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PoreML: A Data-Driven Framework for Learning Multiphase Flow in Porous Media

Chunyang Wang, Mingrui Zhang, Yuyan Zhang, Linqi Zhu, Xin Ju, Edo Sicco Boek, Martin J. Blunt, Gege Wen

arXiv:2610.10314v1cs.LGphysics.flu-dyn

TL;DR

Time-resolved 3D data and unified benchmarks remain scarce for pore-scale multiphase flow. PoreML combines validated simulation, datasets, and physics-aware rollout evaluation; in 64-step tests, AB-UPT leads ϕ MAE across four campaigns while topology remains least well predicted.

  • Problem

    Time-resolved 3D multiphase data and unified learning benchmarks for porous media are limited, despite the need to predict flows on representative domains and real materials.

    Source: §1 · p. 3

  • Method

    PoreML combines a validated GPU-native solver and open dataset with standardized model training and rollout evaluation using field, geometry, and topology metrics.

    Source: §1 · pp. 3–4, §5 · p. 9

  • Results

    Across 64-step rollouts, AB-UPT has the lowest ϕ MAE in all four campaigns, while topology is the least well predicted quantity.

    Source: §4.2 · pp. 7–8

  • Takeaways & Limitations

    PoreML provides a shared foundation for generating data and comparing models across new conditions in porous-media flow.

    Source: §5 · p. 10

    Explicit tests of mass and momentum conservation remain future work.

    Source: §5 · p. 10

Abstract

from arXiv · show

Multiphase flow in porous microstructures is central to CO$_2$ storage, fuel-cell operation, and flip-chip packaging. Predicting these flows remains challenging because wettability and complex pore geometry govern the nonlinear evolution of fluid interfaces. Machine learning holds substantial promise for advancing the field, but progress is constrained by scarce time-resolved 3D datasets and a lack of a unified workflow for training and evaluating models. To fill this critical gap, we introduce PoreML, an open-source framework unifying data generation, model training, and evaluation grounded in pore-scale physics. The framework comprises three core components. (a) A modern GPU-native lattice Boltzmann solver, validated against analytical solutions and published experiments, enables reproducible data generation. (b) A 3.3 TB dataset contains 560 simulation runs and 158,546 stored time steps across four application-driven scenarios. These trajectories span synthetic structures and geometries derived from micro-CT scans of real materials, covering diverse wetting conditions and viscosity ratios. (c) A unified learning framework evaluates one-step prediction and autoregressive rollouts. Its domain-specific evaluation protocols assess predictive accuracy and physical consistency. We evaluate five models of diverse architecture under these protocols. Two complementary challenges assess transfer to larger domains and from synthetic to micro-CT-derived structures. PoreML provides a shared foundation for machine-learning research on multiphase flow in porous media, with the aim of empowering the community to develop reliable predictive models and advance the field.

1 INTRODUCTION

Pore-scale capillary events can reshape fluid connectivity, yet time-resolved 3D data and reliable prediction across domain sizes and geometries remain challenging. PoreML combines simulation, data, and physics-aware model evaluation to address these gaps.

1 INTRODUCTION

  • Snap-off, coalescence, and Haines jumps alter fluid connections or pore filling, and pore-scale events can remain hidden at fixed saturation.These events shape trapping, phase flow, and displacement hysteresis.Source: §1 · p. 2
  • Time-resolved 3D evidence is scarce, while µCT simulation depends on mesh quality and resolution and becomes costly as domains grow.The resulting mismatch is between affordable synthetic ground truth and predictions needed on representative domains and real materials.Source: §1 · p. 3
  • 560 runs and 158,546 snapshots span four applications, generated and µCT geometries, varied wetting and viscosity conditions, and two transfer challenges.Geo-Shift tests generated-to-µCT transfer; Scale-Up tests larger domains at fixed resolution.Source: §1 · pp. 3–4
  • PoreML contributes an open-source validated solver, time-resolved 3D dataset, and standardized five-architecture benchmark with field, geometry, and topology metrics.The solver was validated against an eight-case suite of analytical solutions and published experiments.Source: §1 · p. 4

2 RELATED WORK

Prior resources and learned models provide limited coverage of time-resolved 3D multiphase flow in porous microstructures. PoreML builds on established LBM strengths while bringing color-gradient modeling and geometric wetting into an accelerator-native learning-data workflow.

Learning-based models and data for pore-scale flow

  • Existing models and public datasets cover steady single-phase flow, 2D evolving flow, static states, or scalar summaries, leaving a need for full 3D multiphase trajectories.General PDE collections lack multiphase flow through porous microstructure, while BubbleML lacks a confining porous solid.Source: §2 · p. 4

Lattice Boltzmann solvers for porous media

  • Color-gradient LBM sustains thin interfaces under viscosity contrast and suits narrow throats, though accuracy deteriorates when throats span only a few voxels.Geometric wetting models provide direct contact-angle conditions; prior comparisons distinguish static-angle and dynamic Washburn-flow strengths.Source: §2 · p. 4
  • PoreML brings color-gradient modeling with geometric wetting into an accelerator-native implementation for generating learning data.Prior production solvers include Palabos and LBPM, while JAX-LaB brought a pseudopotential model to JAX.Source: §2 · p. 4

3 POREML: LEARNING MULTIPHASE FLOW IN POROUS MEDIA

PoreML brings together a GPU-native multiphase solver, a dataset spanning generated and scanned geometries across practical flow scenarios, and a learning framework with physics-aware evaluation. Its design targets both field prediction and the geometry and topology of evolving phases.

3.1 A JAX-NATIVE COLOR-GRADIENT LBM SOLVER

  • The GPU-native solver unites thin color-gradient interfaces under viscosity contrast, direct contact-angle control on complex solids, and multi-GPU JAX execution.It generates every PoreML trajectory and is validated against analytical solutions and published experiments.Source: §3.1 · pp. 4–5

3.2 DATASET OVERVIEW

  • The dataset pairs segmented µCT samples with generated geometry families at two domain sizes, with generated structures overlapping scanned samples in local pore size.Families include sphere packs, Gaussian-random-field blobs, polydisperse grains, fiber mats, and parametric flip-chip gaps.Source: §3.2 · p. 5, Figure 4 · p. 5
  • Four campaigns cover drainage, trapping, GDL water intrusion, and underfill, with varied contact angles and viscosity ratios; stored frames include phase, velocity, and pressure.The viscosity-ratio convention differs for underfill, and contact angle is measured through different phases across the campaigns.Source: §3.2 · pp. 5–6, Table 1 · p. 6

3.3 MACHINE LEARNING FRAMEWORK

  • The learning task predicts the next state from state history while conditioning the model on geometry, physical parameters, and boundary protocol.The state includes phase identity, velocity, and pressure.Source: §3.3 · p. 6
  • Minkowski functionals complement field errors by measuring phase volume, interface area, integrated mean curvature, and topology.The Euler characteristic counts connected components, loops, and cavities; curvature is linked to local capillary pressure by Young–Laplace.Source: §3.3 · pp. 6–7

4 EXPERIMENTS AND RESULTS

The experiments compare five architectures on held-out geometries, one-step predictions, 64-step rollouts, and transfers to scanned structures and larger domains. Rollout strengths vary by metric, and topology is less reliable than field accuracy suggests.

4.1 EXPERIMENTAL SETUP

  • Five voxel and point architectures are evaluated on held-out geometries, predicting the next saved (ϕ, u, p) frame from the current frame, solid mask, M, and θ.Only pore voxels are scored; models are trained frame to frame and then fine-tuned with the pushforward trick.Source: §4.1 · p. 7, §4 · p. 7
  • Geo-Shift trains on 64 generated runs and tests on 80 µCT runs per campaign; Scale-Up tests 16 large-domain runs per campaign, with each dimension doubled at fixed resolution.The evaluation framework uses held-out geometries and asks whether rollout fidelity survives transfer to scanned geometries and larger domains.Source: §4.1 · p. 7, §4 · p. 7

4.2 SINGLE-STEP AND ROLLOUT PERFORMANCE

  • Evaluation compares one-step predictions from true frames with step-64 autoregressive rollouts started from successive trajectory windows, scoring field errors and Minkowski functionals.Errors are averaged within each run before averaging across runs.Source: §4.2 · p. 7
  • Over 64-step rollouts, AB-UPT has the lowest ϕ MAE in all four campaigns; P3D leads M0–M2 in drainage, while FNO3D and UNet3D lead topology in three campaigns.Across one-step predictions, UNet3D and P3D lead 16 of 24 columns, but single-step accuracy does not by itself imply good rollout performance.Source: §4.2 · p. 7, Table 2 · p. 8
  • Topology is the least well predicted quantity: median M3 error is 3.6 miscounts per 105 voxels, compared with median M0 error of 11%, and low field error does not guarantee connectivity.The median M3 error is as large as the reference χ density itself (1–9).Source: §4.2 · p. 8

4.3 DISTRIBUTION SHIFT: GEO-SHIFT AND SCALE-UP

  • Across Geo-Shift and Scale-Up, ϕ rollout errors remain bounded, but M3 is consistently least predicted and Scale-Up increases phase-volume and interfacial-area errors more than field error.Geo-Shift tests transfer from generated geometries to µCT geometries; Scale-Up tests doubled spatial dimensions at fixed resolution, reusing weights without retraining.Source: §4.3 · p. 9, Figure 5 · p. 9

5 CONCLUSION

PoreML combines data generation, training, and evaluation tools to address limited time-resolved 3D data and unified benchmarks. Its reported fidelity measures cover fields, interface geometry, and topology, while explicit mass and momentum conservation tests remain future work.

5 CONCLUSION

  • PoreML’s 64-step rollouts and transfer tests assess field accuracy alongside interface geometry and topology, using phase volume, interfacial area, integrated mean curvature, and Euler characteristic.The authors describe the framework as a shared foundation for machine-learning research in porous media.Source: §5 · pp. 9–10
  • Explicit tests of mass and momentum conservation remain future work.The reported evaluation includes field and geometric/topological measures, but the conclusion does not report those conservation tests.Source: §5 · p. 10

AI USE STATEMENT

  • The authors report using generative AI for manuscript editing, LaTeX formatting, literature retrieval, software development, and scripting, but not to interpret results, formulate claims, develop proofs, or design methods or experiments.They state that they reviewed the AI-assisted work and take responsibility for the final content.Source: AI USE STATEMENT · p. 10

REPRODUCIBILITY STATEMENT

  • The reproducibility materials include the solver and tests, validation cases, campaign drivers, dataset and geometries, run configurations, benchmark configurations, frozen challenge splits, checkpoints, and a demo notebook.The authors state that these resources are public and documented in Appendix K.Source: REPRODUCIBILITY STATEMENT · p. 10

A.1 SUPPLEMENTARY METRICS

The supplementary metrics extend the main evaluation with measures of relative phase error, overlap, velocity, saturation, and curvature distributions. The curvature measures also connect interface geometry to capillary pressure.

A.1 SUPPLEMENTARY METRICS

  • Table 3 adds five metrics for the same campaign, study, and model rows as Table 2, addressing questions left open by the main table.Its blocks, averaging, and contributing runs follow Table 2.Source: §A.1 · p. 17
  • Relative phase error (ϕ, Rel. MAE) divides summed absolute phase error by the summed magnitude of the reference field over scored pore voxels, making campaigns and domain sizes comparable.Because |ϕ| is close to one away from the interface, the measure expresses phase MAE as a fraction of the field.Source: §A.1 · p. 17
  • Phase overlap (IoU) measures the shared non-wetting body volume divided by the volume occupied by either body, so it tests whether fluid is in the right place rather than merely present in the right amount.An IoU of one means voxel-for-voxel agreement.Source: §A.1 · p. 17
  • Saturation error is the absolute difference in the fraction of pore volume occupied by the scored phase; an error of 0.01 means the predicted phase volume is off by one percent of pore volume.It is the absolute counterpart of the relative M0 error in Table 2.Source: §A.1 · p. 17
  • The curvature-distribution metric is the Wasserstein-1 distance between predicted and reference mean-curvature histograms, normalized by the reference standard deviation; a score of one means an average shift of one reference standard deviation.Through Young–Laplace, curvature differences correspond to local capillary-pressure differences.Source: §A.1 · p. 17

B.1 CURVATURE AND CAPILLARY PRESSURE

  • At fixed interfacial tension, curvature error translates directly into inferred capillary-pressure error; the M2 pipeline extracts and smooths the interface surface, fits local curvatures, and excludes a neighborhood of the three-phase contact line.M2 integrates mean curvature over the remaining fluid–fluid interface; a complete spherical interface of radius r gives 4πr.Source: §B.1 · p. 17

B.2 ERROR MEASURES

The section defines metrics by applying error measures to descriptors of predicted and reference fields. It specifies field and morphology errors, with metric choices adapted to their interpretation and aggregation.

B.2 ERROR MEASURES

  • Each metric composes an error measure with a descriptor of the predicted and reference fields.Field errors are mean absolute errors of p and ϕ over pore voxels, in the stored frames’ normalized units.Source: §B.2 · pp. 17, 19
  • Supplementary metrics cover overlap, velocity error, saturation, and curvature distributions; lower is better except for IoU.Underfill descriptors score the wetting phase, while the other listed supplementary metrics score the non-wetting phase; values are means of per-run means.Source: Table 3 · p. 18
  • For M0–M2, relative descriptor error enables comparison across campaigns and domain sizes; M3 instead uses Euler-characteristic miscounts per 10^5 voxels.M3 uses miscounts because the signed Euler characteristic passes through zero, where relative error is undefined.Source: §B.2 · p. 19
  • MAE grows linearly with misplaced phase volume and preserves field units, unlike squared error that can penalize a physically benign one-voxel interface offset.Source: §B.2 · p. 19

C.1 COLOR-GRADIENT LATTICE BOLTZMANN METHOD

The color-gradient lattice Boltzmann method advances fluid motion and interface evolution on a common lattice, with wetting and interfacial forces configured for porous geometries. Its solver is validated against analytical benchmarks spanning capillary, viscous, wetting, and imbibition behavior.

C.1–C.2 COLOR-GRADIENT LATTICE BOLTZMANN METHOD

  • CG-LBM tracks two immiscible fluids through color-specific distribution functions, while recoloring enforces separation and the paired interfacial-force formulations recover Young–Laplace behavior.The method advances fluid motion and interface evolution on a common lattice; the solver pairs each wetting condition with its source publication’s surface-tension formulation.Source: §C.1 · pp. 19–20, §C.2 · p. 21

C.3 WETTING BOUNDARY CONDITION; D.1 OVERVIEW

  • Geometric wetting imposes the prescribed contact angle by reorienting the interface normal, and the JAX solver provides CPU, single-GPU, and multi-GPU execution.The Akai and Leclaire wetting conditions are paired with their corresponding surface-tension formulations; Akai–CSF is the default.Source: §C.3 · p. 21, §D.1 · p. 21

D.2–D.4 NUMERICS AND PARAMETERS

  • MRT collision suppresses staggered-mode instabilities that BGK develops at low viscosity and near walls, while the solver’s boundary conditions support velocity-driven and pressure-controlled protocols.The pressure boundaries enable zero-pressure-difference spontaneous imbibition and pressure-controlled drainage.Source: §D.2 · p. 22, §D.3 · p. 22, §D.4 · p. 22

E.1 LAPLACE LAW

  • Sphericity improves from 2.504 to 1.000, and measured pressure jumps are linear in inverse radius with R² ≈ 0.999 at each surface tension.The test spans σ = 0.01–0.05, the range used in porous cases.Source: §E.1 · p. 23, Figure 7 · p. 24

E.2 LAYERED POISEUILLE FLOW

  • The layered-flow profiles match analytic curves across five viscosity ratios, with maximum relative error of 0.95–2.58%, largest at M = 30.At M = 30, the center fluid reaches νr = 0.01.Source: §E.2 · p. 24, Figure 8 · p. 24

E.3–E.4 CONTACT-ANGLE VALIDATION

  • 60.2° and 124.4° are the measured angles for imposed curved-wall angles of 60° and 120°; flat-wall measurements follow a near-linear parity relation across 30–150°.On the curved grain, the fitted droplet radii are 22.0 and 21.9, respectively.Source: §E.4 · p. 25, §E.3 · p. 25, Figure 9 · p. 25

E.5 WASHBURN IMBIBITION

  • R² = 1.000 to three decimals at every contact angle, and the measured imbibition-rate coefficient is 1–6% from the analytic value across θ = 20–70°.The rectified penetration curves are linear in time and follow the two-fluid Washburn solution.Source: §E.5 · p. 26, Figure 11 · p. 27

E.6 DRAINAGE AND CAPILLARY PRESSURE

  • Both tube geometries show drainage plateaus that closely track analytic entry pressures, with the expected pressure ordering across contact angles.After the entry threshold, the non-wetting phase sweeps the uniform cross-section piston-like.Source: §E.6 · p. 27, Figure 12 · p. 28

E.7 DRAINAGE AND IMBIBITION COMPARED TO EXPERIMENT IN A MICROMODEL

The solver reproduces observed throat-filling sequences in micromodel drainage and spontaneous imbibition, and yields the expected displacement regimes when capillary number and viscosity ratio vary. The appendix describes the geometries and protocols used to generate the trajectories.

E.7 DRAINAGE AND IMBIBITION COMPARED TO EXPERIMENT IN A MICROMODEL

  • The simulation reproduces both experimental filling orders: drainage exits through the widest throat T4, while imbibition fills adjacent T2 before narrower T1.During drainage, side throats T1 and T3 remain predominantly wetting-filled; during imbibition, remaining non-wetting fluid retreats through T4.Source: §E.7 · p. 28, Figure 13 · p. 29, Figure 14 · p. 29

E.8 DISPLACEMENT REGIMES IN 3D PORE GEOMETRY

  • Varying only (Ca, M) produces stable displacement, viscous fingering, and capillary fingering with the expected distinct front morphologies.The cases use (10⁻³, 30), (10⁻³, 0.01), and (10⁻⁵, 30), respectively.Source: §E.8 · p. 30, Figure 15 · p. 30

F SIMULATION SETUP

  • The appendix specifies that trajectories are generated using a shared solver configuration, a geometry pipeline, and campaign-specific domains, boundaries, and termination conditions.Resulting run lengths are listed in Table 7.Source: F SIMULATION SETUP · p. 30

F.1 COMMON CONFIGURATION

  • All runs use D3Q19, MRT collision, CSF interfacial tension, recoloring, Akai wetting, and half-way bounce-back walls.Porous-media campaigns use non-shear relaxation rates of 0.8ω; underfill uses fixed rates.Source: §F.1 · pp. 30–31

F.2 GEOMETRIES

  • The geometry set combines scanned sandstone and carbon-paper crops with generated sphere, blob, polydisperse, and fiber structures; samples are screened for flow-axis percolation.Rock and fiber samples are morphologically opened to remove throats too narrow for the solver to resolve.Source: §F.2 · p. 31

F.3 PRIMARY DRAINAGE

  • Primary drainage uses a porous plate that admits wetting fluid but blocks non-wetting entry until its pressure threshold; runs stop at half that entry pressure or 0.75 pore volumes injected.Breakthrough does not end a run, so trajectories include later capillary-controlled filling.Source: §F.3 · p. 32

F.4 CAPILLARY TRAPPING

  • Capillary-trapping runs initialize non-wetting fluid in wide pore bodies and wetting fluid in corners and narrow throats, then equilibrate before flooding.Flood termination tracks movement of the non-wetting body; median residual saturation is 0.39.Source: §F.4 · p. 32

F.5 GDL WATER INTRUSION

  • GDL intrusion injects liquid water through a hydrophobic fiber layer and continues after early breakthrough to capture post-breakthrough redistribution.Runs end at 1.2 times the breakthrough step or after 0.5 pore volumes injected, whichever comes first.Source: §F.5 · p. 32

F.6 FLIP-CHIP UNDERFILL

The flip-chip underfill setup models capillary filling through a wetting encapsulant in a sealed-lateral gap, while parameter campaigns vary viscosity and contact angle across geometries. The selected viscosity ratios are qualitative rather than material-matched to real encapsulant–air flow.

F.6 FLIP-CHIP UNDERFILL

  • The wetting encapsulant enters through a 22-slab inlet strip, with equal-density pressure boundaries and capillary suction driving the front.Runs stop ten blocks after 99% of the ball array fills.Source: §F.6 · p. 32
  • M = 5–30 is far below the real encapsulant–air ratio of approximately 10^3–10^4 and represents a qualitative regime, not a material match.These ratios retain a more viscous invading fluid while staying within the solver’s stable range.Source: §F.6 · pp. 32–33

F.7 PARAMETER SAMPLING

  • Small-domain campaigns cross four viscosity ratios and four contact angles, while large-domain campaigns use θ ∈ {120°, 150°} and shard domains across four GPUs.Underfill assigns 12 (M, θ) pairs to 32 geometries; Table 7 reports run lengths by campaign and domain size, with median frames per run.Source: §F.7 · p. 33, Table 7 · p. 33

G INPUT GEOMETRY EXAMPLES

The geometry collection pairs generated structures with micro-CT-derived rocks and carbon-paper gas-diffusion layers at two domain sizes. The benchmark compares dense-grid and point-based models under a shared prediction and training protocol, with architecture-specific ways to represent spatial structure and long-range interactions.

G INPUT GEOMETRY EXAMPLES

  • The input collection includes scanned sandstone and carbon-paper GDL samples alongside generated rock-like families, whose members share morphology but vary in porosity and connectivity.The large-domain examples include 256^3 sandstone and generated media, and 256×256×128 GDLs at three PTFE loadings.Source: G INPUT GEOMETRY EXAMPLES · p. 33, Figure 16 · p. 34

H BASELINE MODELS

  • All baselines predict the next frame from the solid mask, run conditions, and saved flow fields; models are trained on comparable run passes and fine-tuned with pushforward training.Voxel and point models are scored on the same pore voxels; most parameter counts are near 10.7 million, while Transolver++ retains its 1.7-million published setting.Source: H BASELINE MODELS · p. 35, Table 8 · p. 35

H.1 UNET3D

  • UNet3D uses a dense-grid encoder–decoder that combines local features and coarse context through same-level skip connections.Its encoder halves resolution while doubling channel width at each level, and the decoder restores resolution.Source: §H.1 · p. 35

H.2 FNO3D

  • FNO3D applies learned Fourier-space kernels to spatial fields, with frequency-indexed weights that transfer unchanged across grid sizes.Its spectral layers retain the lowest modes, while pointwise maps and an output projection update and return the latent field.Source: §H.2 · pp. 35–36

H.3 P3D

  • P3D combines convolutional local structure with transformer interactions evaluated only within non-overlapping windows.Its convolutional stem compresses the volume before a U-shaped transformer backbone and decoder restore full resolution.Source: §H.3 · p. 36

H.4 TRANSOLVER++

  • Transolver++ assigns point tokens to a small set of learned eidetic states, attends among those states, and broadcasts updates back to points.Its state assignment uses learned per-point temperatures; evaluation uses noise-free assignments for deterministic predictions.Source: §H.4 · pp. 36–37

H.5 AB-UPT

  • AB-UPT separates geometry, surface, and volume branches, restricting full self-attention to anchor points while other points cross-attend to anchors.This confines quadratic cost to the anchors and makes computation linear in the number of points outside them.Source: §H.5 · p. 37

I FAILURE MODE ANALYSIS

Rollouts can preserve low field error while misrepresenting fluid topology, especially in GDL geometries. The analysis traces Euler-characteristic errors to specks and tunnels, which affect topology while displacing few voxels.

Mechanisms and topological accounting

  • Specks are small islands or bubbles produced by threshold-crossing phase-field oscillations, while tunnels are loops around fibers or pockets of the other fluid.In χ = β0 − β1 + β2, specks add one and tunnels subtract one.Source: I FAILURE MODE ANALYSIS · p. 37

Contribution to the error

  • Roughly one-third to two-thirds of GDL Euler discrepancy comes from specks, and every model overpredicts tunnels in 82–98% of validation windows.For P3D, Transolver++, and AB-UPT, specks reverse the Euler-error sign in most windows; neither mechanism displaces many voxels, so field error is nearly insensitive to them.Source: I FAILURE MODE ANALYSIS · pp. 37–38
  • The mechanisms help explain why low field error does not guarantee correct connectivity: voxel-thin bridges or filled wetting films can change χ with little field impact.A one-voxel opening removes many thin bridges for P3D, Transolver++, and AB-UPT, but not engulfed fibers in FNO3D and UNet3D.Source: I FAILURE MODE ANALYSIS · pp. 37–38

Case study

  • In one GDL case, P3D’s χ has the wrong sign, while FNO3D engulfs three fiber cross-sections and Transolver++ strands enclose twelve wetting-fluid pockets.The reference frame has ten pieces, sixteen tunnels, and χ = −6; the figures illustrate specks and tunnels in crops and full-frame counts.Source: I FAILURE MODE ANALYSIS · p. 38, Figure 17 · p. 38, Figure 18 · p. 39

J LIMITATION AND FUTURE WORK

PoreML evaluates geometric and topological consistency but does not score mass or momentum balance, leaving conservation during rollout as an open question. The authors also identify single-seed baseline training as a limitation and provide public resources, preservation practices, and rollout visualizations.

J LIMITATION AND FUTURE WORK

  • PoreML scores geometry, topology, and mean curvature, but leaves mass and momentum balance unscored as a direction for future study.The authors identify whether topology-preserving surrogates also conserve mass along rollouts as an open question.Source: J LIMITATION AND FUTURE WORK · p. 39
  • The benchmark uses published architectures and recipes trained once from a single seed, rather than contributing new model methodology.The authors expect tuning, seed variation, and long-rollout training strategies to raise scores, and point to connectivity-aware representations and losses as opportunities.Source: J LIMITATION AND FUTURE WORK · p. 39

K.1 RESOURCES AND LINKS

  • Public resources include the solver, 560 trajectories, input geometries, benchmark code, frozen splits, model weights, and a tutorial workflow.The data repository supports downloading selected runs without fetching the full 3.3 TB dataset.Source: §K.1 · pp. 39–40

K.2 MAINTENANCE AND LONG-TERM PRESERVATION

  • The release follows FAIR principles through public versioned repositories, standard HDF5 trajectories, metadata, and recorded solver settings and input-geometry hashes.The resources use MIT or Creative Commons Attribution 4.0 licensing, depending on the repository.Source: §K.2 · p. 40

L MODEL COMPARISON VISUALIZATION

  • The visualization appendix shows matched 64-step rollouts for references and five baselines at six rollout steps, pairing 3D phase fields with mid-plane slices and IoU scores.The paired views let readers compare visual drift and overlap on the same test run.Source: L MODEL COMPARISON VISUALIZATION · pp. 40–41

L.1 IN-DISTRIBUTION TEST RESULTS

Rollout quality varies by flow scenario, and transfer tests expose distinct errors across models. Geo-Shift retains qualitatively right displacement but widens the spread between models.

L.1 IN-DISTRIBUTION TEST RESULTS

  • Step-64 overlaps span 0.77–0.93 in drainage, 0.51–0.67 in trapping, and 0.45–0.71 in GDL intrusion as baselines diverge.AB-UPT reproduces drainage growth at IoU 0.93, while trapping models under-mobilize and GDL endpoint saturations range from 0.12 to 0.31.Source: §L.1 · p. 41, Figure 19 · p. 41, Figure 21 · p. 43
  • Mid-plane rollouts reveal spurious drainage patches, overly full trapped blobs, and premature or stalled GDL intrusion.In drainage, every model eventually opens a spurious patch; in GDL, several models merge patches before the reference while Transolver++ stops growing.Source: Figure 20 · p. 42, Figure 22 · p. 44, Figure 24 · p. 46

L.2 GEO-SHIFT

  • On µCT geometries, baselines bracket reference saturation in trapping and GDL; AB-UPT is closest in rock drainage and trapping, while P3D matches GDL volume.AB-UPT reaches IoU 0.90 in CastleGate drainage and 0.76 in Bentheimer trapping; P3D ends at the GDL reference saturation of 0.19.Source: §L.2 · p. 46, Figure 25 · p. 47, Figure 27 · p. 49
  • Geo-Shift slices show mistimed fronts, non-monotonic overlap, and disagreement over where GDL water first appears.UNet3D overlap dips to 0.54 at step 41 and recovers to 0.66 by step 64 in trapping.Source: Figure 26 · p. 48, Figure 28 · p. 50, Figure 30 · p. 52

L.3 SCALE-UP

  • At larger domains, rankings split by metric: FNO3D leads drainage IoU at 0.81, while trapping and GDL overlap do not align with volume accuracy.The scale-up tests keep resolution fixed while expanding the pore-network extent; in GDL, AB-UPT matches reference volume at 0.19 but has the lowest overlap, 0.56.Source: §L.3 · p. 52, Figure 31 · p. 53, Figure 33 · p. 55
  • Scale-up slices localize errors to channel intrusion, ganglion rims, and the GDL band edge; P3D keeps the band closest to reference width.Transolver++ intrudes into a wetting-filled channel in drainage, while trapping models differ by a few voxels around the eroding ganglion rim.Source: Figure 32 · p. 54, Figure 34 · p. 56, Figure 36 · p. 58
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