{"id":"9d3fdd95-540e-47f6-97ee-f05013646dea","arxiv_id":"2412.00486","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"ADFWI is an open-source PyTorch framework that uses automatic differentiation to replace hand-derived adjoint-state gradients in full waveform inversion across acoustic, elastic, and anisotropic media.","lead":"This paper releases ADFWI, an open-source software framework that uses automatic differentiation to compute gradients for full waveform inversion, removing the need for manually derived adjoint equations. It bundles acoustic, elastic, and anisotropic wave propagators with flexible objective functions, optimizers, regularization, and neural-network reparameterization for seismic imaging.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"AD gradients are only validated for one isotropic acoustic case; a bug in the elastic/VTI or non-L2 objective branches would invalidate ADFWI's central claim.","rationale":"The reader's weakest assumption correctly identifies the single decisive test for ADFWI's central claim: the AD gradients must be correct for every claimed wave equation and objective function. I agree with that assessment. The paper's only direct gradient validation is Supporting Figure S1, which is limited to ISO-acoustic, and the remaining numerical examples are self-consistency tests rather than gradient checks. A framework whose main promise is to remove the need for manual adjoint derivation must at least demonstrate that its AD gradients are accurate for the full supported matrix of propagators and misfits; otherwise, any implementation defect in those branches would be invisible in the reported synthetic inversions, since the same (potentially erroneous) forward model generates both 'observed' and synthetic data. This is not a challenge to the theoretical equivalence of AD and adjoint methods, which is established in the literature; it is a specific implementation risk for the new code. The proposed gradient-check script would resolve the concern in an afternoon on a GPU, and the repository already contains example scripts, so the test is practical. Until this check is run, the reader's CONDITIONAL verdict remains the correct state: the framework is plausible and well-scoped, but the advertised generality is not yet demonstrated.","tokens_in":27915,"tokens_out":6337,"duration_ms":61330,"concrete_test":"Add an examples/gradient_check.py script that reproduces the Figure S1 central-difference comparison for the ISO-elastic and VTI-elastic propagators on a small random heterogeneous 2D model with PML, computing AD and central-difference gradients of the L2 objective with respect to each inverted parameter (vp, vs, rho, epsilon, delta), and repeat for at least one data-alignment objective (soft-DTW or Wasserstein-Sinkhorn) and with checkpointing and mini-batching enabled. Pass criterion: max relative L2 error below 1e-4.","verdict_should_be":"UNCHANGED","load_bearing_attack":"ADFWI's central value proposition is that users can trust automatic differentiation to replace manual adjoint derivation for every supported wave equation and objective function. The only direct validation is Supporting Figure S1, which compares AD gradients against central differences for a single isotropic acoustic model. No equivalent gradient check is reported for the ISO-elastic or VTI/HTI-elastic propagators, nor for any non-L2 objective such as envelope, soft-DTW, or Wasserstein-Sinkhorn. The synthetic inversion tests in Sections 3.1.2, 3.1.3, and 3.2.1 cannot substitute: their observed data are produced by the same forward solver, so a consistent error in the staggered-grid update, the Thomsen-to-stiffness mapping, or the PML boundary would still yield low-misfit, plausible-looking inversions. The mini-batching and checkpointing strategies in Section 4.3 also modify the computation graph; if checkpoint recomputation or gradient accumulation is not exactly consistent with the original forward pass, AD gradients become biased. Because the framework's key promise is that arbitrary new wave equations and objectives can be added without hand-derived adjoints, an unverified gradient branch is the load-bearing risk.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript presents ADFWI, an open-source PyTorch-based automatic-differentiation framework for full waveform inversion. The framework implements forward modeling for isotropic-acoustic, isotropic-elastic, and VTI/HTI-elastic media using staggered-grid finite differences with PML boundaries, and computes gradients by backpropagation rather than by hand-derived adjoint equations. It integrates seven objective functions, eight optimizers, Tikhonov/TV regularization, DNN-based model reparameterization with dropout uncertainty estimation, and memory-reduction strategies (mini-batching and checkpointing). The authors validate the framework on Marmousi2 and Overthrust acoustic tests, an elastic Marmousi2 test, a VTI anomaly test, objective-function and optimizer comparisons, and regularization/uncertainty demonstrations, concluding that ADFWI eliminates manual adjoint derivation and serves as a flexible workbench for FWI.","tokens_in":28163,"tokens_out":8096,"duration_ms":77753,"significance":"ADFWI is a substantial engineering contribution with clear practical value: the public repository and reproducible examples lower the barrier to experimenting with non-L2 misfits, anisotropic wave equations, and neural-network reparameterization. The systematic comparison of objective functions and optimizers under a common setup is useful. If the AD gradients are correct across all supported branches, the framework delivers on its central promise. However, the current evidence does not yet establish that correctness for the elastic, VTI/HTI, and non-L2 objective branches, and several evaluation choices (smoothed-true initial models, same-solver observed data) weaken the generality claims. The missing gradient verification is the main load-bearing gap.","major_comments":[{"comment":"The only direct validation of the AD gradients is Supporting Figure S1, which compares AD gradients with finite-difference gradients for a single isotropic-acoustic experiment. No equivalent gradient check is reported for the ISO-elastic, VTI/HTI-elastic, or any non-L2 objective branch (envelope, global correlation, soft-DTW, Wasserstein-Sinkhorn), nor for the checkpointed or mini-batched computation graphs described in Section 4.3. Because AD differentiates the implemented forward code, a bug in the staggered-grid update, the Thomsen-to-stiffness mapping, the PML boundary, or the objective-function implementation would still yield low-misfit, visually plausible inversions when observed data are generated with the same forward solver. The paper's central claim in Section 5 that ADFWI 'eliminates the need for manual derivation and implementation of adjoint equations and sources' for all supported media and objectives therefore rests on an unverified branch. I request gradient checks (e.g., against finite differences or an adjoint-state reference, with a quantitative error metric) for at least one representative case in each wave-equation family and each objective-function family, or a correspondingly narrowed claim.","section":"Section 2.2 and Supporting Figure S1"},{"comment":"All synthetic inversions start from initial models obtained by Gaussian smoothing of the true model (Table 1; Figures 3b, 4c-d, 6b), and all observed data are generated by the same forward solver used in inversion. The VTI test in Section 3.1.3 goes further: vp, vs, and rho are fixed at their true values, and only epsilon and delta are inverted from constant background values equal to the true background. These tests therefore demonstrate that the framework can refine a good starting model, but they do not independently confirm the correctness of the elastic/VTI forward modeling or the corresponding AD gradients, nor do they exercise the multi-parameter trade-offs that dominate practical elastic/anisotropic FWI. In addition, the HTI case advertised in the abstract and Section 2.1 is not exercised in any numerical test. I recommend adding at least one test with a non-trivial initial model (e.g., from travel-time tomography or a coarse model without smoothing the target) and, if possible, a dataset produced by an independent solver or with added noise, or alternatively stating this limitation explicitly and softening the generality claims in Sections 3.1.3 and 5.","section":"Section 3.1 and Table 1"},{"comment":"The checkpointing and mini-batch strategies modify the computation graph over which gradients are accumulated. The paper reports memory and runtime trade-offs but does not verify that the gradients obtained with checkpointing and gradient accumulation are identical (or acceptably close) to those from a full uncheckpointed backpropagation. Since a mismatch would introduce biased gradients and could silently degrade inversion quality, a gradient accuracy check (e.g., comparing checkpointed and uncheckpointed gradients on the Marmousi2 example) should be added before claiming that these strategies are 'practical for large-scale full waveform inversion' (Section 5).","section":"Section 4.3"}],"minor_comments":[{"comment":"Typos and naming inconsistencies should be corrected: 'forword modeling' in the abstract, 'Pytorch' in Section 2.3 and Figure 1 caption, and 'T-Distribution' in Section 2.3.1 should be 'PyTorch' and 'Student-t distribution'.","section":"Abstract; Section 2.3"},{"comment":"The text states that δ in the anomaly inclusions ranges from 0.1 to 0.25, while the Figure 5 caption states 0.1 to 0.3; these values should be harmonized.","section":"Section 3.1.3 / Figure 5"},{"comment":"The sigmoid weighting expression is missing parentheses: it should read w(i) = 1/(1+exp(-(i - N/2))), and the text should state the value of N used in the WEC test in Section 4.1.","section":"Supporting Text S1, Eq. (7)"},{"comment":"The same objective is called 'Wasserstein-Sinkhorn' in Section 2.3.1 and 'Wasserstein Dist.' in Table 2; use one name consistently throughout.","section":"Section 2.3.1 / Table 2"},{"comment":"The dropout-based uncertainty maps are only qualitative; since no comparison with a reference uncertainty estimate (e.g., from multiple noise realizations or a Bayesian method) is provided, the claim of 'rapid estimation of uncertainty' should be accompanied by a caveat that the maps are uncalibrated.","section":"Section 4.2"},{"comment":"The gradient check reports no quantitative error metric or the Δm used for the finite-difference reference; please add a normalized error or maximum-relative-error value.","section":"Supporting Figure S1"}],"recommendation":"major_revision","confidential_remarks":"The main risk is exactly the one identified in the stress-test note: the missing gradient checks for the elastic, VTI/HTI, and non-L2 objective branches. I do not see a derivation-level circularity; the burden is in the evaluation design, which relies on smoothed-true initial models and same-solver observed data. The paper is otherwise a well-executed engineering contribution, and the requested additions are feasible. If the authors add the gradient checks and temper the scope claims, I would support acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Punchline: ADFWI is a real, usable open-source workbench, and the integration is the contribution. The paper is not claiming new physics or new math; it is claiming that you can do AD-based FWI across acoustic, elastic, and VTI/HTI media with a variety of misfits and regularizers without hand-deriving adjoints. That claim is plausible and mostly supported.\n\nWhat it does well: the code is released, the examples are reproducible, and the authors are honest about some limits—deeper elastic structures are less well recovered, the VTI test fixes vp/vs/rho and inverts only epsilon/delta, and optimizer tuning is acknowledged as necessary. The gradient check against central differences for one acoustic case is the right kind of evidence, and the memory/checkpointing measurements are useful for anyone planning a real run.\n\nWhere it is soft: the central promise is that AD gradients can be trusted for every branch. Only the isotropic acoustic gradient is directly verified; the elastic and VTI branches are validated only through inversion self-consistency, where a systematic error in the propagator or the Thomsen mapping could still produce low-misfit results. The mini-batch and checkpointing strategies change the computation graph, and there is no check that gradients stay correct under those modifications. Also, all tests start from smoothed versions of the true model and use the same solver to generate the observed data, so 'robustness' here is really 'self-consistency.' The optimizer hyperparameters are said to be tuned but not reported, which makes the optimizer comparison hard to reproduce exactly.\n\nNone of these are fatal for an engineering paper. The code being open means the unverified branches can be checked by users, and the framework genuinely lowers the barrier for trying new objective functions or regularizers. The reader's conditional verdict is about right.\n\nWho it is for: seismologists doing FWI method development, especially those comparing misfits or wanting DIP/dropout without building everything from scratch.\n\nRecommendation: send it to peer review as a software/methods paper. A serious referee should run a couple of the examples and, ideally, spot-check the elastic gradient against finite differences. With that, the paper earns its place.","headline":"A genuinely useful open-source AD-FWI workbench, but the 'robustness' headline outruns the synthetic evidence.","tokens_in":28692,"tokens_out":2670,"would_cite":false,"duration_ms":27399,"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":"The paper introduces ADFWI, an open-source automatic-differentiation framework that computes full waveform inversion gradients by backpropagation through the wave simulation, removing the need to derive adjoint equations and adjoint…","keywords":["full waveform inversion","automatic differentiation","adjoint state method","elastic wave equations","seismic anisotropy","deep learning","uncertainty quantification","open-source software"],"falsifier":"For each supported media and objective-function branch, compute the AD gradient on a small model and compare it against a central-difference gradient of the same objective; a mismatch in any branch, or a failed dot-product test between the forward operator and the AD-induced adjoint, would refute the claim of unified gradient correctness.","tokens_in":27723,"feed_emoji":"🌊","tokens_out":13147,"duration_ms":108783,"temperature":0.7,"pith_summary":"Full waveform inversion traditionally obtains its gradients from the adjoint state method, which requires a separate derivation and numerical implementation for each wave equation, objective function, and boundary condition. The paper claims that automatic differentiation removes this burden entirely: if the finite-difference forward simulation is written as a differentiable computational graph, backpropagation through that graph yields the same model gradients without any explicit adjoint equations or adjoint sources. The authors implement this claim in ADFWI, an open-source framework supporting isotropic-acoustic, isotropic-elastic, and VTI/HTI elastic wave propagation, and demonstrate the workflow on synthetic inversions that recover velocity, density, and anisotropy parameters. A sympathetic reader would care because ADFWI turns the steepest part of FWI research, deriving and verifying adjoints for new physics or misfit functions, into a matter of defining a differentiable forward script.","feed_headline":"ADFWI drops hand-derived adjoint equations in waveform inversion","feed_subtitle":"Open-source framework unifies acoustic, elastic, and anisotropic FWI and makes objective-function swaps trivial.","key_machinery":"The central object is the computation graph of the staggered-grid finite-difference wave simulation, traversed in reverse by automatic differentiation. Each arithmetic operation in the forward modeling, from the initial wavefield through all time steps to the misfit evaluation, is recorded, and backpropagation applies the chain rule along this graph to produce gradients with respect to model parameters. This is what lets a single forward code act as its own adjoint, which is why new objective functions, regularizers, or neural-network reparameterizations can be added without deriving adjoint sources. Checkpointing the time axis and processing shots in mini-batches are the mechanisms that keep this graph's memory footprint manageable.","core_discovery":"The central claim is that automatic differentiation can serve as a complete replacement for the adjoint state method in full waveform inversion, provided the wave simulation is coded inside a differentiable computation graph. In this setup, the graph that produces synthetic seismograms also produces the gradient of any differentiable objective with respect to any model parameter, so the framework can support isotropic-acoustic, isotropic-elastic, and VTI/HTI elastic media without per-media adjoint derivations. The paper shows that objective functions such as soft-DTW and Wasserstein-Sinkhorn, whose adjoint sources are difficult to derive, are integrated simply by computing their scalar value and letting backpropagation handle the gradient. Synthetic tests on the Marmousi2 and Overthrust models, an elastic Marmousi2 test recovering both vp and vs, and a VTI anomaly test recovering both epsilon and delta, along with comparisons of objective functions, optimizers, regularizers, and neural-network reparameterization, are offered as evidence that the framework is practical and flexible.","pith_inferences":["If backpropagation is correct for every branch, FWI research shifts from deriving adjoints to implementing accurate forward physics, which should accelerate experimentation with viscoelastic attenuation, three-dimensional media, and other formulations that are currently expensive to derive by hand.","The paper's direct gradient validation covers only one isotropic-acoustic case, so a natural stress test is to repeat the central-difference comparison for the elastic and VTI/HTI branches and for each non-L2 objective; a mismatch in any branch would silently corrupt those inversions.","Dropout-based uncertainty should initially be read as a fast sensitivity indicator tied to the reparameterizing network architecture, not as a calibrated posterior; comparing it with ensemble inversions would clarify what the uncertainty maps measure.","The same computation-graph convenience that makes total-variation and Tikhonov regularization trivial should extend to learned regularizers such as diffusion-model priors or dictionary transforms, though the paper only sketches this direction."],"forward_implications":["Any differentiable misfit, including soft-DTW and Wasserstein-Sinkhorn, becomes immediately usable in FWI because the gradient is supplied by backpropagation rather than by an analytically derived adjoint source.","The same inversion workflow applies across isotropic-acoustic, isotropic-elastic, and VTI/HTI elastic media, so multi-parameter inversions such as vp/vs or epsilon/delta can be run from one codebase.","Neural-network reparameterization becomes a direct optimization route in which automatic differentiation updates the network weights, providing learned regularization and enabling fast dropout-based uncertainty estimates.","Mini-batch shot processing and time-axis checkpointing reduce the memory overhead of automatic differentiation enough to make large-scale AD-based FWI practical on a single GPU.","Because automatic differentiation differentiates through any smooth regularizer, the framework's support for total-variation and Tikhonov regularization extends by construction to future regularizers, since only the regularization value needs to be computed."],"supporting_citations":[{"why":"Establishes the equivalence of AD-computed gradients with the adjoint state method in seismic inversion and provides the earlier ADSeismic framework that ADFWI builds on.","marker":"W. Zhu et al. (2021)"},{"why":"Supplies the automatic-differentiation engine on which ADFWI's computational graphs and backpropagation are implemented.","marker":"Paszke et al., 2017"},{"why":"Validates the use of AD gradients for borehole FWI, a prior check the paper cites for trusting AD-based gradient computation.","marker":"Cao and Liao (2015)"},{"why":"Provides a differentiable wave simulator and AD-based elastic least-squares migration workflow that ADFWI extends.","marker":"Richardson (2023)"},{"why":"Demonstrates AD-based elastic isotropic and anisotropic FWI using recurrent neural networks, supporting the elastic branch of ADFWI.","marker":"W. Wang et al. (2021)"},{"why":"Supplies the staggered-grid velocity-stress finite-difference formulation used for the elastic wave simulations.","marker":"Virieux, 1986; Levander, 1988"},{"why":"Defines the weak-anisotropy parameters used to parameterize VTI/HTI media in the inversion.","marker":"Thomsen, 1986"},{"why":"Introduces the differentiable soft-DTW loss that ADFWI adopts as one of its data-alignment objective functions.","marker":"Cuturi & Blondel, 2017"},{"why":"Brings optimal-transport/Wasserstein misfit into FWI, the basis for the Wasserstein-Sinkhorn objective in ADFWI.","marker":"Engquist et al., 2016"},{"why":"Establishes dropout as approximate Bayesian inference, the basis for the framework's fast uncertainty estimates.","marker":"Gal & Ghahramani, 2015"}],"fun_headline_variants":["AD replaces adjoint equations in flexible seismic inversion","Automatic differentiation eliminates manual adjoint sources in FWI","From acoustic to anisotropic elastic FWI via AD, no hand-derived gradients","ADFWI: one graph for wave simulation and gradient in FWI"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The framework's promise depends on backpropagation through the discretized finite-difference graph giving correct gradients for every wave equation and objective function it supports, but the paper directly validates this against central-difference gradients for only one isotropic-acoustic case.","fun_headline_variants_meta":{"raw":{"variants":["AD replaces adjoint equations in flexible seismic inversion","Automatic differentiation eliminates manual adjoint sources in FWI","From acoustic to anisotropic elastic FWI via AD, no hand-derived gradients","ADFWI: one graph for wave simulation and gradient in FWI"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000881,"raw_usage":{"total_tokens":3845,"prompt_tokens":1022,"completion_tokens":2823,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":638,"completion_tokens_details":{"reasoning_tokens":2752}},"tokens_in":638,"tokens_out":2823,"duration_ms":18714,"temperature":1.0,"reasoning_tokens":2752,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T05:20:43.947516+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"For each supported media and objective-function branch, compute the AD gradient on a small model and compare it against a central-difference gradient of the same objective; a mismatch in any branch, or a failed dot-product test between the forward operator and the AD-induced adjoint, would refute the claim of unified gradient correctness.","supporting_citations":[{"cited_title":"\\ Liao, W","cited_arxiv_id":null,"evidence_quote":"Validates the use of AD gradients for borehole FWI, a prior check the paper cites for trusting AD-based gradient computation."},{"cited_title":", McMechan, G A","cited_arxiv_id":null,"evidence_quote":"Demonstrates AD-based elastic isotropic and anisotropic FWI using recurrent neural networks, supporting the elastic branch of ADFWI."},{"cited_title":"APACrefauthors \\ 1986","cited_arxiv_id":null,"evidence_quote":"Defines the weak-anisotropy parameters used to parameterize VTI/HTI media in the inversion."}],"review_version":1}