Completed long-run evidence

Nested-grid pressure case study

Static figures from a completed long-run. The panels show the model input context, including initial-state fields, plus the true pressure buildup, the prediction, and the signed error at selected timesteps for a held-out case.

Representative held-out case

Nested-grid pressure case study input fields for Representative held-out case
Held-out input fields. Continuous rock properties (e.g. permeability, porosity) are shown in the normalised space used by the model (z-score or min-max, depending on the family) — values are not in physical units. Binary fields (well masks, channel indicators) keep their native 0/1 range. See each panel title for which field is shown and at what depth.
Nested-grid pressure case study true predicted and error panels for Representative held-out case
True, predicted, and signed-error pressure buildup panels through prediction time for the same held-out case. Values are denormalised to physical units (see the unit in the panel title).
Swin UNETR excluded
MONAI divisor=32 requirement incompatible with D=5 vertical dimension

Leaderboard

5 results
   Pres (bar) 
#ModelLossEpochsrel-L²MREMAEParams
1UNet3DRelLp8004.12e-58.46e-60.00186420.8M
2UNet3DRelLp5004.25e-58.99e-60.00198220.8M
3SegResNetRelLp2005.42e-51.75e-50.00385018.8M
4UNet3DRelLp2005.55e-51.40e-50.00308320.8M
5FNO3DRelLp2000.00038.79e-50.02023213.2M

Metrics Over Time

Target variant: default.

DELTA_PRESSURE

Paper Metrics Comparison

Metrics from the shared paper-metric module (utils/paper_metrics.py) evaluated on the held-out test split. Loss column distinguishes the training recipe; lower is better.

#ModelLossEpochsdelta_ppressure_mre_t1pressure_mre_t2pressure_mre_pinit
1UNet3DRelLp8000.00020.02230.01670.0008
2UNet3DRelLp5000.00020.02380.01770.0008
3UNet3DRelLp2000.00040.04010.02830.0013
4SegResNetRelLp2000.00050.05000.03560.0016
5FNO3DRelLp2000.00230.23390.18130.0084

About This Benchmark

This benchmark extends the CO2 storage modeling work of Wen et al. (2023) to a 3D domain using nested local grid refinement (LGR). The simulation domain is a 100x100x5 grid representing a deep saline aquifer with CO2 injection, where the nested mesh provides higher resolution near the injection well and coarser cells in the far field.

The nested grid approach is commonly used in industrial reservoir simulation to balance accuracy near wells (where pressure and saturation gradients are steepest) with computational efficiency in the far field. This makes the dataset a practical test of whether surrogate reservoir simulation models can handle non-uniform spatial resolution — a common challenge in real-world subsurface modeling.

Each simulation produces 24 timesteps of delta pressure (pressure change from the initial hydrostatic state). The target variable is specifically the pressure perturbation rather than absolute pressure, which is the physically meaningful quantity for assessing storage integrity and induced seismicity risk.

Input features include permeability, porosity, and well parameters that define the injection scenario. The 3D nature of the domain with only 5 layers in the vertical direction presents a challenge for architectures that require input dimensions divisible by large powers of 2.

Note: Swin UNETR is excluded from this benchmark because MONAI's implementation requires all spatial dimensions to be divisible by 32 (due to the shifted window attention mechanism), which is incompatible with the depth dimension of 5.

Input features

PermeabilityPorosityWell ParametersGrid CoordinatesInitial Conditions

Paper metrics explained

delta_p
||dp_pred - dp_true||_2 / ||dp_true||_2
Relative L2 error on delta pressure, same formulation as Wen et al. 2022. Averaged over test samples.

Training Configuration

Configuration for the best-performing model (UNet3D).

Training
Epochs800
Learning Rate0.001
Weight Decay0.01
Max Grad Norm1
Batch Size16
Loss FunctionRelLpLossOptimized (p=2, reduction=mean)
SchedulerCosineAnnealingLR (step_size=20, gamma=0.95, T_max=800, eta_min=0.0001)
Model Architecture
in channels7
out channels24
base channels32
kernel size3
depth3
num time steps1
squashed outputfalse
flatten outputtrue