Name: CO2 Radial
Creator: Wen et al.

Completed long-run evidence

CO2 radial saturation case study

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

Representative held-out case

Leaderboard

Loss

34 results

					Pres (bar)			Sat (frac)
#	Target	Model	Loss	Epochs	rel-L²▲	MRE	MAE	rel-L²	MRE	MAE	Params
1	pressure	UNet3D	UFNODerivLoss	500	0.0030	0.0008	0.181463	-	-	-	20.8M
2	pressure	UNet2D	RelLp	500	0.0031	0.0008	0.193750	-	-	-	16.3M
3	pressure	SegResNet2D	RelLp	500	0.0032	0.0009	0.200384	-	-	-	14.2M
4	pressure	UNet2D	RelLp	500	0.0032	0.0010	0.217995	-	-	-	29.0M
5	combined	UNet2D	RelLp	500	0.0034	0.0010	0.232792	0.0708	5.9654	0.001713	16.3M
6	pressure	UNet2D	RelLp	500	0.0037	0.0010	0.235549	-	-	-	29.2M
7	pressure	UNet2D	UFNODerivLoss	500	0.0037	0.0011	0.248648	-	-	-	29.0M
8	pressure	UNet2D	UFNODerivLoss	500	0.0039	0.0011	0.250622	-	-	-	16.3M
9	pressure	UNet2D	UFNODerivLoss	500	0.0039	0.0011	0.246458	-	-	-	16.3M
10	pressure	UNet3D	RelLp	500	0.0040	0.0013	0.286640	-	-	-	20.8M
11	pressure	UNet3D	RelLp	500	0.0042	0.0014	0.291506	-	-	-	20.8M
12	combined	SegResNet2D	RelLp	500	0.0042	0.0012	0.271272	0.0717	7.0054	0.001956	14.2M
13	pressure	UNet3D	UFNODerivLoss	500	0.0045	0.0014	0.296649	-	-	-	20.8M
14	pressure	SwinUNETR2D	RelLp	500	0.0050	0.0013	0.307502	-	-	-	15.2M
15	pressure	FNO2D	UFNODerivLoss	500	0.0057	0.0015	0.350251	-	-	-	20.2M
16	combined	SwinUNETR2D	RelLp	500	0.0059	0.0017	0.397529	0.0951	8.5406	0.002900	15.2M
17	pressure	FNO2D	RelLp	500	0.0064	0.0015	0.376695	-	-	-	9.0M
18	combined	FNO2D	RelLp	500	0.0068	0.0019	0.433446	0.1152	9.9045	0.003185	9.0M
19	saturation	FNO2D	UFNODerivLoss	500	-	-	-	0.1197	9.9107	0.003067	20.2M
20	saturation	FNO2D	RelLp	500	-	-	-	0.1067	8.7535	0.002723	9.0M
21	saturation	SegResNet2D	RelLp	500	-	-	-	0.0711	6.7189	0.001596	14.2M
22	saturation	SwinUNETR2D	RelLp	500	-	-	-	0.0880	7.7030	0.002304	15.2M
23	saturation	UNet2D	RelLp	500	-	-	-	0.0653	6.6551	0.001726	16.3M
24	saturation	UNet2D	RelLp	500	-	-	-	0.0811	8.2827	0.002471	29.2M
25	saturation	UNet2D	RelLp	500	-	-	-	0.0811	8.2827	0.002471	29.2M
26	saturation	UNet2D	UFNODerivLoss	500	-	-	-	0.0829	6.2847	0.002182	16.3M
27	saturation	UNet2D	UFNODerivLoss	500	-	-	-	0.0804	6.4845	0.002141	16.3M
28	saturation	UNet2D	RelLp	500	-	-	-	0.0703	5.2798	0.001675	29.0M
29	saturation	UNet2D	RelLp	500	-	-	-	0.0703	5.2798	0.001675	29.0M
30	saturation	UNet2D	UFNODerivLoss	500	-	-	-	0.0705	6.5478	0.001767	29.0M
31	saturation	UNet3D	RelLp	500	-	-	-	0.0657	6.1184	0.001715	20.8M
32	saturation	UNet3D	RelLp	500	-	-	-	0.1005	5.6692	0.001667	20.8M
33	saturation	UNet3D	UFNODerivLoss	500	-	-	-	0.0954	6.2312	0.002083	20.8M
34	saturation	UNet3D	UFNODerivLoss	500	-	-	-	0.0634	4.0132	0.001151	20.8M

Metrics Over Time

Combined target variant (multiple fields predicted jointly).

Pressure

SATURATION

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.

Targetpressure

#	Model	Loss	pressure_mre_t1▲	pressure_mre_t2
1	UNet2D	RelLp	0.3270	0.2602
2	SegResNet2D	RelLp	0.3399	0.2687
3	SwinUNETR2D	RelLp	0.5143	0.4093
4	UNet3D	UFNODerivLoss	0.5180	0.4067
5	FNO2D	RelLp	0.5939	0.4715
6	UNet2D	RelLp	0.8090	0.6334
7	UNet2D	UFNODerivLoss	0.8522	0.6794
8	UNet2D	UFNODerivLoss	0.9713	0.7676
9	UNet2D	UFNODerivLoss	1.0055	0.7941
10	UNet3D	RelLp	1.0849	0.8559
11	UNet2D	RelLp	1.1047	0.8678
12	UNet3D	UFNODerivLoss	1.8786	1.4621
13	FNO2D	UFNODerivLoss	2.1971	1.7269
14	UNet3D	RelLp	2.2414	1.8172

Targetsaturation

#	Model	Loss	saturation_mape▲	sat_R2_plume
1	UNet3D	UFNODerivLoss	1.3109	0.9922
2	UNet3D	RelLp	1.5488	0.9927
3	UNet2D	RelLp	1.5831	0.9923
4	UNet2D	RelLp	1.5831	0.9923
5	UNet2D	UFNODerivLoss	1.6092	0.9919
6	UNet2D	RelLp	1.6425	0.9932
7	SegResNet2D	RelLp	1.8033	0.9919
8	UNet2D	UFNODerivLoss	1.8531	0.9891
9	UNet2D	UFNODerivLoss	1.8685	0.9894
10	UNet2D	RelLp	2.0092	0.9905
11	UNet2D	RelLp	2.0092	0.9905
12	UNet3D	UFNODerivLoss	2.0292	0.9851
13	UNet3D	RelLp	2.1614	0.9821
14	SwinUNETR2D	RelLp	2.3432	0.9886
15	FNO2D	RelLp	2.9999	0.9835
16	FNO2D	UFNODerivLoss	3.1127	0.9772

Targetcombined

#	Model	Loss	pressure_mre_t1▲	pressure_mre_t2	saturation_mape	sat_R2_plume
1	UNet2D	RelLp	1.0704	0.8395	1.7155	0.9922
2	SegResNet2D	RelLp	1.1156	0.8650	1.9105	0.9921
3	SwinUNETR2D	RelLp	1.6413	1.2700	2.6207	0.9872
4	FNO2D	RelLp	1.7409	1.3629	3.3179	0.9814

About This Benchmark

This benchmark is based on the U-FNO dataset introduced by Wen et al. (2022) for accelerating multiphase CO2-water flow simulations relevant to carbon capture and storage (CCS). The domain is a 2D radial-symmetric cross-section (96 radial cells x 200 vertical cells) representing a deep saline aquifer with CO2 injection.

The simulations model supercritical CO2 injection into a heterogeneous aquifer, capturing the interplay between viscous, gravitational, and capillary forces that govern CO2 plume migration and pressure buildup. The radial symmetry reduces the 3D problem to a computationally efficient 2D representation while preserving the essential physics of single-well injection.

Each simulation produces 24 prediction timesteps capturing the evolution of pressure buildup and gas (CO2) saturation. The input features include the permeability and porosity fields of the aquifer rock, along with injection parameters that control the CO2 injection rate and duration.

This dataset is particularly relevant for risk assessment in CCS projects, where rapid evaluation of thousands of geological scenarios is needed to quantify uncertainty in plume extent and pressure response.

Input features

PermeabilityPorosityInjection Parameters

Paper metrics explained

pres_MRE

mean(|p_pred - p_true| / |p_true|)

Mean Relative Error for pressure buildup, averaged over all cells and test samples.

sat_MPE

mean(|sg_pred - sg_true|)

Mean Pointwise Error for gas saturation. Uses absolute (not relative) error because saturation values near zero make relative error ill-defined.

R2_plume

1 - SS_res / SS_tot (on sg > 0 cells)

R-squared coefficient of determination computed only on cells where the CO2 plume is present (sg > 0), measuring how well the model captures plume geometry.

Training Configuration

Configuration for the best-performing model (UNet3D).

Training

Epochs500

Learning Rate0.0001

Weight Decay0.01

Max Grad Norm1

Batch Size2

Loss FunctionUFNODerivLoss (p=2, reduction=mean, beta=0.5)

SchedulerCosineAnnealingLR (step_size=50, gamma=0.95, T_max=500, eta_min=0.00001)

Model Architecture

in channels12

out channels1

base channels32

kernel size3

depth3

num time steps1

squashed outputfalse

flatten outputtrue