Property Type

geostat

Fault Config

Variable Throw

Well Control

Rate Control

Grid Dimensions

64 x 64 x 32

Train Samples

3200

Val Samples

400

Test Samples

400

Models Evaluated

Dataset protocol

Current data provenance for this dataset.

These details come from the Arena protocol metadata and should be updated there when the simulation or preprocessing pipeline changes.

Simulation target

Simulator: OPM Flow

Physics: Two-phase oil-water flow

Reported outputs: Pressure (bar), Water saturation (fraction)

Split and geometry

Split rule: Sequential split by unique grid/property pair; all cases sharing the same grid and property sample stay in the same split.

Fault multipliers: 2 realizations per structural model

Variable-throw cases are mapped from simulator CPG grids to a conformal 32-layer ML grid; static website flow figures show raw simulator targets on the CPG grid.

Results

Loss

9 results

				Sat (frac)			Pres (bar)
#	Model	Loss	Epochs	rel-L²▲	MRE	MAE	rel-L²	MRE	MAE	Params
1	UNet3D	MSE	200	0.1894	0.3519	0.054428	0.0461	0.0359	8.486502	35.9M
2	SegResNet	AbsLp(p=2)	200	0.1963	0.3673	0.053504	0.0473	0.0362	8.372307	29.4M
3	SegResNet	MSE	200	0.2009	0.3689	0.053885	0.0471	0.0361	8.347742	29.4M
4	UNet3D	AbsLp(p=2)	200	0.2010	0.3629	0.055984	0.0467	0.0364	8.458871	35.9M
5	UNet3D	MSE+grad(w=1)	200	0.2109	0.3744	0.054545	0.0481	0.0372	8.508275	35.9M
6	SwinUNETR	AbsLp(p=2)	200	0.2664	0.5028	0.071910	0.0672	0.0519	11.766338	36.2M
7	SwinUNETR	MSE	200	0.2802	0.5160	0.074990	0.0684	0.0527	12.038026	36.2M
8	FNO3D	AbsLp(p=2)	200	0.3744	0.7287	0.098138	0.1098	0.0830	20.213245	35.7M
9	FNO3D	MSE	200	0.3791	0.7203	0.084728	0.1190	0.0903	21.365623	35.7M

Metrics Over Time

Water Saturation (SWAT)

Pressure

Validation vs Test

Each point is one run (model × loss variant). Points on the y=x diagonal generalize from val to test consistently; points far above it overfit val. Six panels per field cover rel-L², MAE, and the four MRE / MAPE variants from the published literature so the choice of denominator is exposed rather than hidden.

geostat_vt_rate pressure val vs test cross-plots — **Pressure**: rel-L², MRE_t1, MRE_t2, MRE_Pinit, MRE_abs, MAE.

geostat_vt_rate SWAT val vs test cross-plots — **SWAT**: rel-L², MAPE, MRPE, R², MAE, MRE.

Training Configuration

Configuration for the best-performing model (UNet3D).

Training

Epochs200

Learning Rate0.0001

Weight Decay0.001

Max Grad Norm1

Batch Size16

Loss FunctionMSEGradientLoss (gradient_weight=0, dx=50, dy=50, dz=3.6)

SchedulerCosineAnnealingLR (T_max=200, eta_min=0.00001)

Input Features

POROPERMXSWAT_0PRESSURE_0MULTXMULTYDEPTHZ_MLGRID

Output Fields

SWATPRESSURE

Model Architecture

in channels8

out channels40

base channels42

kernel size3

depth3

num time steps1

squashed outputfalse

flatten outputtrue