Property Type

channels

Fault Config

Zero Throw

Well Control

Bottom-Hole Pressure Control

Grid Dimensions

64 x 64 x 8

Train Samples

1600

Val Samples

200

Test Samples

200

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

8 results

				Sat (frac)			Pres (bar)
#	Model	Loss	Epochs	rel-L²▲	MRE	MAE	rel-L²	MRE	MAE	Params
1	UNet3D	MSE	200	0.2230	0.4164	0.054551	0.0319	0.0249	6.217045	20.8M
2	UNet3D	AbsLp(p=2)	200	0.2232	0.4314	0.055996	0.0323	0.0259	6.439610	20.8M
3	SegResNet	AbsLp(p=2)	200	0.2519	0.4642	0.062831	0.0372	0.0295	7.337576	18.8M
4	SegResNet	MSE	200	0.2599	0.4837	0.060852	0.0391	0.0304	7.615905	18.8M
5	SwinUNETR	AbsLp(p=2)	200	0.3605	0.6761	0.084165	0.0574	0.0446	11.190115	16.3M
6	SwinUNETR	MSE	200	0.3607	0.6707	0.079274	0.0581	0.0456	11.334703	16.3M
7	FNO3D	AbsLp(p=2)	200	0.4080	0.7672	0.089509	0.0860	0.0697	17.261770	20.1M
8	FNO3D	MSE	200	0.4119	0.8244	0.090742	0.0856	0.0688	17.075972	20.1M

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.

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

channels_zt_bhp 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 Size32

Loss FunctionMSEGradientLoss (gradient_weight=0, dx=50, dy=50, dz=8)

SchedulerCosineAnnealingLR (T_max=200, eta_min=0.00001)

Input Features

POROPERMXSWAT_0PRESSURE_0MULTXMULTYDEPTH

Output Fields

SWATPRESSURE

Model Architecture

in channels7

out channels40

base channels32

kernel size3

depth3

num time steps1

squashed outputfalse

flatten outputtrue