Property Type

channels

Fault Config

Variable Throw

Well Control

Bottom-Hole Pressure 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	0.2384	0.4567	0.065744	0.0344	0.0266	6.697660	35.9M
2	UNet3D	MSE+grad(w=1)	200	0.2402	0.4734	0.067157	0.0344	0.0269	6.753836	35.9M
3	UNet3D	AbsLp(p=2)	200	0.2506	0.5251	0.069934	0.0354	0.0276	6.904829	35.9M
4	SegResNet	MSE	200	0.2595	0.4797	0.067640	0.0367	0.0280	7.051733	29.4M
5	SegResNet	AbsLp(p=2)	200	0.2614	0.5246	0.070700	0.0373	0.0282	7.175670	29.4M
6	SwinUNETR	AbsLp(p=2)	200	0.3575	0.7163	0.097087	0.0586	0.0457	11.429111	36.2M
7	SwinUNETR	MSE	200	0.3653	0.7118	0.090665	0.0594	0.0462	11.591043	36.2M
8	FNO3D	AbsLp(p=2)	200	0.4708	0.9126	0.105809	0.1008	0.0799	20.026644	35.7M
9	FNO3D	MSE	200	0.4785	0.9393	0.102066	0.1039	0.0824	20.654514	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.

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

channels_vt_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 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