{"id":"b3a2f5d2-62ae-4e78-b1bb-6937143cf0d4","arxiv_id":"2501.06466","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A CNN trained on CT images predicts the permeability tensor components of Bentheim sandstone at multiple deformation states with R^2 around 0.98.","lead":"This paper trains 3D convolutional neural networks to predict the permeability of deformed sandstone directly from binarized CT images, using lattice Boltzmann simulations to generate the training data. The method could replace expensive pore-scale flow simulations in multiscale porous media modeling.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Random crop-level splitting leaks shared CT-volume and strain-level information, so the reported R^2 may substantially overstate generalization to unseen microstructures.","rationale":"The reader's weakest_assumption identified the same issue I consider most load-bearing: random shuffling of cropped subvolumes makes the test set non-independent from training, and the paper's evaluation protocol (Section 4.1) does not guard against it. If this concern lands, the central quantitative claim — accurate prediction on “unseen data” with R^2 ≈ 0.985/0.983 — is not established, even though the CNN architecture and LBM data pipeline may be sound. The proposed group-wise split is a decisive, low-cost check because the source code is provided. I therefore agree with the reader and would keep the verdict CONDITIONAL: the paper is a plausible methods contribution, but its headline accuracy claim requires a demonstration of generalization to unseen parent volumes or strain levels. I also note secondary issues (input-size inconsistencies between Section 3.1, Section 4.1 / Fig. 4, and Section 6.2; no error bars; no baseline), but none is more central than the leakage risk.","tokens_in":18772,"tokens_out":5868,"duration_ms":52898,"concrete_test":"Re-run Model 1 (and Model 2) with group-wise splits: (a) leave out all crops from one or more entire original CT volumes, and (b) leave out entire strain levels (e.g., train on εV ∈ {2,4,6,8,10,20}% and test on {30,40}%). Compute R^2 for the held-out groups and compare with the reported 0.985 and with a strain-level mean baseline. If group-wise R^2 drops markedly (e.g., below 0.9) or approaches the baseline, the random-split R^2 is inflated by leakage. The code at the provided DOI makes this check directly executable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central accuracy claim (Sections 4.2 and 5, R^2 ≈ 0.985/0.983) rests on the test set being genuinely unseen. The paper builds 448 3D samples by cropping from a small number of original µ-CT volumes (Section 3.1: 8 three-dimensional samples of 700×700×700 voxels; Section 3 says each deformation state comprises 8 samples), then says only that “data indices are shuffled to randomize the samples” before splitting (Section 4.1). A random crop-level split puts subvolumes from the same parent rock volume and same deformation state in both training and test sets. Because subvolumes of one CT scan share pore structure, and because porosity and permeability are strongly controlled by strain level (Figs. 2–3), the network can memorize parent- or state-specific features and effectively interpolate within familiar volumes. The reported R^2 therefore does not measure prediction for unseen microstructures or unseen deformation states. With only eight strain levels and a strong strain–permeability correlation, even a model that regresses the strain-level mean can achieve high R^2 on random splits. No group-wise split by parent sample or strain level, no confidence intervals, and no trivial baseline are reported, so the strongest claim is currently unsupported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes convolutional neural network (CNN) surrogates that take binarized micro-CT images of Bentheim sandstone as input and predict porosity and the diagonal components of the intrinsic permeability tensor at different volumetric strain levels. Three models are studied: a baseline CNN that outputs nF and K_11, K_22, K_33; an 'informed' CNN that adds porosity and specific surface area as auxiliary inputs; and a transfer-learning variant pretrained on GAN-generated synthetic microstructures and fine-tuned on the real data. The LBM is used to compute reference permeabilities, and the TPM framework provides the macroscopic flow context. Reported test-set R² values are about 0.985 for Model 1 and 0.983 for Model 2, with Model 3 mainly showing faster convergence. The authors conclude that CNN-based permeability prediction is accurate enough for use in multiscale porous-media modeling.","tokens_in":19032,"tokens_out":4626,"duration_ms":38601,"significance":"If the reported accuracy holds under correctly designed validation, the work would be a useful and practical surrogate for pore-scale LBM permeability computations, with a clear path toward embedding deformation-dependent permeability in TPM models. The strengths of the paper are its use of real µ-CT data, LBM-generated ground truth, reproducible open-source code, and a physics-aware baseline in the form of the TPM/Darcy-Brinkman formulation. The regression task itself is not circular: the CNN is fitted to LBM outputs and compared with independent held-out LBM simulations. However, the central generalization claim is currently undermined by the random crop-level splitting scheme and by the mismatch between the claimed 'permeability tensor' output and the actually predicted diagonal-only tensor.","major_comments":[{"comment":"The manuscript states: 'Before splitting into training, validation, and test subsets, data indices are shuffled to randomize the samples.' Because the 448 3D samples are crops extracted from a small number of parent µ-CT volumes (Section 3.1), a purely random crop-level split places subvolumes from the same parent rock volume and the same strain level in both training and test sets. These subvolumes share pore structure and deformation state, so the reported R² values in Sections 4.2 and 5 measure interpolation within familiar volumes rather than generalization to unseen microstructures or unseen strain levels. The authors should re-evaluate using group-wise splits (for example, leave-one-parent-volume-out and leave-one-strain-level-out) and report the resulting R² values, including the dispersion across repeated splits.","section":"Section 4.1, data preparation"},{"comment":"The manuscript computes the full symmetric off-diagonal components in Eq. (25) and then states that 'the non-diagonal components computed for Bentheim sandstone are much smaller than the diagonal components. Thus, we neglect them for simplicity from the ML model.' Yet the abstract and conclusions claim that the CNN predicts 'the symmetric second-order permeability tensor' and 'anisotropic intrinsic permeability tensor.' If only K_11, K_22, and K_33 are trained and predicted, the output is a diagonal tensor, not a general anisotropic permeability tensor. Either the off-diagonal components should be included in the training targets, or the claims and title should be revised to say that diagonal permeability components are predicted; in addition, the magnitude of the neglected off-diagonal components should be quantified.","section":"Section 3.3, Eq. (26)"},{"comment":"The reported R² values are based on a single randomly chosen test split, with no confidence intervals, no repeated cross-validation, and no trivial baseline comparison. Figures 2 and 3 show that porosity and permeability vary strongly and nearly monotonically with strain level; under a random split, a model that only regresses the strain-level mean could achieve a high R². The authors should report repeated k-fold splits with standard deviations and compare against baselines such as the strain-level mean or a porosity-only regression, so that the reader can assess the added value of the CNN beyond the known strain-dependence of permeability.","section":"Sections 4.2 and 5, R² results"},{"comment":"For the synthetic GAN data, the binarization threshold is selected 'to ensure that the resulting porosity matches that of the ground truth.' This is a calibration step that introduces a free parameter, but its sensitivity is not analyzed and no threshold value is reported for the real CT images in Section 3.1. In addition, the transfer-learning experiment shows faster convergence (initial loss around 0.03 versus 1) but the final loss values of the two models are similar; therefore the conclusion that transfer learning 'improves model performance' should be limited to learning efficiency unless final accuracy on a held-out set is shown to improve.","section":"Section 6.1 and Section 6.2"}],"minor_comments":[{"comment":"The loss definitions appear to use the index k without an explicit summation over k = 1, 2, 3; as written, k is a free index. The equations should include an explicit sum over the three permeability components.","section":"Eqs. (28) and (30)"},{"comment":"The input dimensions are inconsistent: Section 3.1 states that the 3D samples have size 150×150×150 voxels, while Figures 4 and 7 show an input of 256×256×32 voxels, and Section 6.2 refers to samples of 108×108×108 voxels. The authors should unify the reported input dimensions.","section":"Figures 4 and 7, and Section 3.1"},{"comment":"The description 'data indices are shuffled' should specify the random seed, the train/validation/test split ratio, and whether any stratification by strain level or parent volume was used.","section":"Section 4.1"},{"comment":"The binarization threshold for the real µ-CT images is not reported, whereas the threshold for the synthetic images in Section 6.1 is tied to porosity matching; reporting the threshold and its sensitivity would improve reproducibility.","section":"Section 3.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and contains solid LBM/TPM groundwork, but the central accuracy claim depends on the experimental design of the data split. If the group-wise split analysis requested in Major Comment 1 reveals a large drop in R², the contribution would be substantially weaker; the revision should therefore be evaluated on whether the authors provide a clean, leakage-free evaluation rather than on the current R² numbers alone."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a legitimate application of 3D CNNs to predict deformation-dependent permeability of a real sandstone from CT images, with code and data. The paper is honest about its own scope in several places. But its central accuracy claim — R2 ≈ 0.985 on unseen data — is not backed by the evaluation as described.\n\nWhat's new: the combination of deformed-state CT volumes, LBM-computed anisotropic permeability, and CNN regression is not in the papers it cites. The authors also build two variants (with and without a physical-parameter branch) and test transfer learning from GAN-generated synthetic microstructures. The LBM/TPM background is standard and correctly applied. The paper clearly states that off-diagonal permeability components are neglected because they are small; that's a limitation but not a hidden one. The availability of exemplary source code is a real plus.\n\nThe soft spot is the evaluation protocol. The dataset is 448 subvolumes cropped from a small number of original CT volumes across eight strain levels. Section 4.1 says only that indices are shuffled before splitting. A random crop-level split can put subvolumes from the same parent rock volume and same deformation state into both training and test sets. Since subvolumes of one scan share pore structure and since permeability is strongly controlled by strain level, the network can effectively interpolate within familiar volumes. The reported R2 therefore does not measure prediction for unseen microstructures or deformation states. The stress-test note is right about this, and it is the main thing keeping me from trusting the headline number. A proper group-wise split by parent volume or strain level, plus a baseline like regressing strain-level mean permeability, would settle it. No error bars or uncertainty estimates also weaken the comparison.\n\nMinor issues: the abstract and intro say '2D CNN' while the architecture and figures describe a 3D CNN; and the input size in Fig. 4 (256×256×32) does not match the stated 150×150×150 samples. Both are easily fixed.\n\nVerdict: the paper deserves a serious referee. The idea is reasonable, the execution is mostly careful, and the data leakage issue is fixable with re-splitting and re-evaluation. If the numbers hold after group-wise validation, this is a useful surrogate for permeability estimation. If not, it is still a decent demonstration of the workflow. I would ask for revision before acceptance, not reject it outright.","headline":"Useful application paper, but the central R2 claim rests on a crop-level split that likely inflates generalization; needs group-wise evaluation before that claim is credible.","tokens_in":19532,"tokens_out":2413,"would_cite":true,"duration_ms":22286,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["76S05","68T07"],"pacs":["47.56.+r"],"model":"deepseek-v4-flash","headline":"A convolutional neural network predicts the anisotropic permeability tensor and porosity of deforming sandstone directly from binarized micro-CT images, matching pore-scale simulations with an R^2 near 0.985.","keywords":["machine learning","convolutional neural networks","permeability tensor","porous media flow","multiscale modeling","deformable porous media","lattice Boltzmann method","micro-CT imaging"],"falsifier":"Retrain the same models using leave-one-strain-out or leave-one-sample-out splitting, so that all crops from one deformation state or one original scan are held out together, and compare the $R^2$ scores. If the score drops well below $0.985$, the high accuracy partly reflects information leakage across shared microstructures rather than a learned microstructure-to-permeability mapping.","tokens_in":18602,"feed_emoji":"🪨","tokens_out":9700,"duration_ms":88362,"temperature":0.7,"pith_summary":"This paper tries to establish that a convolutional neural network can learn the mapping from binarized micro-CT images of a deformable sandstone to the macroscopic intrinsic permeability tensor and porosity, reproducing lattice-Boltzmann simulation results with $R^2$ scores around $0.985$ on held-out subvolumes. If correct, the CNN becomes a fast surrogate for pore-scale flow simulations, allowing a macroscopic porous-media model to update permeability at each deformation state without rerunning expensive fluid dynamics. The study builds the dataset from Bentheim sandstone imaged at eight volumetric strain levels, computes ground-truth permeability with lattice-Boltzmann simulations, and tests three CNN variants, including one informed by physical parameters and one pretrained on synthetic microstructures.","feed_headline":"CNN predicts sandstone permeability from CT scans, R^2 ≈ 0.985","feed_subtitle":"A fast image-based surrogate for pore-scale flow simulations, across eight deformation states of sandstone.","key_machinery":"The central mechanism is a 3D convolutional neural network, a network that slides learned filters over grid-like image data, with four convolutional blocks with increasing filter counts and kernel sizes, each followed by max pooling, then a flatten layer, two dense layers, and a linear output layer for porosity and the three permeability components. The input is a binarized 3D CT subvolume; the training target is produced by lattice-Boltzmann simulations in which average fluid velocities under imposed pressure gradients are converted to intrinsic permeability through Darcy's law. This architecture lets the network act as a learned homogenization map from a fixed microgeometry to effective hydraulic properties, with deformation entering only through the changed binary pore structure at each strain level.","core_discovery":"The paper claims that the deformation-dependent anisotropic permeability tensor can be predicted directly from microstructure images. A 3D CNN with four convolutional blocks and two dense layers takes binarized CT subvolumes as input and outputs porosity together with the three diagonal intrinsic permeability components $K^S_{11}$, $K^S_{22}$, $K^S_{33}$, reaching $R^2 \\approx 0.985$ for Model 1 and $R^2 \\approx 0.983$ for Model 2 on unseen data. Ground truth is generated by single-phase lattice-Boltzmann simulations under two boundary-condition settings, with permeability recovered by inverting Darcy's law; the off-diagonal components are found to be much smaller than the diagonal ones and are omitted from the learning target. The informed model, which feeds porosity and specific surface area as extra inputs, does not meaningfully outperform the plain image-driven model, while transfer learning from synthetic GAN-generated microstructures mainly accelerates convergence rather than improving final accuracy.","pith_inferences":["A direct extension would be to train on the full permeability tensor including off-diagonal components, which would test whether the CNN can capture shear-driven anisotropy rather than only the nearly isotropic diagonal case shown here.","The same image-to-property architecture should transfer to other porous materials such as foams or biological tissues, but cross-material generalization remains untested because only one sandstone type is used.","Because the CNN maps a microstructure to several effective properties at once, it could plausibly be extended to predict electrical conductivity, elastic stiffness, or other homogenized quantities from the same CT inputs.","The transfer-learning result suggests that on even smaller real datasets synthetic pretraining could shift from a speed convenience to a necessity, a hypothesis the paper states but does not test."],"forward_implications":["A trained CNN can replace lattice-Boltzmann simulations inside a macroscopic porous-media model, making deformation-dependent permeability updates effectively instantaneous.","The same pipeline, binarized CT volumes in and permeability tensor out, can supply material laws for reservoir, hydrology, and geotechnical simulations without repeated pore-scale computation.","Jointly predicting porosity with permeability gives the surrogate model a consistent deformation state variable, matching how porosity changes with volumetric strain in the full theory.","Pretraining on synthetic microstructures offers a practical route to faster training when real CT data are scarce, even though it did not raise final accuracy on this dataset."],"supporting_citations":[{"why":"Establishes the practice of downscaling CT volumes to 150x150x150-voxel subvolumes and using a 3D CNN for rapid permeability estimation from digital rock images.","marker":"[46]"},{"why":"Supplies the two-boundary-condition lattice-Boltzmann procedure for recovering diagonal and off-diagonal intrinsic permeability components from average velocities.","marker":"[50]"},{"why":"Introduces the informed-CNN approach of adding physical parameters such as porosity as network inputs, which Model 2 adapts.","marker":"[72]"},{"why":"Provides the open-access synthetic Bentheim sandstone microstructures used for pretraining in the transfer-learning variant.","marker":"[60]"},{"why":"Earlier neural-network surrogate linking lattice-Boltzmann permeability data to macroscopic porous-media flow, the baseline this CNN approach extends.","marker":"[44]"},{"why":"Machine-learning-supported LBM-TPM surrogate for unsaturated, anisotropic, deformable porous media, providing the broader modeling context.","marker":"[17]"},{"why":"Open-source lattice-Boltzmann solver used to run the pore-scale flow simulations that produce the permeability ground truth.","marker":"[51]"},{"why":"Defines the single-relaxation-time collision operator used in the lattice-Boltzmann simulations.","marker":"[6]"},{"why":"Supplies the pressure and velocity boundary conditions applied in the lattice-Boltzmann flow simulations.","marker":"[73]"},{"why":"Public micro-CT dataset of Bentheim sandstone at multiple deformation states that supplies all real training images.","marker":"[58]"}],"fun_headline_variants":["CNN maps CT scans to sandstone permeability, R^2 ≈ 0.985","Deep learning reads rock CT to predict flow permeability","Image-based CNN gives sandstone permeability tensor quickly","Predicting anisotropic permeability from micro-CT with CNN","CNN surrogate maps rock images to flow permeability"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The reported accuracy rests on the assumption that randomly shuffling 448 cropped subvolumes, many taken from the same original CT scans, produces independent training and test sets.","fun_headline_variants_meta":{"raw":{"variants":["CNN maps CT scans to sandstone permeability, R^2 ≈ 0.985","Deep learning reads rock CT to predict flow permeability","Image-based CNN gives sandstone permeability tensor quickly","Predicting anisotropic permeability from micro-CT with CNN","CNN surrogate maps rock images to flow permeability"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00067,"raw_usage":{"total_tokens":3080,"prompt_tokens":995,"completion_tokens":2085,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":611,"completion_tokens_details":{"reasoning_tokens":2009}},"tokens_in":611,"tokens_out":2085,"duration_ms":13913,"temperature":1.0,"reasoning_tokens":2009,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:58:43.623778+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Retrain the same models using leave-one-strain-out or leave-one-sample-out splitting, so that all crops from one deformation state or one original scan are held out together, and compare the $R^2$ scores. If the score drops well below $0.985$, the high accuracy partly reflects information leakage across shared microstructures rather than a learned microstructure-to-permeability mapping.","supporting_citations":[{"cited_title":"Acta Geotech 10(4):399–419","cited_arxiv_id":null,"evidence_quote":"Supplies the two-boundary-condition lattice-Boltzmann procedure for recovering diagonal and off-diagonal intrinsic permeability components from average velocities."},{"cited_title":"Sci Bull 63(18):1215–1222, DOI 10.1016/j.scib.2018.08.006","cited_arxiv_id":null,"evidence_quote":"Introduces the informed-CNN approach of adding physical parameters such as porosity as network inputs, which Model 2 adapts."},{"cited_title":"Int J Numer Anal Methods Geomech 45(9):1212–1237, DOI 10.1002/ nag.3196 20 Yousef Heider1,∗ et al","cited_arxiv_id":null,"evidence_quote":"Earlier neural-network surrogate linking lattice-Boltzmann permeability data to macroscopic porous-media flow, the baseline this CNN approach extends."},{"cited_title":"Int J Numer Anal Methods Geomech pp 1–22, DOI 10.1002/nag.3668","cited_arxiv_id":null,"evidence_quote":"Machine-learning-supported LBM-TPM surrogate for unsaturated, anisotropic, deformable porous media, providing the broader modeling context."},{"cited_title":"Phys Fluids 9(6):1591–1598","cited_arxiv_id":null,"evidence_quote":"Supplies the pressure and velocity boundary conditions applied in the lattice-Boltzmann flow simulations."},{"cited_title":"http://www.digitalrocksportal.org/ projects/223, DOI 10.17612/1a36-rn45","cited_arxiv_id":null,"evidence_quote":"Public micro-CT dataset of Bentheim sandstone at multiple deformation states that supplies all real training images."}],"review_version":1}