{"id":"8ddfb7c2-4a2d-4393-8637-20f26c3aa8dc","arxiv_id":"2608.05937","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A single Fourier-enhanced DeepONet trained on simulated EFISH data reconstructs vertical and horizontal electric field profiles with Monte Carlo dropout uncertainty and out-of-distribution detection.","lead":"PC-FDON is a machine-learning model that reconstructs electric field profiles from EFISH laser measurements, covering both vertical and horizontal field components and a range of optical parameters. It also returns pointwise uncertainty estimates and flags out-of-distribution inputs, which is useful for trusting field reconstructions in plasma experiments.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"OOD flag, the paper's safeguard for its acknowledged profile-shape limitation, is validated on only two SDBD cases with no hard in-distribution controls; its false-positive behavior is unmeasured.","rationale":"I read the paper as making two coupled claims: (1) one conditional operator network can invert EFISH for both polarizations over the trained u range, and (2) MC-dropout uncertainty provides a reliable OOD detector. The reconstruction claim is supported by the synthetic tests, the unseen vertical function families, and the experimental forward consistency, though profile-shape coverage is acknowledged to be narrow. The OOD claim is the load-bearing safeguard precisely because the shape coverage is narrow; the reader's weakest assumption picks the shape coverage itself, while my concern is that the paper's own answer to that limitation, the OOD flag, is not actually stress-tested. Only two positive OOD cases (disk and gear SDBD) and four negative experimental cases are shown; there is no ROC-style analysis, no hard in-distribution controls, and no false-positive or false-negative rates. The thresholds are fit to the validation set and then applied to the same model, so overfitting of the confidence calibration is possible. A concrete test suite with labeled hard-in-distribution and true-OOD inputs would settle whether the exceedance fraction measures distribution shift or merely prediction difficulty. I do not see an internal inconsistency in the forward model or the architecture; the issue is an unsupported empirical subclaim. The reader's conditional verdict remains appropriate, so I keep the verdict unchanged, with partial agreement: the OOD concern is a more actionable version of the reader's shape-coverage worry.","tokens_in":22746,"tokens_out":10493,"duration_ms":117031,"concrete_test":"Generate a labeled test suite of EFISH profiles: (A) in-distribution profiles sampled at the extreme edges of the training ranges for the profile parameters and for u, with additive noise from SNR 30 down to 10 dB and with cropping down to 30% of the profile width; (B) true OOD profiles, such as asymmetric vertical profiles, triple-peaked vertical profiles, and multi-lobe horizontal profiles. For each input, compute the MC-dropout exceedance fractions of Eq. (11) and apply the four-level rule of Eq. (12). Report the confusion matrix, ROC curve, and false-positive rate at the 'low-confidence' threshold. If the false-positive rate on group (A) approaches the detection rate on group (B), the abstract's OOD claim is not supported; if the separation is clean, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.3.1 presents two SDBD cases flagged as OOD by the exceedance criterion of Eq. (12), and Section 3.3.2 shows four experimental cases classified as in-distribution. This is the entire empirical support for the abstract claim that the MC-dropout confidence metric 'flags inputs outside the training distribution... as low-confidence.' The thresholds in Eq. (12) are calibrated on the validation set, but no control group of hard-but-in-distribution inputs is reported. The metric may therefore be responding to input difficulty (noise, extreme parameter values within the trained ranges, severe cropping, high-curvature but in-family profiles) rather than to true distribution shift. Since Section 3.3.3 concedes that reconstruction is limited to specific profile shapes, the OOD flag is the only mechanism preventing silent failure on real discharges; if it has a high false-positive rate for difficult in-distribution signals, or a high false-negative rate for genuinely OOD shapes, the central safety claim collapses. The paper's own two-cause discussion in Section 3.3.2 (noise-induced versus shape-induced OOD) shows that the metric is not a pure distribution-shift detector, but no quantitative separation of these causes is provided. This is a validation gap in the central claim, not a contradiction of the forward model.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces PC-FDON, a DeepONet-style operator network for reconstructing electric field profiles from EFISH measurements. The architecture combines a Fourier-enhanced branch, a FiLM/gated polarization-conditioning branch, an auxiliary polarization classifier, and a physics-informed loss term. Training data are synthetic EFISH profiles derived from the forward integral in Eq. (3), covering vertical (bell-shaped/double-peak) and horizontal (bipolar) field families over seven discrete phase-mismatch values. The authors report reconstruction rates of 99.6%, 94.3%, and 95.1% below an MSE threshold of 0.004 for noise-free, incomplete, and noisy inputs, respectively; generalization tests on Quartic and Raised Cosine families show performance comparable to their earlier DDON. An MC-dropout uncertainty estimate is summarized by location-dependent exceedance fractions, and this OOD flag is applied to two simulated SDBD configurations, which are flagged as out-of-distribution, and to experimental disk-disk and sphere-sphere fields, which are classified as in-distribution. The paper explicitly acknowledges in Section 3.3.3 that the model remains limited to symmetric bell-shaped/double-peak vertical profiles and bipolar horizontal profiles.","tokens_in":23042,"tokens_out":4196,"duration_ms":50157,"significance":"If the results hold, PC-FDON would be a practically useful unified inverse solver for EFISH: one trained operator network would handle both polarization components and a range of optical parameters, with a built-in confidence/OOD indicator. The paper is strong in engineering detail: the architecture, hyperparameters, dataset sizes, and training schedule are specified in Tables A.1 and B.1, and the synthetic performance numbers are clearly quantified. The decision to state the profile-shape limitation explicitly is also a strength. However, the claimed advances are not yet fully evidenced: the OOD flag rests on a very small validation set without false-positive/false-negative controls, and the three architectural innovations are never isolated by ablations. The synthetic validation and the physics-informed loss also share the same forward model, so the reported MSEs primarily demonstrate self-consistency with Eq. (3) rather than absolute accuracy against independent field measurements.","major_comments":[{"comment":"The OOD detection claim is validated only on two SDBD cases, with no hard in-distribution controls and no measured false-positive or false-negative rates. Since Section 3.3.3 concedes that reconstruction is limited to specific profile shapes, the OOD flag is the only safeguard against silent failure on real discharge profiles. The authors should report performance on a controlled test set that includes difficult but in-distribution inputs (e.g., extreme u values, high noise, heavy cropping, high-curvature in-family profiles) and genuinely out-of-family shapes, and should quantify the trade-off between the p95/p99 thresholds in Eq. (12).","section":"§3.3.1 and Eq. (12)"},{"comment":"The exceedance-fraction metric is calibrated on validation-set percentiles but its relationship to actual reconstruction error is never demonstrated. The paper shows that OOD flags can arise from two distinct causes, noise-induced and shape-induced, but provides no quantitative separation of these causes. A calibration analysis, such as a reliability diagram or a plot of exceedance fraction versus true MSE on held-out in-distribution and OOD sets, is needed to support the claim that the metric reflects model confidence rather than merely input difficulty.","section":"§2.5 and §3.3.2"},{"comment":"The paper claims three targeted advances, Fourier enhancement, polarization conditioning via FiLM/gating, and a physics-informed loss, but no ablation isolates their contributions. The comparison in Section 3.2 is only PC-FDON versus the authors' previous DDON, so it cannot attribute any observed difference to the Fourier branch, the FiLM/gated mechanism, or the PINN term. I recommend adding ablation variants, each removing one component while keeping the training data and evaluation protocol identical, and reporting the resulting MSE distributions and OOD behavior.","section":"§2.3 and §3.2"},{"comment":"The training data, the physics-informed loss, and the synthetic test sets all use the same forward model, Eq. (3). Consequently, the reported fractions below MSE = 0.004 establish that the network has learned the inverse of the assumed forward operator, but they do not by themselves validate the model against the real EFISH physics. The paper should state this limitation explicitly and discuss how model-form error in Eq. (3) could affect field reconstruction, in addition to the already-listed experimental limitations.","section":"Eq. (3) and §2.1"}],"minor_comments":[{"comment":"The loss terms are written without sample indices; for reproducibility, define the per-sample MSE and BCE operations explicitly over the training batch.","section":"Eq. (9)"},{"comment":"The caption reports SNR = 20 dB for the noisy condition, while the jitter-layer augmentation in Section 2.1 uses SNR ≈ 26 dB; clarify whether the test noise level is intentionally different from the training augmentation level.","section":"Figure 2 caption"},{"comment":"The phrase 'the model’s confidence is well-placed' is not quantitatively supported; a comparison of uncertainty estimates with the actual reconstruction error would make this statement precise.","section":"Section 3.3.2"},{"comment":"The 'Num' column for layer counts is difficult to parse; including a small legend or explicitly listing the number of repetitions for each block would improve reproducibility.","section":"Table A.1"},{"comment":"Equation (5) mixes dimensional quantities (z, y, l) with a dimensionless acosh term; since all profiles are later peak-normalized, state clearly which variables are in units of z_R before normalization.","section":"Section 2.1.2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is technically sound in its core engineering and the authors are transparent about limitations, but the OOD validation is too thin to support the abstract's safety claim and the absence of ablations weakens the novelty claims. I would encourage the editor to request the additional control experiments and ablations; they are within the scope of a revision and should be feasible with the existing pipeline."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid, incremental extension of the authors' earlier DDON to the case where you don't know the polarization and want one model for vertical and horizontal EFISH inversion across a range of phase mismatches. The central claim — a single conditioned operator network handles both polarizations with accuracy comparable to the polarization-specific baseline — is backed by quantified synthetic results and two experimental configurations. The uncertainty/out-of-distribution machinery is the most interesting part, and it is also the softest part.\n\nWhat's genuinely new: the earlier DDON was vertical-only, single phase mismatch u=-0.068. PC-FDON adds a Fourier branch, FiLM conditioning on polarization, a physics-consistency loss, and MC-dropout based OOD detection. The paper documents the architecture and training in enough detail to reproduce, and the synthetic numbers are good: 99.6%, 94.3%, 95.1% of test profiles under MSE 0.004 for noise-free, incomplete, and noisy (SNR=20dB) inputs. The experimental reconstruction of vertical and horizontal fields for disk-disk and sphere-sphere electrodes agrees with simulation, which is genuine evidence the approach transfers.\n\nSoft spots, in order of importance. First, the OOD flag is validated on only two SDBD cases, both positive examples. There are no hard-but-in-distribution controls, so we don't know how often the flag goes off for a difficult but in-family input. Given the paper's own Section 3.3.3 admits the model only handles certain profile shapes, the OOD flag is the main safeguard against silent failure — and its false-positive and false-negative rates are unmeasured. That is a real validation gap, not a fatal one. Second, no ablations: the Fourier layers, FiLM, and physics loss are all claimed as advances, but nothing isolates their individual contribution, and the only baseline is the authors' own DDON. Third, no code or data release, which makes independent verification harder. The profile-shape limitation itself is acknowledged and is the core structural constraint; it means the model is a practical tool for symmetric/bipolar profiles, not a general inverter.\n\nVerdict: worth a serious referee. The paper is honest, clearly written, and the central accuracy claim holds. I would ask for OOD negative controls and at least one ablation before acceptance, but this is a legitimate contribution to the EFISH diagnostics subfield, not a desk reject.","headline":"Useful incremental extension of the authors' DDON to both polarizations and variable phase mismatch; the OOD-flag validation is the main soft spot, but the paper is honest and worth reviewing.","tokens_in":23573,"tokens_out":2333,"would_cite":false,"duration_ms":23771,"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":"PC-FDON reconstructs both vertical and horizontal electric field profiles from EFISH signals with one polarization-conditioned operator network, and its dropout-based confidence metric flags measurements outside the trained profile…","keywords":["Electric field induced second harmonic generation","EFISH","Polarization-conditioned","Deep operator network","Operator-learning","Machine learning","Physics-informed reconstruction"],"falsifier":"Generate a synthetic EFISH signal from a clearly asymmetric, single-peaked vertical field profile inside the trained phase-mismatch range $u\\in[-0.01,-1]$, feed it to PC-FDON, and compare the reconstruction against the known ground truth: if the error stays below the paper's $\\epsilon_{\\mathrm{MSE}}=4\\times10^{-3}$ threshold and the exceedance fraction remains in-distribution, the stated shape limitation is false; if the error is large or the OOD flag fires, the limitation holds as stated.","tokens_in":22565,"feed_emoji":"⚡","tokens_out":8146,"duration_ms":79464,"temperature":0.7,"pith_summary":"Electric-field-induced second-harmonic generation (EFISH) measures a plasma electric field only through a coherent line-of-sight integral, so recovering the field profile is an ill-posed inverse problem. This paper claims that a single operator-learning network, the Polarization-Conditioned Fourier-enhanced DeepONet (PC-FDON), can solve that inverse problem for both vertical and horizontal field components at once, across the phase-mismatch range $u\\in[-0.01,-1]$, by conditioning the reconstruction on the signal polarization and on optical parameters. It also claims that Monte-Carlo dropout gives pointwise epistemic uncertainty whose profile-level exceedance fraction reliably flags inputs outside the training distribution, such as surface dielectric barrier discharge profiles. If these claims hold, one trained model plus an uncertainty check replaces separate polarization-specific solvers and tells an experimentalist when a measurement cannot be trusted.","feed_headline":"One network reconstructs E-fields from both EFISH polarizations","feed_subtitle":"Fourier-enhanced operator learning plus dropout uncertainty flags out-of-distribution plasma measurements before you trust them.","key_machinery":"The central object is the dimensionless EFISH forward integral $$$P^{{(2\\omega)}}$_{\\mathrm{norm}}(z'_o) \\propto \\left|\\int_{-\\infty}^{\\infty} \\frac{E'_{\\mathrm{ext}}(z'-z'_o)\\,$e^{{iuz'}}$}{1+iz'}\\,dz'\\right|^2,$$ which maps the field profile to the measured signal and whose kernel carries the Gouy phase $1/(1+iz')$ and the wave-vector mismatch $e^{iuz'}$. PC-FDON learns the inverse of this integral as an operator: a Fourier-enhanced branch extracts global spectral features, a FiLM-conditioned polarization branch modulates those features according to the polarization label, a trunk network evaluates the operator at query positions, and a physics-informed loss enforces that the predicted field, when pushed back through the forward integral, reproduces the measured signal. The MC-dropout procedure turns the same trained network into a Bayesian approximation whose pointwise standard deviation, compared against validation percentile thresholds via the exceedance fraction of Eq. (11), yields the paper's confidence levels.","core_discovery":"On the paper's own terms, the discovery is that EFISH inversion can be performed by one physics-informed operator network rather than by polarization-specific networks tuned to a single phase mismatch. The network takes a normalized EFISH signal profile, the phase-mismatch parameter $u$, and a binary polarization label $\\psi$, and outputs the normalized electric field profile $E'_{\\mathrm{ext}}(z')$ together with a predicted polarization class. Fourier layers give the branch a spectral inductive bias for the Gouy-phase and wave-vector-mismatch part of the forward kernel; FiLM and a gated unit modulate the shared features by polarization; and a physics-informed loss re-inserts the predicted field into the forward integral of Eq. (3) to enforce self-consistency. Trained on symmetric bell-shaped and double-peaked vertical profiles and bipolar horizontal profiles at seven discrete $u$ values, the model reconstructs noise-free, incomplete, and noisy inputs, generalizes to unseen Quartic and Raised Cosine families at accuracy comparable to the earlier polarization-specific model, and its MC-dropout exceedance fraction flags SDBD profiles as out-of-distribution while accepting experimental electrostatic measurements.","pith_inferences":["As an editorial extension, the OOD flag certifies similarity to the training manifold, not physical correctness, so a user who sees a low-confidence label still needs the paper's recommended noise-level check to decide whether the field is genuinely new or the measurement is just noisy.","A testable extension is to add asymmetric vertical and multi-peaked profile families to the training set; if the Fourier layers and physics-informed loss then reconstruct them accurately, the symmetry assumption in Section 3.3.3 would be shown to be a data limitation rather than an architectural one.","The same polarization-conditioning and Fourier-bias recipe should transfer to other line-of-sight-integrated plasma diagnostics, such as emission spectroscopy, because those diagnostics share the structure of an integral kernel modulated by a discrete experimental parameter."],"forward_implications":["One trained PC-FDON replaces separate vertical- and horizontal-polarization reconstruction models; running it once with each polarization label yields both components of the electric field vector.","Across the phase-mismatch range $u\\in[-0.01,-1]$, the model reconstructs profiles without retuning for each optical setup, covering the common 1064 nm and 532 nm configurations listed in the paper.","The location-dependent exceedance fraction gives a profile-level confidence label (very high, high, borderline, low) that flags measurements outside training, so a user can reject a reconstruction instead of trusting it blindly.","The physics-informed loss plus forward-signal comparison allows validation against the measured EFISH profile when no ground-truth field is available, which is the normal experimental situation.","On unseen Quartic and Raised Cosine profile families at SNR=20 dB, the unified model stays comparable to the previous polarization-specific model, with the paper attributing the small gap to the halved vertical-polarization training budget."],"supporting_citations":[{"why":"Supplies the vertical-polarization function families from Fuzzy and Voigt profiles, the incomplete-input cropping strategy, and the generalization benchmark on Quartic and Raised Cosine families.","marker":"[14]"},{"why":"Establishes the deep-learning EFISH inversion task and the profile-scanning convention the dataset follows.","marker":"[9]"},{"why":"Shows how the electric-field profile shape alters the EFISH signal through the forward integral, justifying shape-aware inversion.","marker":"[4]"},{"why":"Provides the tensor-polarization dependence of EFISH, the physical basis for conditioning on vertical versus horizontal polarization.","marker":"[17]"},{"why":"Gives the dropout-as-Bayesian-approximation result on which the MC-dropout uncertainty and exceedance-fraction OOD metric are built.","marker":"[24]"},{"why":"Supplies the DeepONet operator-learning formulation behind the branch-trunk architecture.","marker":"[31]"},{"why":"Defines Feature-wise Linear Modulation, the conditioning mechanism the polarization branch uses to modulate EFISH features.","marker":"[39]"},{"why":"Introduces the Fourier Neural Operator whose spectral convolutions motivate the Fourier-enhanced sub-branch.","marker":"[35]"},{"why":"Introduces the original EFISH two-cylinder analytical field, the source of the horizontal bipolar profile family.","marker":"[2]"}],"fun_headline_variants":["One network inverts EFISH for both polarizations","Single operator network handles dual EFISH polarizations","Fourier-boosted operator network for EFISH field retrieval","Single physics-informed model reconstructs EFISH E-fields"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the true electric field profile belongs to the trained shape families: symmetric bell-shaped or double-peaked vertical profiles and bipolar horizontal profiles; the paper states in Section 3.3.3 that asymmetric, triple-peaked, or otherwise non-smooth profiles remain outside the model's scope and are at best caught by the out-of-distribution flag rather than reconstructed correctly.","fun_headline_variants_meta":{"raw":{"variants":["One network inverts EFISH for both polarizations","Single operator network handles dual EFISH polarizations","Fourier-boosted operator network for EFISH field retrieval","Single physics-informed model reconstructs EFISH E-fields"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000933,"raw_usage":{"total_tokens":4058,"prompt_tokens":1077,"completion_tokens":2981,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":693,"completion_tokens_details":{"reasoning_tokens":2915}},"tokens_in":693,"tokens_out":2981,"duration_ms":23206,"temperature":1.0,"reasoning_tokens":2915,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T20:44:21.605510+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Generate a synthetic EFISH signal from a clearly asymmetric, single-peaked vertical field profile inside the trained phase-mismatch range $u\\in[-0.01,-1]$, feed it to PC-FDON, and compare the reconstruction against the known ground truth: if the error stays below the paper's $\\epsilon_{\\mathrm{MSE}}=4\\times10^{-3}$ threshold and the exceedance fraction remains in-distribution, the stated shape limitation is false; if the error is large or the OOD flag fires, the limitation holds as stated.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the vertical-polarization function families from Fuzzy and Voigt profiles, the incomplete-input cropping strategy, and the generalization benchmark on Quartic and Raised Cosine families."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the deep-learning EFISH inversion task and the profile-scanning convention the dataset follows."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows how the electric-field profile shape alters the EFISH signal through the forward integral, justifying shape-aware inversion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the tensor-polarization dependence of EFISH, the physical basis for conditioning on vertical versus horizontal polarization."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the dropout-as-Bayesian-approximation result on which the MC-dropout uncertainty and exceedance-fraction OOD metric are built."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the DeepONet operator-learning formulation behind the branch-trunk architecture."},{"cited_title":"Perez, F","cited_arxiv_id":null,"evidence_quote":"Defines Feature-wise Linear Modulation, the conditioning mechanism the polarization branch uses to modulate EFISH features."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the original EFISH two-cylinder analytical field, the source of the horizontal bipolar profile family."}],"review_version":1}