in-silico map of how high-frequency densification shifts the critical frequency, but the headline time savings rest on a closed synthetic loop; needs experimental validation before trusting the transfer. read the letter →

arxiv 2607.19307 v1 pith:PAAA35HG submitted 2026-07-21 physics.data-an physics.chem-ph

Qiuyu Shi , Naohiro Fujinuma , Yonatan Kurniawan , Runze Zhang , Ali Jaberi , Ashley Dale , Jason Hattrick-Simpers This is my paper · ORCID
classification physics.data-anphysics.chem-ph
keywords electrochemicalimpedancespectroscopycriticalfrequencyBayesianinferenceequivalentcircuitmodelhigh-frequencysamplingmeasurementtimereductionlow-frequencynoisepartial-spectrumreconstruction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Electrochemical impedance spectroscopy is slow and noisy at low frequencies, and this paper argues that the slow part can often be skipped entirely. The proposal is to measure extra points in the clean high-frequency region and let a Bayesian fit of an equivalent-circuit model reconstruct the low-frequency response that was never recorded. The paper introduces a 'critical frequency' fc — the highest cutoff at which the full response is still reliably recovered — and shows that densifying the high-frequency sampling shifts fc upward and narrows uncertainty bands. For a single-RC circuit the modeled measurement time falls by more than 98%; for a two-RC circuit the saving is smaller and depends on noise level and the number of added points. The result is a practical design rule: characterize a system once at full spectrum, then measure only from the top frequency down to fc for routine testing.

What carries the argument

The load-bearing object is the critical frequency fc, defined as the highest cutoff frequency at which the full EIS response can still be reliably recovered, with 'reliably' operationalized as a Bayesian posterior whose Q-Q plot against a Gaussian has average R^2 > 0.95 across circuit parameters. The densification machinery is recursive subdivision: insert one point in log frequency between every adjacent pair, then repeat to produce 3, 7, and 15 extra points per original interval. The fitted model is a chosen equivalent circuit (single-RC or dual-RC with constant-phase elements), and the inference is Bayesian, so each added point constrains the posterior over resistor and CPE parameters; th

What would settle it

Run a real EIS experiment on a battery or electrocatalyst cell: record a full spectrum, then separately record only the high-frequency window with 7 extra points per interval, and apply the paper's Bayesian reconstruction. If the reconstructed low-frequency impedance or parameter posteriors deviate significantly from the directly measured low-frequency data, or if fc measured with real extra points does not exceed the original fc, the central claim fails. A second, sharper falsifier: generate the extra points from one ECM and fit with a different ECM topology—if the fc shift disappears under m

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Extended reading notes

Core claim

The central claim, stated in the paper's own terms, is that 'additional high-frequency sampling can not only shift fc to higher values but also reduce the total measurement time.' Concretely, when extra samples are inserted between neighboring high-frequency points (1, 3, 7, or 15 per interval) and those augmented spectra are fit with Bayesian inference over equivalent-circuit parameters, the inferred model can reproduce the low-frequency impedance semicircle that the partial spectrum no longer contains. In the proof-of-concept dual-RC example, adding 7 points lifts fc from 4.52 Hz to 10.23 Hz and visibly tightens the posterior predictive band at low frequency; across systematic tests, fc ri

Load-bearing premise

The extra high-frequency data are not experimental measurements but synthetic points generated from the very equivalent-circuit parameters the Bayesian fit is trying to estimate, so the claimed fc shift and time savings presuppose that the fitted model is exactly true and that the composite noise model captures reality.

Editorial extensions

If this is right

  • For single-RC systems, the modeled time saving exceeds 98% at every tested noise level and densification, so this class of electrodes could in principle be screened with a short high-frequency-only sweep.
  • For dual-RC systems (batteries, CO2 electrocatalysis), high-frequency densification still shifts fc upward and saves time in most conditions, but the benefit saturates and can reverse at 5% noise with 15 added points.
  • The critical frequency is not a fixed property: it increases with added high-frequency points and decreases with noise, meaning the measurement window can be tuned per system using a once-per-system full-spectrum calibration.
  • When the low-frequency semicircle dominates the polarization resistance (1:2 RC ratio), fc is highest, suggesting the skipped low-frequency process leaves a stronger trace in the high-frequency data.
  • The workflow provides a quantitative stopping rule (three consecutive failed posterior checks) that can be automated, enabling adaptive truncation of the measurement.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The entire demonstration is synthetic: extra points are generated from the optimized equivalent-circuit parameters and the same composite noise model used in fitting, so the reported fc shifts should be read as the behavior of a perfect-model world; a real measurement campaign with added experimental points is the necessary next test.
  • A model-free version of this idea—using distribution-of-relaxation-times analysis or a nonparametric impedance model instead of a fixed ECM—would test whether high-frequency densification helps without assuming the circuit topology in advance.
  • The uniform recursive subdivision is likely not information-optimal; placing extra points at frequencies where the Fisher information about the low-frequency parameters is largest could push fc further with the same number of added measurements.
  • If the reconstruction holds on real cells, the method applies naturally to long-duration cycling studies where repeated full EIS scans are prohibitive, turning each cycle's check into a short high-frequency measurement plus an inference step.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes a Bayesian-inference framework for reducing the amount of low-frequency EIS data needed to recover a full impedance spectrum. The method adds synthetic high-frequency sampling points, fits the augmented partial spectrum with equivalent circuit models (ECMs) via AutoEIS, and introduces a critical frequency fc defined as the highest cutoff frequency at which the full response can still be reliably reconstructed. Reconstruction quality is judged by averaging Q-Q plot R² values of posterior parameter distributions. The authors report that high-frequency densification shifts fc to higher frequencies and reduces modeled measurement time, with single-RC systems saving over 98% of the time. All experiments are performed on synthetic data generated from the same ECMs used in fitting.

Significance. If the central claim were established, the work would be a practical contribution to accelerated EIS, with a useful organizing metric (fc) and a systematic study of noise level, densification, and ECM structure. The Bayesian fitting workflow is standard, the synthetic study covers multiple noise levels and random seeds, and the paper is clear about its use of synthetic data. However, the evidence is entirely self-referential: the extra high-frequency points are generated from the same optimized parameters that the Bayesian fit estimates, and the ground-truth spectra are generated from the same ECM used for fitting. The reported fc shifts and time savings are therefore currently statements about internal consistency in a synthetic world, not about transfer to real electrochemical measurements. With independent validation, the framework could be significant, but that validation is missing.

major comments (4)
  1. [Sec. 2.4 and Sec. 3.1] The additional high-frequency points are generated 'based on optimized ECM parameters and noise' (Sec. 2.4). This closes the loop: the densified data are drawn from the same parameter values that the Bayesian fit will estimate from the partial spectrum. The extra points therefore cannot carry any information beyond the model's own predictions plus the calibrated noise in Eq. (1). The observed fc shifts (e.g., 4.52 Hz to 10.53 Hz in Sec. 3.1) and the >98% single-RC time savings in Sec. 3.4 are thus self-consistency results. To make the central claim load-bearing, the extra points should come from independent ground-truth parameters fixed before fitting, or from real measurements; the limitation discussion in Sec. 5 mentions only uniform subdivision and does not acknowledge this closed-loop issue.
  2. [Sec. 2.2 and Sec. 3.1] The ground truth is generated from the same ECM (R1-[P2,R3] or R1-[P2,R3]-[P4,R5]) that is later fit to the data. This excludes model mismatch, unmodeled physical processes (e.g., diffusion, inductive artifacts), non-stationarity beyond the fitted drift, and instrument-specific noise statistics. The definition of fc as the frequency above which 'the full EIS response can still be reliably recovered' is therefore only meaningful within the assumed model. The paper should include at least one test where the data-generating ECM differs from the fitting ECM, or better, an experimental validation, to show that the reconstruction claim is not an artifact of model self-consistency.
  3. [Sec. 3.4, Eq. (2)] The time-saving formula in Eq. (2) is ambiguous. The text states the optimized measurement runs 'from the highest frequency to the critical frequency, fc,' but the equation sums ∑_{j=c}^{M} 1/f_j. If c is the index of fc in a descending-frequency array, the sum should run from the highest index to c (or j=1 to c with appropriate reindexing). As written, it is unclear whether the added high-frequency points are included in the numerator. The reported >98% single-RC time savings depend directly on this summation. Please clarify the indexing and re-derive the percentages.
  4. [Sec. 3.2 and Fig. 4] The fc criterion (average Q-Q R² > 0.95, with a three-consecutive-failure rule) is an indirect proxy for reconstruction quality. The paper validates it against only a single example (Fig. 4), comparing the R²-based fc to a qualitative visual assessment of the Nyquist predictions. To make fc a reliable metric, the authors should demonstrate, across multiple noise levels and densification factors, that the R² threshold corresponds to a direct error measure in the reconstructed low-frequency impedance (e.g., relative error in the omitted frequency range). Without this calibration, the reported fc values remain tied to an ad hoc threshold.
minor comments (6)
  1. [Sec. 3.4] The paragraph describing the time-calculation method is duplicated verbatim immediately before Eq. (2). One copy should be removed.
  2. [Sec. 3.4, text] Typo: 'reversely protentional' should be 'inversely proportional.' Also, the phrase 'data points and times' in Sec. 3.4 is unclear; consider 'the number of added data points and the resulting measurement time.'
  3. [Data and Code Availability] The statement that data and code 'will be made publicly available upon acceptance' is not sufficient for peer review. Please provide the code/scripts used for the synthetic generation, BI fitting, and fc determination as supplementary material, or at least include a detailed pseudo-code appendix.
  4. [Figures 5 and 6] The captions should explicitly state that error bands/error bars are mean±standard deviation over the four random seeds, and that the same random seeds were used for both synthetic data generation and inference. This is mentioned in the text but not in the captions.
  5. [Eq. (1)] Define the units and meaning of f in the flicker-noise term. Also clarify whether a, b, and c are fixed constants or tunable hyperparameters; the text says they are adjustable but only one set is used.
  6. [References] Several references are incomplete or non-standard (e.g., ref. 1 lacks author and journal details; ref. 36 appears to be an unpublished note). Please ensure all references follow the journal style and include complete bibliographic information.

Circularity Check

1 steps flagged · score 6.0 of 10

fc shift is a self-consistency result: added high-frequency points are generated from the same optimized ECM parameters the fit estimates, so the low-frequency 'reconstruction' is the model's own forward response.

  1. self definitional [Sections 2.2 and 2.4; claim in Abstract and Sec 3.1]
    "we use noisy synthetic EIS data instead of noisy experimental data to efficiently obtain ground truth and systematically control the noise level ... We addressed shifts in the critical frequency, fc, by generating additional high-frequency data points based on optimized ECM parameters and noise."

    The extra high-frequency points are generated from the same optimized ECM parameters that the Bayesian fit estimates, and the ground-truth full spectrum is generated from the same ECM (Sec 2.2). Thus the 'reconstruction' of low-frequency behavior is the forward model evaluated at the inferred parameters: it cannot fail due to model mismatch or unmodeled physics. The fc shift is therefore a measure of internal identifiability in a synthetic world, not an empirical prediction about real EIS. The closed loop is reinforced by Sec 3.3, which uses the same random seed for data generation and inference. The headline time saving is a direct consequence of this self-consistent fc shift.

full rationale

The paper's own equations close the loop. Section 2.2 states 'we use noisy synthetic EIS data instead of noisy experimental data to efficiently obtain ground truth and systematically control the noise level,' and Section 2.4 says the extra high-frequency points are 'generated ... based on optimized ECM parameters and noise.' Because those optimized parameters are exactly the target of the AutoEIS/Bayesian fit, and because the ground-truth full spectrum is generated from the same ECM, the 'reconstruction' of low-frequency behavior is the forward model evaluated at the inferred parameters. The reported fc shifts (e.g., dual-RC ~4.5 Hz to ~10.5 Hz in Sec 3.1) therefore measure parameter identifiability within the synthetic model class, not the ability to recover real unmeasured physics that is absent from the generator. This is a genuine circularity for the central empirical claim: densifying high-frequency data with model-generated points cannot reveal model mismatch, unmodeled diffusion/inductive/contact effects, or noise statistics beyond Eq. (1). The paper is transparent about the synthetic setup and does not claim experimental validation, but the conclusion that the framework 'challenges standard sampling paradigms' rests on this closed loop. The acknowledged limitation (Sec 5) concerns uniform subdivision, not the closed-loop generator. The self-citations to refs 10 and 26 for fc, the noise model, and AutoEIS are methodology inheritance, not a separate load-bearing circularity. Because the Bayesian inference itself is a real computation and densification genuinely improves identifiability in some cases, the circularity is partial: score 6.

Assumptions & free parameters 5 free parameters · 5 assumptions · 2 invented entities

The central claim rests on a closed simulation loop: the ECM is the assumed true generator (Section 2.2); the noise model is calibrated to one spectrum with coefficients chosen by hand (Section 2.2, Eq. 1); the acceptance metric is an internal R2>0.95 Q-Q rule inherited from the group's prior work (Section 2.3, refs 10, 26); and the extra high-frequency samples that produce the headline fc shifts are drawn from the fitted parameters themselves (Section 2.4). The time-savings arithmetic (Eq. 2) is the only fully parameter-free step. Counted this way, the paper contributes the systematic sweep and the fc-versus-noise-versus-densification maps; the reconstruction power that makes the savings possible is assumed by construction.

free parameters (5)
  • Noise mixing ratios a, b, c = a=0.01, b=0.01, c=10
    Chosen by hand in Section 2.2 to mimic one CO2-reduction experimental spectrum; the flicker coefficient c=10 dominates low-frequency noise and directly shapes where fc falls.
  • Global noise ratio eta = 0.01–0.05 (swept)
    Scales all three noise components simultaneously (Section 2.2, Eq. 1); the fc values and time-savings curves are parametrized by it, not derived from it.
  • Average Q-Q R2 threshold = 0.95
    Acceptance criterion for a "robust fit" (Sections 2.3, 3.2); justified by hand as aligning with two-sigma regions but never calibrated against a ground-truth reconstruction error; fc depends directly on this threshold.
  • Consecutive-failure count = 3
    Section 3.2 defines fc as the frequency preceding three consecutive runs with mean R2<0.95; an ad hoc smoothing rule whose value changes the reported fc.
  • Densification factors = 1, 3, 7, 15
    Extra samples per original interval following a (2^n−1) progression (Section 2.4); a design choice, not an optimized sampling schedule, and the paper itself flags uniform subdivision as a limitation in Section 5.
assumptions (5)
  • domain assumption The chosen equivalent circuit model (single-RC or dual-RC) is the correct data-generating process for the system.
    Section 2.2 builds all synthetic "ground-truth" spectra from the ECM, so the inference problem is always model-consistent; model mismatch is excluded by construction.
  • domain assumption The composite noise model (parameter drift + |Z|-proportional Gaussian + 1/f flicker) captures real EIS noise.
    Equation (1) with coefficients calibrated to a single example spectrum (Section 2.2); no test against independent noise measurements or a second system.
  • ad hoc to paper Average Q-Q plot R2 across circuit parameters measures whether a partial spectrum carries enough information to reconstruct the full response.
    Section 2.3 uses R2 of Q-Q plots as the fit-quality metric; this is an indirect proxy (posterior Gaussianity) rather than a direct check of reconstruction error against the true spectrum, and it is validated only qualitatively in Section 3.1.
  • domain assumption Measurement time per frequency point is proportional to 1/f.
    Section 3.4, Equation (2); a standard approximation that ignores per-point overhead, settling times, and parallel measurement schemes such as multisine EIS (refs 23–24).
  • ad hoc to paper Synthetic extra points derived from the fitted parameters behave like real additional high-frequency measurements.
    Section 2.4 generates the augmentation from "optimized ECM parameters and noise" — the very values the inference will re-fit — guaranteeing self-consistency and excluding any information that real measurements might carry (or fail to carry).
invented entities (2)
  • Critical frequency fc
    purpose: Headline metric: the highest cutoff frequency at which the full EIS response can still be reliably recovered from a truncated spectrum; used to quantify sampling-efficiency gains.
    fc is defined via the internal R2>0.95 average-Q-Q criterion and the three-consecutive-failure rule, both inherited from the group's own prior work (refs 10, 26), and evaluated only inside the synthetic same-ECM loop; no independent benchmark links fc to a true reconstruction error on real spectra.
  • Noisy frequency threshold fn
    purpose: Operational cutoff below which low-frequency measurements are considered sufficiently noise-affected to distrust; used in the workflow (Section 2.1) to decide whether additional sampling is needed.
    A user-defined threshold ("varies in different electrochemical systems") supplied externally rather than derived; the workflow's stopping condition, and hence the reported benefit, shifts with this free choice.

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Cite this review

Pith. "Pith review of Accelerating Electrochemical Impedance Spectroscopy Measurements by Reducing Reliance on Noisy Low-Frequency Data." pith.science (2026). https://pith.science/paper/PAAA35HG

@misc{pith2026260719307,
  author       = {Pith},
  title        = {Pith review of: Accelerating Electrochemical Impedance Spectroscopy Measurements by Reducing Reliance on Noisy Low-Frequency Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PAAA35HG}},
  note         = {Machine review of arXiv:2607.19307}
}
read the original abstract

Electrochemical impedance spectroscopy (EIS) is a powerful tool for probing kinetic and transport processes in electrochemical systems, but its practical use is often limited by the long acquisition time and noise sensitivity of low-frequency measurements. Here, we present a statistical inference-assisted framework that reduces the reliance on low-frequency sampling by increasing the sampling density in cleaner high-frequency regions. Using AutoEIS and Bayesian inference, the augmented high-frequency data are fitted to selected equivalent circuit models (ECMs) to reconstruct the full impedance spectrum and quantify parameter uncertainty. To evaluate reconstruction performance, we introduce the critical frequency (fc), defined as the highest cutoff frequency at which the full EIS response can still be reliably recovered. The results show that additional high-frequency sampling can not only shift fc to higher values but also reduce the total measurement time. The specific improvement depends on the noise level of the EIS data, the number of added data points, and the ECM structure. Overall, this work provides a practical framework for designing fast and efficient EIS data acquisition and offers guidance for applying partial-frequency EIS reconstruction in real electrochemical characterization.

Figures

Figures reproduced from arXiv: 2607.19307 by the authors.

Figure 1
Figure 1. The overall workflow for critical frequency (fc) determination for original EIS data and extra sampling EIS data. 2.2 EIS Data Preparation In this study, two distinct equivalent circuit models (ECMs) representing common electrochemical systems were investigated. As shown in Figure S1, the single-RC system, described by the ECM R1-[P2, R3], exhibits one semicircle in the Nyquist plot, which is commonly observed in th… view at source ↗
Figure 3
Figure 3. Impact of high-frequency data augmentation on Bayesian posterior predictions and critical frequency for an example dual-RC EIS. Panels (a-d) show the original EIS sampling, while (e-h) show the augmented sampling with 7 points between every original point. The results cutoff frequencies are: (a, e) 0.7 Hz, (b, f) 4.52 Hz, (c, g) 5.71 Hz, (d) 9.10Hz, and (h) 10.53 Hz. 3.2 Quantitative Inference Results Analysis [PIT… view at source ↗
Figure 4
Figure 4. Example of automated quantitative evaluation method of BI results comparing the original EIS against the 7-point high-frequency augmented dataset: Average R2 across all circuit parameters as a function of the minimum EIS frequency (Hz). 3.3 Generalizability Investigation with Various Noise Levels and Number of Extra Points With the successful proof-of-concept study and evaluation metrics validation, we continue expl… view at source ↗
Figures from the paper (1 more)
Figure 6
Figure 6. Figure 6: For the single-RC case, our method can save over 98% measurement time across all tested cases with various extra added points and levels of noisy data. This significant reduction in measurement time is a direct consequence of shifting the critical frequency toward a si…

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