Learning Pore-scale Multiphase Flow from 4D Velocimetry

Chunyang Wang; Linqi Zhu; Yuxuan Gu; Robert van der Merwe; Xin Ju; Catherine Spurin; Samuel Krevor; Rex Ying

cs.LGMar 12, 2026

Learning Pore-scale Multiphase Flow from 4D Velocimetry

Authors: Chunyang Wang, Linqi Zhu, Yuxuan Gu, Robert van der Merwe, Xin Ju, Catherine Spurin, Samuel Krevor, Rex Ying,

Organizations: Department of Earth Science and Engineering, Imperial College London. · Department of Geology, Ghent University. · Department of Energy Science and Engineering, Stanford University. · Department of Computer Science, Yale University. ·

Abstract

Multiphase flow in porous media underpins subsurface energy and environmental technologies, including geological CO $_2$ storage and underground hydrogen storage, yet pore-scale dynamics in realistic three-dimensional materials remain difficult to characterize and predict. Here we introduce a multimodal learning framework that infers multiphase pore-scale flow directly from time-resolved four-dimensional (4D) micro-velocimetry measurements. The model couples a graph network simulator for Lagrangian tracer-particle motion with a 3D U-Net for voxelized interface evolution. The imaged pore geometry serves as a boundary constraint to the flow velocity and the multiphase interface predictions, which are coupled and updated iteratively at each time step. Trained autoregressively on experimental sequences in capillary-dominated conditions ( $Ca\approx10^{-6}$ ), the learned surrogate captures transient, nonlocal flow perturbations and abrupt interface rearrangements (Haines jumps) over rollouts spanning seconds of physical time, while reducing hour-to-day--scale direct numerical simulations to seconds of inference. By providing rapid, experimentally informed predictions, the framework opens a route to ''digital experiments'' to replicate pore-scale physics observed in multiphase flow experiments, offering an efficient tool for exploring injection conditions and pore-geometry effects relevant to subsurface carbon and hydrogen storage.

Figures & tables

Figure 1: Overview of the Pore Scale GNS framework for learning multiphase fluid dynamics in porous media from 4D velocimetry experimental data. (A) At each time step, the model takes as input the particle velocity field and the multiphase interface, both obtained from high-resolution 4D micro-velocimetry experiments, alongside the static dry image of the pore geometry. These inputs are processed through a multimodal architecture combining a graph neural network and a 3D U-Net. The model is trained to autoregressively predict future states, enabling long-horizon rollout of pore-scale multiphase flow. (B) Representative velocity field predictions over time compared to ground truth, showing the accurate reconstruction of the spatiotemporal flow structures. (C) Corresponding predicted versus actual multiphase interface evolution, demonstrating the model’s ability to recover dynamic interfacial morphology.

Figure 2: Multimodal prediction of particle-scale flow and fluid interface dynamics. (A) Comparison of predicted and ground truth particle trajectories for two different meniscus configurations. Left: Experiment $\alpha$ , Right: Experiment $\beta$ . $R^{2}$ measured on velocity tracer position prediction for 30 time steps. (B) Temporal evolution of velocity error across 30 frames (top), along with frame-wise comparison of predicted and ground truth flow fields in a representative slice for Exp. $\alpha$ . Error maps highlight that most discrepancies arise near high-gradient regions. (C) Comparison between naïve architecture inference (top path) and multimodal prediction (bottom path) from the same initial interface. The naïve method, relying solely on surface history, introduces nonphysical artifacts (upper center). In contrast, our approach incorporates particle velocity, a complementary modality, to guide interface prediction, effectively avoiding artifacts and producing a physically-consistent geometric surface. Regional Dice Score is reported for the Haines jump area.

Experiment Setup	Vol. Err. (%)	Surf. Err. (%)	Dice	Vel. MAE ( $\text{\penalty\ }\mathrm{\SIUnitSymbolMicro m}\text{/}\mathrm{s}$ )	Traj. $R^{2}$
Exp. $\alpha$ - Train, One-Step (30 Fr.)	0.174	0.220	0.990	0.707	0.9999
Exp. $\alpha$ - Test, One-Step (30 Fr.)	0.187	0.348	0.989	0.738	0.9999
Exp. $\alpha$ - Train, Rollout (30 Fr.)	0.198	0.221	0.985	0.919	0.9999
Exp. $\alpha$ - Test, Rollout (30 Fr.)	0.351	0.613	0.986	1.000	0.9999
Exp. $\beta$ - Test, One-Step (30 Fr.)	0.683	1.221	0.991	0.098	0.9999
Exp. $\beta$ - Test, Rollout (30 Fr.)	0.735	1.324	0.990	0.119	0.9999

Table 1: Evaluation metrics for fluid topology and velocity prediction across different datasets and rollout settings. Volume and surface area errors are reported as relative percentage errors, while the Dice score quantifies voxel-wise agreement. The velocity field is interpolated based on the predicted tracer velocity. The lower MAE in Exp.

\beta

compared to Exp.

\alpha

is attributed to its lower mean velocity magnitude. The trajectory

R^{2}

measures the coefficient of determination between predicted and ground truth particle positions. All metrics for rollout test sets are averaged over time.

Figure 3: Zero-shot generalization to a new rock type (Ketton). (A) Predicted versus ground-truth particle trajectories and velocity visualization (including a zoomed-in view of the pore space) for an independent drainage experiment in Ketton limestone, evaluated strictly zero-shot (no fine-tuning). The reported $R^{2}$ is computed from agreement in particle positions along trajectories. (B) Velocity distribution comparing model predictions with ground truth for Ketton, used to quantify performance under the cross-rock shift. (C) Domain-shift characterization: distributions of key pore-scale descriptors for the training medium (Sintered glass) versus the new medium (Ketton), including pore radius, throat radius, and velocity-magnitude statistics.

Figure 4: Multimodal information exchange between geometry and velocity. (A) Information from the predicted interface $\mathcal{S}$ is passed from the U-Net surface model to the GNS velocity model by extracting local voxel patches centered on particles. The patch size is selected based on experimental velocity correlation data, shown in the plot. The GNS model uses a 10-hop graph structure, with each hop attending to 32 neighbors, resulting in an effective receptive field of 320 voxels, which corresponds to the spatial extent over which velocity correlations remain significant. (B) Velocity data from particles are transferred to the U-Net by projecting the voxelized velocity onto a 3D grid. Pooling-based downsampling (downsample factor 4 here for demonstration) is applied to reduce memory cost while enabling efficient integration of flow information. Naïve downsampling via slicing leads to severe information loss due to the sparsity and three-dimensional nature of the data (retaining only 1.56% of particles). In contrast, pooling-based downsampling preserves local velocity extremes and retains 99.97% of particles.

\hat{\mathbf{v}}_{i}^{(t)}\leftarrow\mathrm{GNS}\left(\{\mathbf{p}_{i}^{(t)}\},\{\dot{\mathbf{p}}_{i}^{(t)}\},\{\mathcal{S}^{(t)}\},\mathcal{G}\right)

Algorithm 1 Multimodal Rollout of Velocity and Interface Evolution

Figure 5: Ablation Experiments. (A) The sintered glass matrix (gray) under the green plane is made transparent to expose the non-wetting phase (blue). Velocity tracer trajectories are color-mapped by their instantaneous velocity magnitude. When interface and pore structure inputs are removed from the GNS, particles exhibit unphysical behavior, including escaping beyond the fluid interface in the Haines jump region. (B) Geometry representation benchmarks: triplane and VecSet degrade interface detail, while voxel-based U-Net reconstructions preserve ground truth geometry.

Figure S1: Failure modes of the learned rollout under long-horizon prediction and cross-rock generalization. (A) Extended rollout failure. Predicted interface evolution and particle velocities remain consistent with the ground truth at early timesteps (frames 15–45), but visible deviations emerge by frame 70 as errors accumulate autoregressively. This degradation is reflected in the increasing RMSE and decreasing $R^{2}$ over time, particularly toward the end of the rollout. (B) Generalization-induced failure under cross-rock shift. Zero-shot inference on a Ketton limestone sample using a model trained exclusively on sintered-glass data. While the overall velocity field and particle statistics remain well correlated with the ground truth, localized regions exhibit degraded trajectory tracking and velocity alignment, highlighting limitations under pronounced pore-structure domain shift.

Figure S2: Supplementary training data for improved in-domain generalization. Two additional drainage experiments from the sintered-glass sample used in Exp. $\alpha$ (Exp. $\alpha^{\prime}$ and Exp. $\alpha^{\prime\prime}$ ) are incorporated into training. The data are split into two folds, with performance evaluated on the corresponding held-out test sets. Reported metrics include $R^{2}$ computed from tracer trajectory agreement and comparisons of velocity-component distributions between predictions and ground truth for both experiments.

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Oct 7, 2026

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

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.

Chunyang Wang, Mingrui Zhang, Yuyan Zhang +5

Imperial College London · Stanford University · EarthFlow AI, Inc. +1

Porous Media Flow Neural Surrogate Modeling Computational Fluid Dynamics

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Aug 23, 2026

A Query-Time Framework for Transient 2D Pore-Scale Flow Prediction and Generative Design

Pore-scale flow governs transport and permeability behaviour in porous media engineering applications, yet repeated lattice Boltzmann method (LBM) simulation across many geometries and design queries remains costly for repeated deployment. This study formulates transient pore-scale flow prediction as a geometry-conditioned query-time operator and introduces QSGS-Transient-7606, a benchmark of 7,606 two-dimensional porous structures each paired with 30 logarithmically sampled LBM states. The proposed continuous-time pore-scale flow surrogate model (CT-PoreFlow) integrates topology-aware geometry encoding, compressed spectral mixing, and log-time conditioning with a late-time flux-calibration objective. On unseen test geometries, CT-PoreFlow achieves a velocity relative L2 of 0.2248 and a terminal permeability error of 12.81%. Frozen morphology and computed tomography image audits confirm reasonable cross-geometry robustness without fine-tuning. The surrogate is then embedded in an inverse design workflow, screening 9,216 generative adversarial network and diffusion candidates across 18 property targets prior to LBM verification. Guided GAN sampling attains 98.11% through-connectivity and 72.28% conditional design success, exceeding diffusion-based generation. The framework unifies transient flow prediction, transport-aware screening, and LBM-verified inverse design for porous media.

Yiming Wang, Jiale Zhu, Zhichen Ye +4

School of Civil Engineering, The University of Sydney, Sydney, 2006, NSW, Australia · MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou, 310058, China · College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, 310058, China +2

Porous Media Flow Neural Surrogate Modeling Computational Fluid Dynamics Inverse Design Benchmark Construction

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May 18, 2026

Physics-informed convolutional neural networks for fluid flow through porous media

Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly in intricate porous domains. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method uses a convolutional encoder-decoder architecture with skip connections to preserve spatial detail while extracting multi-scale features. Physical consistency is encouraged through a custom loss function combining velocity reconstruction with incompressibility, no-flow conditions inside solids, periodicity constraints, and agreement with the global tortuosity index. We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy. Several CNN backbones are evaluated to identify architectures providing accurate and robust predictions. The generalization ability of the trained model is tested on samples outside the training distribution, including changes in obstacle geometry, boundary conditions, porosity, and realistic porous structures. Finally, we demonstrate a practical use of the predicted velocity fields as initial conditions for Lattice-Boltzmann simulations. This warm-start strategy accelerates solver convergence, reducing the number of iterations in over 90% of tested cases.

Rafał Topolnicki, Paweł Dłotko, Maciej Matyka

Dioscuri Center in Topological Data Analysis, Institute of Mathematics, Polish Academy of Sciences, ul. ´Sniadeckich 8, 00-656, Warsaw, Poland · Institute of Experimental Physics, Faculty of Physics and Astronomy, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland · Institute of Theoretical Physics, Faculty of Physics and Astronomy, University of Wrocław, pl. M. Borna 9, Wrocław, 50-204, Poland +1

PDE Surrogate Modeling Physics-Informed ML Convolutional Neural Networks Computational Fluid Dynamics Porous Media Flow

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