cs.LGMar 12, 2026
SaveLearning Pore-scale Multiphase Flow from 4D Velocimetry
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 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 (), 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 , Right: Experiment . 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. . 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 ( ) | Traj. |
| Exp. - Train, One-Step (30 Fr.) | 0.174 | 0.220 | 0.990 | 0.707 | 0.9999 |
| Exp. - Test, One-Step (30 Fr.) | 0.187 | 0.348 | 0.989 | 0.738 | 0.9999 |
| Exp. - Train, Rollout (30 Fr.) | 0.198 | 0.221 | 0.985 | 0.919 | 0.9999 |
| Exp. - Test, Rollout (30 Fr.) | 0.351 | 0.613 | 0.986 | 1.000 | 0.9999 |
| Exp. - Test, One-Step (30 Fr.) | 0.683 | 1.221 | 0.991 | 0.098 | 0.9999 |
| Exp. - 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. compared to Exp. is attributed to its lower mean velocity magnitude. The trajectory 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 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 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.
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 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. (Exp. and Exp. ) are incorporated into training. The data are split into two folds, with performance evaluated on the corresponding held-out test sets. Reported metrics include computed from tracer trajectory agreement and comparisons of velocity-component distributions between predictions and ground truth for both experiments.