{"id":"0aec54e6-443c-4348-9a80-623fbd65652d","arxiv_id":"2606.25479","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"An AD-enabled full-waveform inversion framework retrieves sub-pulse-width time-dependent scattering rate, plasma frequency, and resonance frequency from 2D THz-TDS signals using JAX optimization.","lead":"The paper presents a full-waveform inversion method that uses automatic differentiation on 2D THz time-domain signals to recover time-dependent material parameters at resolutions finer than the probe pulse width. This addresses a key limitation in ultrafast spectroscopy where standard response functions fail for rapid dynamics.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Uniqueness of recovering three time-dependent parameters from E(t_g, t_pp) is shown only via numerical examples, not derived from the forward model.","rationale":"The reader's weakest_assumption directly identifies the missing uniqueness argument. The numerical benchmarks in the paper provide supporting evidence but do not close the gap; the proposed test would decide whether the gap is merely formal or actually fatal to the claim.","tokens_in":1785,"tokens_out":352,"duration_ms":18554,"concrete_test":"Discretize the three parameter functions on a 2 fs grid over a 1 ps window; generate two distinct trajectories that differ only inside a 100 fs window, compute the corresponding E(t_g, t_pp) with the exact forward model used in the paper, add realistic noise, and rerun the JAX optimizer from multiple random initializations; if the recovered parameters differ by more than 5 % in L2 norm while the forward signals agree to within 1 % RMS, uniqueness does not hold.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that the 2D waveform E(t_g, t_pp) (after convolution with finite probe width) maps injectively onto the triple of functions {γ(t), ω_p(t), ω_0(t)} under the assumed Drude-Lorentz form. The paper demonstrates successful retrieval on synthetic and experimental data via Adam+L-BFGS but supplies no analytic argument (e.g., injectivity of the Fréchet derivative or rank of the discretized Jacobian) that different parameter trajectories cannot produce identical signals within experimental noise. Without this, the numerical success could be specific to the chosen test cases rather than generally true.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript presents an automatic-differentiation-enabled full-waveform inversion framework for time-resolved THz-TDS. Using the 2D measured field E(t_g, t_pp) and gradient-based optimization (Adam + L-BFGS in JAX), it retrieves the time-dependent parameters γ(t), ω_p(t), and ω0(t) under a Drude-Lorentz model at sub-pulse-width resolution, where the conventional conductivity σ(ω, t_pp) becomes unreliable.","tokens_in":1928,"tokens_out":465,"duration_ms":13834,"significance":"If the uniqueness and robustness claims hold, the approach would allow extraction of well-defined physical observables during ultrafast non-equilibrium dynamics that standard response-function analysis cannot access. The AD/JAX implementation provides a concrete strength in computational efficiency and reproducibility for optimization against experimental noise and pulse distortions.","major_comments":[{"comment":"Abstract and central claim: the assertion that the inverse problem can be 'uniquely solved' is supported only by numerical self-consistent benchmarks and experimental examples; no analytic argument (e.g., injectivity of the Fréchet derivative of the forward map or full-rank condition on the discretized Jacobian) is supplied to establish that distinct trajectories {γ(t), ω_p(t), ω0(t)} cannot map to identical E(t_g, t_pp) within noise.","section":"Abstract"},{"comment":"Forward-model section: the recovery is performed under an assumed Drude-Lorentz response; the manuscript does not derive or test the conditions under which the three-parameter mapping remains injective after convolution with finite probe width, nor does it supply exclusion criteria or noise-dependent error bounds that would falsify uniqueness.","section":"Methodology (forward model)"}],"minor_comments":[{"comment":"Notation: define t_g and t_pp explicitly on first use and maintain consistent subscripting throughout the equations and figures.","section":"Notation"},{"comment":"Figures: include quantitative uncertainty estimates (e.g., standard deviation across noise realizations) on the retrieved parameter traces in the experimental benchmarks.","section":"Results figures"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their positive assessment of the significance of our work and for the constructive major comments. We respond to each point below, and propose revisions where appropriate.","responses":[{"response":"We agree that the manuscript does not provide an analytic proof of uniqueness. Our claim is based on the observation that the optimization procedure, initialized from different starting points, consistently recovers the ground-truth parameters in self-consistent numerical tests even in the presence of noise and pulse distortions, and yields physically consistent results on experimental data. A rigorous mathematical analysis of the injectivity of the nonlinear forward operator is a substantial undertaking that lies beyond the scope of this primarily methodological paper in condensed-matter physics. We will revise the abstract to replace 'uniquely solve' with 'reliably retrieve' to better reflect the evidence presented.","revision_made":"partial","referee_comment":"[Abstract] Abstract and central claim: the assertion that the inverse problem can be 'uniquely solved' is supported only by numerical self-consistent benchmarks and experimental examples; no analytic argument (e.g., injectivity of the Fréchet derivative of the forward map or full-rank condition on the discretized Jacobian) is supplied to establish that distinct trajectories {γ(t), ω_p(t), ω0(t)} cannot map to identical E(t_g, t_pp) within noise."},{"response":"The forward model incorporates the convolution with the finite probe pulse width through the full time-domain simulation of E(t_g, t_pp). While we do not derive general analytic conditions for injectivity, the numerical benchmarks explicitly include the effects of finite pulse width and demonstrate successful recovery. We will add a new subsection discussing the robustness of the retrieval under varying noise levels and probe distortions, including examples where the optimization fails to converge, thereby providing practical exclusion criteria based on convergence behavior and residual error.","revision_made":"yes","referee_comment":"[Methodology (forward model)] Forward-model section: the recovery is performed under an assumed Drude-Lorentz response; the manuscript does not derive or test the conditions under which the three-parameter mapping remains injective after convolution with finite probe width, nor does it supply exclusion criteria or noise-dependent error bounds that would falsify uniqueness."}],"tokens_in":1394,"tokens_out":462,"duration_ms":26039,"standing_objections":["A complete analytic proof of uniqueness via Fréchet derivative injectivity or Jacobian rank analysis."]},"desk_editor":{"model":"grok-4.3","letter":"The core advance here is showing that automatic differentiation through a forward model lets you optimize directly for γ(t), ω_p(t), and ω_0(t) from the measured E(t_g, t_pp) even when those quantities vary inside the probe pulse width. They implement this with Adam followed by L-BFGS in JAX, test it on synthetic data with known trajectories, and then apply it to real ultrafast THz measurements. That combination is not just a routine extension of earlier FROG-style ideas; the 2D signal plus gradient-based fitting appears to give usable recovery where standard conductivity extraction breaks down.\n\nThe method is presented as robust to noise and pulse distortions, and the benchmarks look reasonable on the data they show. The optimization converges and produces plausible time traces.\n\nThe soft spot is the uniqueness claim. The abstract states one can “uniquely solve” the inverse problem, yet the supporting evidence is successful retrieval on chosen test cases rather than an argument that the mapping from the three functions to the convolved 2D waveform is injective. Different parameter paths could in principle produce indistinguishable signals within noise; without a Jacobian-rank check or similar, the numerical success might be case-specific. The Drude-Lorentz assumption is also baked in, so the method recovers parameters inside that model, not model-free observables.\n\nThis is aimed at groups already running THz-TDS on photoinduced dynamics who hit the sub-pulse limit. A reader working on similar inversion problems or needing faster-than-pulse resolution would get concrete value from the implementation details. It is worth sending to referees; the numerical and experimental demonstrations are solid enough to merit technical review even if the uniqueness question needs tightening.","headline":"The paper gives a practical AD+JAX route to pull time-dependent Drude-Lorentz parameters out of 2D THz waveforms at sub-pulse resolution, but uniqueness rests on numerical examples rather than a derived guarantee.","tokens_in":2424,"tokens_out":430,"would_cite":false,"duration_ms":11325,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Automatic differentiation applied to two-dimensional THz signals retrieves time-dependent scattering rate, plasma frequency and resonance frequency at sub-pulse-width resolution.","keywords":["THz-TDS","automatic differentiation","inverse problem","time-dependent parameters","full-waveform inversion","non-equilibrium dynamics","sub-pulse resolution"],"falsifier":"Forward-simulating E(t_g, t_pp) from the retrieved γ(t), ω_p(t) and ω0(t) and finding systematic, noise-exceeding mismatches with the original measured 2D waveform.","tokens_in":2693,"feed_emoji":"📡","tokens_out":669,"duration_ms":17257,"temperature":0.7,"pith_summary":"Standard analysis in time-resolved terahertz spectroscopy fails when material properties change faster than the probe pulse, rendering the usual conductivity unreliable. The paper shows that the full two-dimensional time-domain waveform E(t_g, t_pp) together with automatic differentiation supplies enough information to invert uniquely for three well-defined time-dependent quantities: the scattering rate γ(t), plasma frequency ω_p(t) and resonance frequency ω0(t). Gradient-based optimization (Adam plus L-BFGS) makes the inversion stable against noise and pulse shape errors. A reader cares because the method recovers ultrafast non-equilibrium dynamics that conventional response-function approaches cannot access.","feed_headline":"AD on 2D THz signals retrieves sub-pulse material parameters","feed_subtitle":"Scattering rate, plasma frequency and resonance frequency are recovered even when conductivity becomes unreliable due to fast changes.","key_machinery":"Full-waveform inversion framework that uses automatic differentiation on the measured 2D signal E(t_g, t_pp) to optimize the three time-dependent parameters γ(t), ω_p(t) and ω0(t).","core_discovery":"By leveraging automatic differentiation on the two-dimensional time-domain signal E(t_g, t_pp), the inverse problem of retrieving the time-dependent scattering rate γ(t), plasma frequency ω_p(t) and resonance frequency ω0(t) can be solved uniquely at sub-pulse-width resolution, even though the optical conductivity becomes unreliable when dynamics occur on or below the probe-pulse timescale; the resulting optimization via JAX is robust to experimental noise and probe distortions.","pith_inferences":["The method may transfer to other pulsed spectroscopies that face analogous pulse-width limits on the observable.","If additional independent signal dimensions can be recorded, further time-dependent parameters could be retrieved.","Open implementation of the JAX-based optimizer would allow direct testing on existing THz datasets."],"forward_implications":["Dynamics on timescales shorter than the probe pulse become accessible in photoinduced non-equilibrium experiments.","The retrieved parameters remain physically meaningful and well-defined even when conventional conductivity spectra are not.","Gradient optimization yields stable results in the presence of realistic experimental noise and pulse distortions.","The same framework is validated by both self-consistent numerical tests and actual ultrafast THz measurements."],"fun_headline_variants":["AD retrieves sub-pulse parameters from 2D THz signals","Sub-pulse THz parameters recovered from 2D signals using AD","Time-dependent material params extracted via AD from THz data","AD retrieves sub-pulse scattering rate and frequencies from 2D THz","2D THz signals allow sub-pulse param retrieval by AD"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The two-dimensional measured signal E(t_g, t_pp) encodes enough independent information to determine uniquely the three time-dependent parameters despite the finite duration of the probe pulse.","fun_headline_variants_meta":{"raw":{"variants":["AD retrieves sub-pulse parameters from 2D THz signals","Sub-pulse THz parameters recovered from 2D signals using AD","Time-dependent material params extracted via AD from THz data","AD retrieves sub-pulse scattering rate and frequencies from 2D THz","2D THz signals allow sub-pulse param retrieval by AD"]},"model":"grok-4.3","cost_usd":0.007364,"raw_usage":{"total_tokens":3402,"prompt_tokens":698,"num_sources_used":0,"completion_tokens":81,"cost_in_usd_ticks":73637000,"prompt_tokens_details":{"text_tokens":698,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2623,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":698,"tokens_out":81,"duration_ms":15230,"temperature":1.0,"reasoning_tokens":2623,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-25T20:23:21.450252+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Forward-simulating E(t_g, t_pp) from the retrieved γ(t), ω_p(t) and ω0(t) and finding systematic, noise-exceeding mismatches with the original measured 2D waveform.","supporting_citations":[],"review_version":1}