{"id":"e0bca5cb-8652-4c65-a17a-85e464bad9b1","arxiv_id":"2412.10896","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":18,"one_line_summary":"A numerical frequency-domain impedance method with automatic differentiation enables fast fitting of 18 grouped single-particle-with-electrolyte model parameters to measured battery impedance.","lead":"This paper introduces open-source software that computes the impedance of physics-based battery models from their equations using automatic differentiation, and uses it to fit 18 grouped parameters of a battery model to measured data. A smart generalist would read it because it offers a faster, non-invasive route to characterising commercial lithium-ion batteries, with validation on an LG M50LT cell and a drive cycle.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The numerical impedance method is validated, but the claim that measured SPMe parameters are correctly assigned to electrodes is not: the low-frequency misfit is blamed on OCP hysteresis while OCP curves are treated as fixed, so fitted diffusion/stoichiometry parameters can absorb that error.","rationale":"I read the central claim as having two parts: (1) PyBaMM-EIS computes accurate impedance faster than brute-force simulation, and (2) the SPMe can be parametrised from measured EIS data with parameters assigned to the correct electrodes. Part (1) is solid: Section 3 validates against brute-force time-domain simulation with <0.4% relative error, and the code is publicly available. Part (2) is where the paper is conditional. The measured fit in Sec. 7.2 excludes 10% and 90% SOC, has eight parameters at bounds, and is poor at low frequencies; the paper explicitly blames OCP hysteresis, but then uses the OCP as a fixed input. Since Eq. (15) makes the low-frequency impedance proportional to the OCP slope, OCP error can be absorbed by diffusion and stoichiometry parameters, which are precisely the parameters claimed to be electrode-assigned. The drive-cycle validation supports terminal-voltage accuracy but does not validate electrode-level parameter identity. The reader's weakest assumption identified the same root cause, so I agree with that diagnosis. The proposed OCP-direction refit is a direct test of whether the concern actually lands. Because the reader's conditional verdict already reflects this risk, I do not change the verdict.","tokens_in":32553,"tokens_out":6856,"duration_ms":68198,"concrete_test":"Refit the same LG M50LT dataset with the identical PyBOP fitting configuration used in Sec. 7.2 (Tables 4-5), but replace the single-valued About:Energy OCP curves with half-cell OCP data recorded in the discharge direction and, separately, in the charge direction. Compare the resulting grouped parameters, especially tau_d+/- and c0%+/-/c100%+/-. A shift larger than the reported run-to-run scatter, or a reversal of which electrode carries the larger diffusion time-scale, would show that OCP hysteresis undermines the electrode-assignment claim. Stable estimates would refute the concern.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The numerical frequency-domain impedance computation (Secs. 2-3) is well supported: automatic-differentiation linearisation is validated against brute-force simulation with <0.4% relative error, so that part of the central claim is not in question. The load-bearing step is the extrapolation from a terminal-voltage/impedance fit to correct electrode-level parameters. The measured-data fit in Sec. 7.2 excludes 10% and 90% SOC, leaves eight of the eighteen grouped parameters at their optimisation bounds (Table 5), and gives 2.4-3.6% mean fitting errors with visibly poor low-frequency tails. The paper itself attributes this low-frequency misfit to OCP hysteresis (Sec. 7.2), yet the OCP curves enter the model as single-valued, equilibrium inputs. Because Eq. (15) makes the diffusion tail proportional to U'(cm,±), an error in OCP slope directly shifts the estimated diffusion time-scales and stoichiometry bounds; these are exactly the parameters claimed to be assigned to the correct electrode. The drive-cycle validation (Sec. 7.3) confirms terminal-voltage prediction but is insensitive to the clipped parameters, so it does not establish that the inferred electrode-specific parameters are correct. The SNLDR value of 82 at 60% SOC is secondary; the decisive risk is the fixed OCP input under hysteresis.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents PyBaMM-EIS, a numerical frequency-domain impedance computation method for battery models that uses automatic differentiation to linearize the discretized DAE system about an operating point. The method is validated against brute-force time-domain simulation for the SPM and SPMe with relative errors below 0.4%, and it is shown to be much faster than brute-force simulation. The paper then uses the method to compare SPM, SPMe, and DFN impedance, selects the SPMe as a parsimonious model, derives a grouped-parameter SPMe, and performs an impedance sensitivity analysis. Parameter estimation is carried out with PyBOP on simulated impedance data (18 grouped parameters) and on measured LG M50LT impedance data. The simulated-data fits recover most large-feature parameters, while the measured-data fit has poor low-frequency agreement, several parameters at optimisation bounds, and excludes the 10% and 90% SOC spectra. A drive-cycle validation yields a 5.3 mV RMSE.","tokens_in":33036,"tokens_out":5593,"duration_ms":46254,"significance":"If the numerical impedance method is accepted, it is a valuable open-source contribution: it removes the need for analytical impedance derivations for arbitrary PyBaMM models and may substantially speed up EIS-based parametrisation. The grouped-parameter SPMe and the SOC-dependent sensitivity analysis are also useful. However, the central claim that measured SPMe parameters can be accurately determined and assigned to the correct electrode is only partially supported by the evidence, as detailed in the major comments. The paper is therefore significant but needs substantial revision to substantiate the parametrisation claims.","major_comments":[{"comment":"The simulated-data identifiability results show that several parameters are estimated at their optimisation bounds (τe+ = 200 s, ζ+ = 0.5, τe_sep = 200 s, Qe = 500 As) and several others have large relative standard deviations over the ten runs (τe− 20.9%, ζ− 41.9%, τct+ 26.5%, C+ 13.9%). This directly qualifies the Abstract's claim that parameters 'can be accurately determined'; the claim holds only for the parameters associated with large impedance features. The authors should either soften the claim or provide a formal identifiability analysis (e.g., profile likelihood or Fisher information) to delineate which parameters are identifiable.","section":"Sec. 6.1, Table 3"},{"comment":"In the measured-data fit, eight of the eighteen fitted parameters are at their optimisation bounds (τe+, τe−, τe_sep, ζ+, ζ−, Qe, t+, C+). This indicates that the optimiser's bounds, not the impedance data, are constraining these values. The paper notes these are related to small features, but this undermines the broader claim that parameters are accurately determined from measured data. The authors should assess whether wider bounds or different parameter scaling change the results, or explicitly state that these parameters are not identifiable from the available data.","section":"Sec. 7.2, Table 5"},{"comment":"The paper attributes the poor low-frequency fits to OCP hysteresis, but the model treats the OCP curves as fixed, single-valued equilibrium inputs. Since Eq. (15) shows the diffusion-tail impedance is proportional to U′±(cm,±), any error in the OCP slope directly propagates into the estimated diffusion time-scales τd± and the stoichiometry bounds c0%± and c100%± — exactly the parameters claimed to be assigned to the correct electrode. Without quantifying the hysteresis-induced OCP uncertainty or validating the electrode-level parameters against independent measurements (e.g., half-cell data or post-mortem analysis), the electrode-assignment claim is not established.","section":"Sec. 7.2, Eq. (15)"},{"comment":"The measured-data fitting excludes the 10% and 90% SOC spectra because they were 'hard to fit'. This exclusion removes the operating points where the OCP slope is steepest and where the diffusion tail and stoichiometry information are most informative. The paper's claim that fitting must be done simultaneously across a wide SOC range is weakened by excluding exactly the extreme SOCs. The authors should report the fits at these SOCs, discuss why they fail, and quantify how their exclusion affects the remaining parameter estimates.","section":"Sec. 7.2"}],"minor_comments":[{"comment":"The DFN impedance is computed but not validated against brute-force simulation, as the brute-force DFN computation was prohibitively long. The paper should state this limitation explicitly in the validation section, rather than only in the table caption.","section":"Sec. 3, Table 1"},{"comment":"The signal-to-nonlinear distortion ratio is defined as |V(ω)/V(2ω)| at the lowest frequency, but the text does not specify whether V denotes the voltage Fourier coefficient or the impedance. Please clarify the notation.","section":"Sec. 7.1, Eq. (18)"},{"comment":"In Eqs. (A.8) and (C.7), the two logarithmic terms are written identically, which appears to be a typo; presumably one refers to the electrode-surface value and the other to the electrode-average value of the electrolyte concentration. Please correct the expressions.","section":"Appendix A, Eq. (A.8) and Appendix C, Eq. (C.7)"},{"comment":"The time-scale ranges are described as approximate, but the overlap between particle and electrolyte diffusion time-scales (τd+ = 6812 s, τe+ = 409 s) is large; a brief discussion of how this overlap affects the interpretation of the diffusion 'bump' would improve the section.","section":"Sec. 5.2"}],"recommendation":"major_revision","confidential_remarks":"The numerical impedance method is the strongest part of the paper and is likely publishable. The measured-data parametrisation section needs substantial work before the claims in the abstract are supported. I suggest the editor weigh the value of the open-source contribution when evaluating the required revisions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe headline: this is a genuinely useful methods paper, and the measured-data part is where the claims outrun the evidence. PyBaMM-EIS's AD-based impedance computation is a real contribution—validated against brute-force simulation with sub-0.4% relative error for SPM/SPMe—and the multi-SOC grouped-parameter fitting workflow is practical. On simulated data the 18-parameter fit works well, with most parameters recovered and correct electrode assignment. That part deserves credit.\n\nThe soft spot is the measured LG M50LT parametrisation. The paper excludes 10% and 90% SOC, eight of eighteen parameters clip at their bounds, and low-frequency fits are visibly poor. The authors blame OCP hysteresis, but the OCP enters the model as a single-valued fixed curve. Since Eq. (15) makes the diffusion tail proportional to U'(c), an error in OCP slope can shift the estimated diffusion timescales and stoichiometry—exactly the parameters claimed to be assigned to the correct electrode. The drive-cycle validation confirms terminal-voltage prediction but is insensitive to those clipped parameters, so it does not rescue the electrode-level claim.\n\nThe stress-test note is fair on this point. I would add that the authors are transparent about the poor low-frequency fit and model limitations, and they frame the drive-cycle validation as what the parametrised model is actually good for. The abstract, though, overstates: \"the parameters that directly affect the response of the SPMe can be accurately determined and assigned to the correct electrode\" is supported by the simulated-data experiment, not by the measured-data fit.\n\nMinor issues: DFN impedance is not validated against brute-force because of cost, and the measured EIS data are not publicly released. Neither is fatal, but a referee should ask for the data and for a sensitivity check on the OCP curves.\n\nVerdict: solid methods paper, honest about its limits, with one load-bearing claim that needs tempering or extra evidence. Send it to peer review.","headline":"A solid AD-based impedance tool and simulated-data parametrisation study; the measured-data electrode-assignment claim is overstated.","tokens_in":33569,"tokens_out":2168,"would_cite":true,"duration_ms":19630,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that electrochemical impedance spectra can be used to parametrise physics-based battery models directly, because exact linearisation via automatic differentiation makes model impedance fast to compute, removing the need…","keywords":["electrochemical impedance spectroscopy","single particle model with electrolyte","SPMe","model parametrisation","automatic differentiation","lithium-ion battery","parameter identifiability","PyBaMM"],"falsifier":"Measure the second-harmonic distortion ratio across the entire frequency range used for fitting, not just at 400 µHz as in the paper; if the signal-to-nonlinear-distortion ratio drops below roughly 80 at any fitting frequency, the spectra are not linear and the reported parameter values and electrode assignment would change.","tokens_in":32378,"feed_emoji":"🔋","tokens_out":6466,"duration_ms":60146,"temperature":0.7,"pith_summary":"This paper establishes that battery-model parametrisation from electrochemical impedance spectroscopy (EIS) need not start from a hand-derived impedance formula. By discretising the model and linearising it exactly at an operating point with automatic differentiation, the impedance of any model in the open-source PyBaMM framework can be computed quickly and accurately. The authors show this on the single-particle model, the single-particle model with electrolyte (SPMe), and the Doyle-Fuller-Newman model, then identify the SPMe as a parsimonious choice that captures the measured impedance features. They reduce the SPMe to 18 grouped parameters and estimate them from both simulated and measured EIS data, arguing that simultaneous fitting across many states of charge is essential for attributing parameters to the correct electrode. If this is right, routine EIS measurements become a practical route to calibrating physics-based battery models without deriving closed-form impedance expressions.","feed_headline":"Automatic differentiation computes battery impedance fast and exactly","feed_subtitle":"EIS data alone recovers 18 grouped battery parameters and assigns them to the right electrode.","key_machinery":"The load-bearing object is the numerical frequency-domain impedance formula: after discretising the model into a system of differential-algebraic equations, the impedance at frequency $\\omega$ is $Z_m(\\omega,\\theta) = [(j\\omega M_{\\theta,m}-J_{\\theta,m})^{-1}B]_{N_x+1}$, where $M_{\\theta,m}$ is the mass matrix evaluated at the operating point, $J_{\\theta,m}$ is the Jacobian of the model's right-hand side, and the selected entry is the voltage. Automatic differentiation provides the Jacobian exactly and avoids the cost and error of finite-difference linearisation. The second supporting mechanism is parameter grouping: by non-dimensionalising the SPMe and keeping only the dimensions of time, current, and voltage, the paper reduces the model to 22 grouped parameters, and with known cell capacity and relative electrode thicknesses, 18 of these need to be estimated from impedance data.","core_discovery":"The central claim is that the impedance of any physics-based battery model implemented in PyBaMM can be computed numerically by exact linearisation followed by a frequency-domain solve. After spatial discretisation the model becomes a DAE system, $M_{\\theta,m}\\frac{d\\tilde{x}}{dt}=J_{\\theta,m}\\tilde{x}+Bi(t)$, and its impedance is the voltage entry of $(j\\omega M_{\\theta,m}-J_{\\theta,m})^{-1}B$, where $J_{\\theta,m}$ is the Jacobian of the right-hand side at the operating point, computed exactly by automatic differentiation. The paper validates this against brute-force time-domain simulation, finding relative errors below 0.4% while being orders of magnitude faster, which makes impedance-based fitting practical inside an optimisation loop. Applying the method to the SPMe, the paper groups parameters into 18 estimable quantities, shows how each affects distinct impedance features, and demonstrates that fitting simultaneously over a wide range of SOCs recovers the parameters that directly influence the response and assigns them to the correct electrode. The method is released as open-source software that works with any PyBaMM model at any operating point.","pith_inferences":["Because the negative-electrode diffusion timescale is nearly invisible at 50% SOC where the graphite OCP is flat, an implicit design rule follows: choose SOC operating points where each electrode's open-circuit-potential slope is large to make that electrode's diffusion parameters identifiable; the paper's multi-SOC protocol implements this rule without stating it.","The same exact-linearisation machinery could be extended to predict higher harmonics by retaining second-order Taylor terms, turning the linear impedance calculator into a nonlinear-EIS diagnostic that would strengthen the paper's single-frequency linearity check.","If the poor low-frequency fits are indeed caused by OCP hysteresis, as the paper suggests, then fitting the model to impedance spectra acquired with the SOC approached from both charge and discharge directions would separate hysteresis from genuine model deficiency; the reported measurements approach every operating point from discharge only.","Because impedance computation is cheap for any PyBaMM model, the method turns model selection into an automated loop: candidate extensions such as state-dependent diffusivity, particle-size distributions, or multi-particle models can be compared purely by their ability to fit measured impedance, without hand-deriving any impedance."],"forward_implications":["Any model implemented in PyBaMM, including user-defined ones, can be given an impedance response at any operating point without deriving an analytic impedance expression, opening EIS-based calibration to a broad class of physics-based models.","The comparison of SPM, SPMe, and DFN shows that electrolyte dynamics add a diffusion 'bump' seen in measured data, and that the SPMe is the parsimonious model that captures the relevant impedance features while the DFN is similar but more expensive.","The 18 grouped SPMe parameters are identifiable when fitted jointly to impedance data across several SOCs, and the parameters that directly affect the response can be assigned to the correct electrode.","Fitting from impedance data is more informative than time-domain voltage data for short-timescale parameters, while long-timescale diffusion parameters are recovered with similar accuracy from both.","For the LG M50LT cell, the SPMe fitted to measured EIS data predicts a drive-cycle voltage with a root-mean-square error of 5.3 mV and a maximum error near 15 mV, despite poor low-frequency impedance fits."],"supporting_citations":[{"why":"Supplies the PyBaMM model-discretisation machinery and analytical model equations that the impedance method builds on.","marker":"[31]"},{"why":"Provides the automatic-differentiation implementation used to compute the exact Jacobian of the discretised model.","marker":"[32]"},{"why":"The earlier finite-difference numerical-differentiation approach to extracting EIS from physics-based models, which the paper's exact Jacobian method improves upon.","marker":"[30]"},{"why":"Derives analytic SPM impedance and studies parameter identifiability, serving as the baseline and reference for the SPMe analysis.","marker":"[29]"},{"why":"Introduces the SPM with double-layer capacitance and the OCP-slope dependence of the diffusion tail, which the paper extends to the SPMe.","marker":"[23]"},{"why":"Provides the asymptotic derivation of the single-particle model with electrolyte, the model the paper groups and parametrises.","marker":"[10]"},{"why":"Supplies the improved averaging scheme used in the SPMe equations with electrolyte dynamics.","marker":"[11]"},{"why":"Provides the Chen2020 electrode parameter set for the LG M50 cell that supplies the true parameter values for simulated impedance and time-scale calculations.","marker":"[45]"},{"why":"The open-source optimiser PyBOP used to carry out the particle-swarm parameter estimation in both simulated and measured-data fits.","marker":"[35]"},{"why":"Sets out the linearity and stationarity conditions for EIS measurement and underlies the signal-to-nonlinear-distortion-ratio check used on the measured data.","marker":"[38]"}],"fun_headline_variants":["Auto-diff impedance makes battery fitting fast and exact","Impedance fitting for batteries made easy with auto-diff","18 battery parameters from impedance data alone","PyBaMM-EIS: exact impedance for any battery model","SPMe fits impedance data and yields 18 parameters"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The recorded impedance spectra are small-signal, stationary responses, and the half-cell open-circuit-potential curves used in the fits are the cell's true equilibrium voltages; the paper checks these only thinly and blames their failure for the poor low-frequency fits.","fun_headline_variants_meta":{"raw":{"variants":["Auto-diff impedance makes battery fitting fast and exact","Impedance fitting for batteries made easy with auto-diff","18 battery parameters from impedance data alone","PyBaMM-EIS: exact impedance for any battery model","SPMe fits impedance data and yields 18 parameters"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000624,"raw_usage":{"total_tokens":2918,"prompt_tokens":1002,"completion_tokens":1916,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":618,"completion_tokens_details":{"reasoning_tokens":1839}},"tokens_in":618,"tokens_out":1916,"duration_ms":12874,"temperature":1.0,"reasoning_tokens":1839,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T15:30:37.588662+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the second-harmonic distortion ratio across the entire frequency range used for fitting, not just at 400 µHz as in the paper; if the signal-to-nonlinear-distortion ratio drops below roughly 80 at any fitting frequency, the spectra are not linear and the reported parameter values and electrode assignment would change.","supporting_citations":[{"cited_title":"Sulzer, S","cited_arxiv_id":null,"evidence_quote":"Supplies the PyBaMM model-discretisation machinery and analytical model equations that the impedance method builds on."},{"cited_title":"Bradbury, R","cited_arxiv_id":null,"evidence_quote":"Provides the automatic-differentiation implementation used to compute the exact Jacobian of the discretised model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The earlier finite-difference numerical-differentiation approach to extracting EIS from physics-based models, which the paper's exact Jacobian method improves upon."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Derives analytic SPM impedance and studies parameter identifiability, serving as the baseline and reference for the SPMe analysis."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the SPM with double-layer capacitance and the OCP-slope dependence of the diffusion tail, which the paper extends to the SPMe."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the asymptotic derivation of the single-particle model with electrolyte, the model the paper groups and parametrises."},{"cited_title":"Brosa Planella, M","cited_arxiv_id":null,"evidence_quote":"Supplies the improved averaging scheme used in the SPMe equations with electrolyte dynamics."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Chen2020 electrode parameter set for the LG M50 cell that supplies the true parameter values for simulated impedance and time-scale calculations."},{"cited_title":"Hallemans, D","cited_arxiv_id":null,"evidence_quote":"Sets out the linearity and stationarity conditions for EIS measurement and underlies the signal-to-nonlinear-distortion-ratio check used on the measured data."}],"review_version":1}