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REVIEW 4 major objections 5 minor 39 references

One supervised data point converts a wildly wrong PINN into a sub-1% oxide-film simulator.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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A hybrid PINN anchored by one FEM data point reproduces point-defect-model film thicknesses to about 1% error, while the pure PINN overpredicts by 2,400-5,700%.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection A useful failure-mode study of PINNs for the point defect model, but the headline accuracy claim is overstated and the validation is too thin to take the central claim at face value. the 4 major comments →

arxiv 2510.02872 v4 pith:SZ2XYKCF submitted 2025-10-03 cond-mat.mtrl-sci

A physics-informed neural network approach to the point defect model for electrochemical oxide film growth

Mohid Farooqi , Ingmar B\"osing , Conrard G. Tetsassi Feugmo This is my paper
classification cond-mat.mtrl-sci
keywords physics-informed neural networkspoint defect modeloxide film growthelectrochemical passivationneural tangent kernelmoving boundaryhybrid trainingcorrosion
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper tries to establish that a physics-informed neural network (PINN) can simulate oxide film growth on metals under the Point Defect Model—a stiff, coupled, moving-boundary problem—if it is given one additional piece of supervised data. Without that anchor, the pure PINN converges to a mathematically valid but physically meaningless solution and overpredicts film thickness by 2,400% to 5,700%. With a single data point drawn from a validated finite-element solution, the hybrid PINN matches FEM film-thickness predictions to within roughly 1% across the tested voltage range. The authors identify four failure modes—loss imbalance, scale disparity, stiff boundary constraints, and convergence to unphysical solutions—and show that nondimensionalization and NTK-based loss rebalancing fix the first two, while the single anchor resolves the fourth. A sympathetic reader would care because this suggests costly parameter sweeps and inverse problems for electrochemical passivation could be done with a mesh-free, data-efficient PINN instead of a full FEM solver.

Core claim

The paper claims that a segregated, nondimensionalized, NTK-weighted PINN learns the correct Point Defect Model physics but lands on a physically meaningless branch of a non-unique solution manifold. A single supervised data point from a validated FEM solution (e.g., t=150,000 s, E=0.1 V, L=1.27 nm) acts as an anchor, bringing final-thickness relative errors from 2,412–5,708% down to 0.32–2.18% across 0.1–1.8 V. The authors interpret this as under-constraint rather than mis-training, and report robustness across five random anchor selections with <10% variation.

What carries the argument

The load-bearing mechanism is the hybrid training anchor: one supervised data point from a validated FEM solution acts as a branch selector on the non-unique solution manifold of the PDM equations. Supporting machinery includes nondimensionalization with characteristic scales (1 nm length, diffusive time, thermal voltage) to bring all variables to order one; Neural Tangent Kernel (NTK)-based adaptive weighting, where the trace of the NTK matrix of each loss component is computed every 100 steps to rebalance losses spanning 4–6 orders of magnitude; and a segregated network architecture with separate nets for potential, cation vacancies, anion vacancies, and film thickness, with the thickness

Load-bearing premise

The entire result rests on the assumption that one supervised data point at (150,000 s, 0.1 V, 1.27 nm)—selected at random from the FEM solution—is enough to pull the PINN onto the physically correct solution branch for all voltages from 0.1 to 1.8 V across 250 hours of simulated time, a generalization tested with only five random selections.

What would settle it

Run the hybrid training with a single anchor at a higher voltage (e.g., 1.0 V) or evaluate the trained hybrid PINN at an untrained voltage (e.g., 0.2 V or 1.2 V) against FEM; if the relative error jumps well above a few percent, the single-anchor generalization fails. Also reproduce the 1.6 V case: Table 1 reports 2.18% error, so the 'sub 1%' claim must be amended to 'sub 3%' or shown to be an average.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the single-anchor result holds, PINNs can reproduce validated FEM film-growth predictions to roughly 1–2% relative error, meaning electrochemical parameter sweeps and inverse problems could be run with minimal data.
  • The authors claim the methodological fixes—nondimensionalization, NTK weighting, segregated networks, and hybrid anchoring—are general to any multiphysics problem with coupled PDEs and a moving boundary, such as solidification fronts, fluid–structure interaction, or phase-change modeling.
  • The pure-PINN failure demonstrates that low training loss is not evidence of physical correctness; loss landscape analysis is proposed as a diagnostic to identify poorly satisfied constraints.
  • The robustness check with five random anchor selections (<10% relative-error variation) suggests the hybrid method does not depend on a hand-picked anchor point, supporting the under-constraint interpretation.
  • The paper recommends PINNs for sparse-data and inverse-problem settings and frames hybrid training as the practical near-term pathway until fully autonomous PINNs become possible.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If one anchor at 0.1 V suffices across 0.1–1.8 V, an active-learning strategy that picks the single most informative measurement could generalize the method to untested regimes or other materials, potentially eliminating the need for any FEM benchmark.
  • The paper's own Table 1 lists 2.18% relative error at 1.6 V, contradicting the abstract's blanket 'sub 1%' claim; resolving this discrepancy (as an outlier or an average) would determine how the headline result should be quoted.
  • The anchor's success hints that a global physical constraint (strict positivity of concentrations, or an integral charge balance) might tame the solution manifold and make the hybrid model fully autonomous.
  • Pure-PINN overprediction grows with voltage (2,412% at 0.1 V to 5,708% at 1.0 V), suggesting the unconstrained network's preferred branch scales differently with potential; testing an anchor at higher voltage could reveal whether the low-voltage anchor is optimal or merely adequate.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript develops a physics-informed neural network (PINN) approach to the Refined Point Defect Model (R-PDM) for electrochemical oxide film growth on iron in halide-free solutions. The authors identify four failure modes: imbalanced loss components, scale disparities, boundary-condition enforcement difficulties, and convergence to unphysical solution branches. They propose nondimensionalization, Neural Tangent Kernel (NTK)-based loss balancing, segregated network architectures, and hybrid training that adds a single supervised data point drawn from a finite-element (FEM) solution. The central claim is that pure PINNs overpredict film thickness by roughly 2,400–5,700%, while the hybrid PINN achieves 'sub 1%' relative error against FEM benchmarks across 0.1–1.8 V. The paper also documents unsuccessful attempts with Augmented Lagrangian methods, residual connections, and positivity-preserving output transformations, and recommends loss-landscape analysis as a diagnostic tool.

Significance. If fully supported, the result would be a valuable demonstration that a PINN with one data anchor can reproduce moving-boundary electrochemical film growth to engineering accuracy, and the paper gives a useful, systematic catalog of practical failure modes and mitigation strategies. The methodological contributions—nondimensionalization to extend stable simulation to 250 h, NTK-based loss rebalancing, and the single-anchor hybrid concept—are credible and worth pursuing. The authors also provide code via GitHub and promise organized supplementary materials. However, the current evidence does not fully support the headline claim. The abstract/conclusion assertion of 'sub 1%' errors is directly contradicted by the paper's own Table 1 (2.18% at 1.6 V). More importantly, the claim that one low-voltage anchor selects the correct physical branch across the entire voltage range is not established: the paper validates only the film thickness L(t), not the full concentration and potential fields, and the robustness check is a vague 'N=5' statement. The validation also relies exclusively on FEM data from a co-author's solver, which is the same source that supplied the anchor. These issues are

major comments (4)
  1. [Abstract and §6 (Conclusion), vs. §5.1 Table 1] The abstract claims 'sub 1% relative error' and the conclusion repeats 'errors below 1% across all tested voltages,' but Table 1 reports a Hybrid PINN error of 2.18% at 1.6 V. This is not a typographical nuance: the central quantitative claim of the paper depends on this bound. Please either correct the claim (e.g., 'below 2.2%') or specify the exact error metric and show how 2.18% is consistent with 'sub 1%'.
  2. [§5.1, Table 1, Fig. 4] A single anchor point (t=150000 s, E=0.1 V, L=1.27 nm) is claimed to select the physically correct solution branch across 0.1–1.8 V and 250 h. The pure-PINN overprediction factors vary strongly and nonlinearly with voltage (2412% at 0.1 V, 5708% at 1.0 V, 5001% at 1.8 V), so a low-voltage point does not trivially rescale all voltages. The reported robustness check ('N=5 random selections with relative error varying by less than 10%') gives no anchor locations, no uncertainty bounds, and no full-field comparison. Since Fig. 2 and §5.5.1 admit that the pure network has negative cation concentrations and non-linear potential profiles, the paper does not establish that the anchored network actually selects the physically realizable branch rather than merely matching L(t). Please provide full-field comparisons (potential and vacancy concentrations vs. FEM) and a more systematic anchor-sensiti
  3. [§5.1 and §6] The accuracy evaluation is performed against FEM benchmarks from Bösing's solver, which is the same source that provided the single supervised anchor. This is not strictly circular because only one point is used for training and the comparison is over full time traces, but the validation is not independent. Moreover, §3 states that the primary experimental metric is the polarization curve, yet no comparison to experimental polarization data is presented. Please report errors on withheld FEM runs/voltages (e.g., leave-one-voltage-out) and, if possible, compare predicted polarization curves to experimental data. Otherwise the 'prediction' claim is hard to separate from 'fitting the reference solver.'
  4. [§5.1, §5.5.1] The pure PINN solution is repeatedly described as 'mathematically valid' and the phrase 'successfully learning the physics' is used to motivate the single-anchor approach. However, the paper itself reports negative cation concentrations and non-linear potential profiles for the pure model, which are physically inadmissible, and no PDE-residual verification is shown for either the pure or hybrid solutions. The authors should either demonstrate pointwise PDE satisfaction (e.g., residual norms) or soften the 'mathematically valid' characterization. This distinction matters because the argument that one anchor suffices rests on the premise that the physics is already correctly encoded in the pure PINN.
minor comments (5)
  1. [Throughout] Typos and grammatical slips: 'necesary' (abstract), 'preditions' (§5.1), 'prescence' (§6.2), 'V oltage' (Table 1 header), and the duplicated 'the the' in §4.6. These should be corrected.
  2. [Eq. (27)] The NTK weight update formula as written, w_j = (1/µXj) Σ µXj, appears to give the same value for every j unless the sum is over j and the expression is meant to be normalized differently. Please clarify the normalization.
  3. [Fig. 2] The axis descriptions ('time evolution on y-axis, space on x-axis') are ambiguous. It would help to specify which field is shown and at which slices (constant time or constant potential) are plotted.
  4. [§5.1] The sentence 'This indicates that choosing the specific data point does dictate the level of accuracy' appears to contradict the preceding robustness claim that the result is not sensitive to the chosen point. Likely the intended meaning is 'does not dictate'; please rephrase.
  5. [Declarations] The data/code availability statements are inconsistent: 'Data and code will be made available' vs. 'Python implementation available at https://github.com/Feugmo-Group/PINNACLE'. Please state clearly what is available now, including a version/commit identifier.

Circularity Check

1 steps flagged

The 0.1 V hybrid result is partly a trained-on-the-benchmark fit; the cross-voltage generalization retains independent content.

specific steps
  1. fitted input called prediction [Section 5.1, Table 1; final Conclusion paragraph]
    "To test this hypothesis and address catastrophic overprediction, we implemented hybrid training by augmenting the physics-informed losses with a single supervised data point from the FEM solution. The data point, selected at point (t= 150000s, E= 0.1V, L= 1.27nm). ... By incorporating a single supervised data point from validated FEM solutions, we achieved remarkable accuracy with errors below 1% across all tested voltages."

    The single supervised anchor is drawn from the same FEM benchmark family against which the hybrid model is scored, so the comparison is not fully independent. At 0.1 V the paper itself observes that "almost no film growth is observed"; with L(t) nearly flat, the t=150000s, L=1.27nm anchor essentially fixes the 0.1 V thickness trajectory, making the reported 0.32% final-thickness error at 0.1 V a measure of how well the model retained its training anchor rather than an extrapolated prediction. The other voltage rows are not directly fitted, so the circularity is partial, but the headline 'sub 1% relative error as compared to Finite Element Benchmarks' is stated for the whole tested voltage set and thus depends in part on an anchor taken from the reference it is compared with.

full rationale

The core methodology—segregated PINN architecture, non-dimensionalization, NTK-based loss balancing, and the stated PDM equations—is not circular: NTK weighting is imported from an external source (Chen et al. [29]), the R-PDM is formulated in the cited Bosing work [10] and solved independently by FEM, and no uniqueness theorem is imported from the authors' own prior work. The main reduction to inputs is the hybrid anchor: one supervised point from the FEM solution is used in training, and the same FEM benchmark family is used for evaluation. This is most consequential at 0.1 V, where the paper notes that almost no film growth is observed, so the anchor at t=150000s, L=1.27nm effectively sets the flat thickness curve and the 0.32% error is not an independent prediction. For 0.4–1.8 V, the data are not directly fitted, and the N=5 random-anchor robustness test mitigates cherry-picking, so those results retain genuine predictive content. Separately, the conclusion's 'errors below 1% across all tested voltages' is inconsistent with Table 1's 2.18% at 1.6 V; that is a correctness/consistency issue rather than circularity. Overall, the central cross-voltage claim is not forced by construction, but the 0.1 V prediction and the blanket sub-1% headline are partially anchored to the reference they claim to reproduce.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The paper introduces no new physical entities. Its free parameters are the hand-chosen non-dimensional concentration scales and the single FEM anchor point; the latter is the load-bearing ingredient for the reported accuracy. The axioms are the PDM equations themselves, the presumed validity of the FEM reference, the representational power of the PINN, and standard statistical machinery.

free parameters (2)
  • Characteristic concentration scales c_c,cv and c_c,av = 1e-5 mol/m^3
    Chosen by hand 'to promote numerical stability' (Section 4.5, Eqs. 12-13); the paper notes experimentally determined reference concentrations would be preferable. These scales set the non-dimensional concentrations and influence the trained solution.
  • Single FEM anchor data point for hybrid training = (t=150000 s, E=0.1 V, L=1.27 nm)
    The hybrid model's dramatic error reduction hinges on this one supervised example from the FEM benchmark (Section 5.1). It is not a fitted constant in the PDEs, but it is a selected input on which the reported accuracy depends.
axioms (4)
  • domain assumption R-PDM governing equations (Nernst-Planck, Poisson, Butler-Volmer, film-growth ODE) adequately model halide-free iron passivation.
    Section 2 states the model and limits it to cation and anion vacancies for simplicity, neglecting electronic carriers. The physical fidelity of the result inherits the fidelity of this model.
  • domain assumption The FEM solution by Bosing et al. is the correct reference solution.
    Section 5.1 uses validated FEM simulations from reference [10], a co-author, as both the anchor and the benchmark. No independent experimental polarization data is used.
  • domain assumption The PINN architecture with NTK weighting can approximate the PDM solution sufficiently well when anchored.
    Section 4 assumes that segregated fully-connected networks with Swish activation and NTK-based loss balancing can represent the solution. The paper's own pure-PINN results show this assumption fails without data anchoring.
  • standard math Central Limit Theorem justifies the sampled NTK weight estimates.
    Section 4.6 uses the CLT to argue that batch-sampled NTK traces converge to the full trace, and sets batch sizes with a coefficient-of-variation threshold.

reviewed 2026-08-04 · how reviews work

0 comments
Cite this review

Pith. "Pith review of A physics-informed neural network approach to the point defect model for electrochemical oxide film growth." pith.science (2026). https://pith.science/paper/SZ2XYKCF

@misc{pith2026251002872,
  author       = {Pith},
  title        = {Pith review of: A physics-informed neural network approach to the point defect model for electrochemical oxide film growth},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SZ2XYKCF}},
  note         = {Machine review of arXiv:2510.02872}
}
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abstract

Physics-informed neural networks (PINNs) offer a novel AI-driven framework for integrating physical laws directly into neural network models, facilitating the solution of complex multiphysics problems in materials engineering. This study systematically explores the application of PINNs to simulate oxide film layer growth in halide-free solutions using the point defect model (PDM). We identify and analyze four key failure modes in this context: imbalanced loss components across different physical processes, numerical instabilities due to variable scale disparities, challenges in enforcing boundary conditions within multiphysics systems, and convergence to mathematically valid but physically meaningless solutions. To overcome these challenges, we implement and validate established techniques including nondimensionalization for training stabilization, Neural Tangent Kernel-based adaptive loss balancing, robust enforcement of boundary conditions and hybrid training with sparse data. Our results demonstrate the effectiveness of these strategies in enhancing the reliability and physical fidelity of PINNs, achieving sub $1\%$ relative error as compared to Finite Element Benchmarks with the hybrid model. Thereby showing that PINNs can be used for high fidelity electrochemical simulations with minimal data requirements and highlight necesary factors for fully autonomous PINN simulations.

Figures

Figures reproduced from arXiv: 2510.02872 by Conrard G. Tetsassi Feugmo, Ingmar B\"osing, Mohid Farooqi.

Figure 1
Figure 1. Figure 1: Full PINN Structure Schematic 5 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Predictions Overview using NTK weighting with Xavier Initialization simulating 250 hours. Top row left to [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Film Thickness Predictions: Pure PINN vs FEM [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Film Thickness Predictions: Hybrid PINN vs FEM [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Potential profiles, showing potential vs [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Log Loss vs Step plots, the solid lines indicate moving averaged numbers and the translucent backgrounds [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Log Losses vs Step. Translucent background indicates raw data, solid lines indicate smoothed loss [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Loss vs Step plots for AL and Hybrid AL NTK methods [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Interior and Boundary Loss Landscape Plots with and without residual connections [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Polarization Curve Applied Potential in Volts vs Current Density in Amps per square meter [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Loss Landscape Plots To illustrate the use of loss landscape plots we consider an instructive example. In [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

discussion (0)

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.