CoGameReg: Cooperative-Game-Based Collaborative Semi-Supervised Regression for Seismic Reservoir Property Prediction

Zhiyu Guo; Jiwei Jia; Lei Li

cs.LGOct 9, 2026

CoGameReg: Cooperative-Game-Based Collaborative Semi-Supervised Regression for Seismic Reservoir Property Prediction

Authors: Zhiyu Guo, Jiwei Jia, Lei Li

Organizations: School of Mathematics, Jilin University, Changchun, China · AI for Science and Engineering Center, Shenzhen Loop Area Institute, Shenzhen, China · BGP Inc., China National Petroleum Corporation, Zhuozhou, China · National Engineering Research Center of Oil & Gas Exploration Computer Software, Zhuozhou, China

Abstract

Accurate estimation of reservoir properties from seismic data remains challenging when well-log labels are sparse but three-dimensional seismic observations are abundant. We present CoGameReg, a cooperative-game-based semi-supervised regression framework that uses contribution-weighted predictions of heterogeneous regressors to construct shared pseudo-labels. This design makes each regressor's influence explicit in the learning targets generated for unlabeled seismic samples under sparse well control. The Tri-Game Shapley mechanism combines a rank-MSE performance game with a pairwise consistency game to estimate nonnegative regressor weights from labeled training data. These weights remain fixed during collaborative training and are reused for final prediction fusion. Candidate pseudo-labels are screened using a common local k-nearest-neighbor error-reduction criterion before retraining. We evaluate CoGameReg on 10 public regression datasets, a synthetic three-dimensional P-wave velocity prediction task, and a field water-saturation application. The benchmark advantage is most pronounced at the 2.5% labeled-data ratio and decreases as supervision increases. CoGameReg obtains the best blind-well metrics in the synthetic experiment. In the field application, predictions clipped to 0-100% yield a pooled coefficient of determination of 0.5942, a root mean square error of 5.7441 percentage points, and a Pearson correlation of 0.8265 across three blind wells. CoGameReg has the highest Pearson correlation among the four field methods. The results support the use of CoGameReg to integrate sparse well labels with dense seismic attributes, with performance varying across metrics and well locations.

Figures & tables

Figure 1: Overall workflow of the proposed CoGameReg framework.

Name	Instances	Features	Target	Original source
Abalone	4,176	8	Rings	UCI
Bank32nh	8,192	32	rej	Delve
Elevators	9,517	6	Se	Delve
Folds5x2_pp	9,568	4	PE	UCI
Kin8nm	8,192	8	y	Delve
Parkinsons	5,875	21	PPE	UCI

Table 1: Summary of the 10 public benchmark regression datasets.

Ratio	Dataset	XGBoost	KNN	TabM	Avg. Ensemble	Self-KNN	COREG	Mean Teacher	SSDKL	UCVME	CoGameReg
2.5%	Abalone	$0.1014_{\pm 0.0058}$	$0.0979_{\pm 0.0021}$	$0.0996_{\pm 0.0170}$	$0.0927_{\pm 0.0062}$	$0.0975_{\pm 0.0022}$	$0.0971_{\pm 0.0030}$	$\mathbf{0.0904_{\pm 0.0037}}$	$0.1029_{\pm 0.0122}$	$0.0978_{\pm 0.0068}$	$\mathbf{0.0904_{\pm 0.0042}}$
	Bank32nh	$0.1415_{\pm 0.0075}$	$0.1485_{\pm 0.0042}$	$\mathbf{0.1316_{\pm 0.0204}}$	$0.1478_{\pm 0.0146}$	$0.1502_{\pm 0.0046}$	$0.1478_{\pm 0.0035}$	$0.1387_{\pm 0.0055}$	$0.1451_{\pm 0.0065}$	$0.1586_{\pm 0.0257}$	$0.1342_{\pm 0.0071}$
	Elevators	$0.0670_{\pm 0.0040}$	$0.0663_{\pm 0.0027}$	$0.0841_{\pm 0.0247}$	$0.0635_{\pm 0.0033}$	$0.0646_{\pm 0.0024}$	$0.0640_{\pm 0.0022}$	$0.0630_{\pm 0.0027}$	$0.0659_{\pm 0.0064}$	$0.0674_{\pm 0.0070}$	$\mathbf{0.0608_{\pm 0.0039}}$
	Folds5x2_pp	$0.0746_{\pm 0.0056}$	$0.0867_{\pm 0.0043}$	$0.0736_{\pm 0.0171}$	$0.0698_{\pm 0.0054}$	$0.0855_{\pm 0.0049}$	$0.0811_{\pm 0.0045}$	$0.0706_{\pm 0.0063}$	$0.0730_{\pm 0.0101}$	$0.0883_{\pm 0.0135}$	$\mathbf{0.0654_{\pm 0.0047}}$
	Kin8nm	$0.1626_{\pm 0.0055}$	$0.1641_{\pm 0.0059}$	$0.1682_{\pm 0.0194}$	$0.1599_{\pm 0.0050}$	$0.1638_{\pm 0.0051}$	$0.1621_{\pm 0.0044}$	$\mathbf{0.1514_{\pm 0.0040}}$	$0.1576_{\pm 0.0108}$	$0.1716_{\pm 0.0183}$	$0.1539_{\pm 0.0046}$
	Parkinsons	$0.0759_{\pm 0.0090}$	$0.0867_{\pm 0.0069}$	$0.1270_{\pm 0.0479}$	$0.1041_{\pm 0.0288}$	$0.0884_{\pm 0.0068}$	$0.0834_{\pm 0.0073}$	$0.0783_{\pm 0.0080}$	$0.0830_{\pm 0.0184}$	$0.1140_{\pm 0.0390}$	$\mathbf{0.0713_{\pm 0.0057}}$

Table 2: Comparison of RMSE performance across different methods under varying labeled-data ratios.

Ratio	Method	W/T/L	$p$	Holm- $p$	$r$
2.5%	XGBoost	10/0/0	$1.95\mathrm{E}{-}03$	$1.76\mathrm{E}{-}02$	0.886
	KNN	10/0/0	$1.95\mathrm{E}{-}03$	$1.76\mathrm{E}{-}02$	0.886
	TabM	9/0/1	$3.91\mathrm{E}{-}03$	$1.76\mathrm{E}{-}02$	0.854
	Avg. Ensemble	9/0/1	$3.91\mathrm{E}{-}03$	$1.76\mathrm{E}{-}02$	0.854
	Self-KNN	10/0/0	$1.95\mathrm{E}{-}03$	$1.76\mathrm{E}{-}02$	0.886
	COREG	10/0/0	$1.95\mathrm{E}{-}03$	$1.76\mathrm{E}{-}02$	0.886

Table 3: Per-ratio Wilcoxon signed-rank test results with Holm correction.

Ratio	Dataset	SL-CoGameReg	Avg. Ensemble	Shap. Ensemble	$\alpha$ -Shap. Ensemble	$\beta$ -Shap. Ensemble	$\gamma$ -Shap. Ensemble	SSR-Avg. Ensemble	Decoupled CoGameReg	CoGameReg
2.5%	Abalone	$0.0962_{\pm 0.0091}$	$0.0927_{\pm 0.0062}$	$0.0925_{\pm 0.0051}$	$0.0913_{\pm 0.0054}$	$0.1086_{\pm 0.0089}$	$0.0909_{\pm 0.0060}$	$0.0943_{\pm 0.0056}$	$0.0911_{\pm 0.0042}$	$\mathbf{0.0904_{\pm 0.0042}}$
	Bank32nh	$0.1442_{\pm 0.0049}$	$0.1478_{\pm 0.0146}$	$0.1422_{\pm 0.0119}$	$0.1443_{\pm 0.0151}$	$0.1543_{\pm 0.0216}$	$0.1466_{\pm 0.0158}$	$0.1445_{\pm 0.0079}$	$0.1364_{\pm 0.0067}$	$\mathbf{0.1342_{\pm 0.0071}}$
	Elevators	$0.0740_{\pm 0.0207}$	$0.0635_{\pm 0.0033}$	$0.0611_{\pm 0.0039}$	$0.0606_{\pm 0.0034}$	$0.0737_{\pm 0.0077}$	$\mathbf{0.0588_{\pm 0.0033}}$	$0.0692_{\pm 0.0054}$	$0.0626_{\pm 0.0039}$	$0.0608_{\pm 0.0039}$
	Folds5x2_pp	$0.0835_{\pm 0.0073}$	$0.0698_{\pm 0.0054}$	$0.0661_{\pm 0.0047}$	$0.0692_{\pm 0.0053}$	$0.0776_{\pm 0.0088}$	$0.0674_{\pm 0.0052}$	$0.0726_{\pm 0.0081}$	$0.0682_{\pm 0.0071}$	$\mathbf{0.0654_{\pm 0.0047}}$
	Kin8nm	$0.1693_{\pm 0.0135}$	$0.1599_{\pm 0.0050}$	$0.1573_{\pm 0.0057}$	$0.1568_{\pm 0.0047}$	$0.1780_{\pm 0.0138}$	$0.1562_{\pm 0.0045}$	$0.1541_{\pm 0.0051}$	$\mathbf{0.1528_{\pm 0.0046}}$	$0.1539_{\pm 0.0046}$
	Parkinsons	$0.0889_{\pm 0.0113}$	$0.1041_{\pm 0.0288}$	$0.0733_{\pm 0.0061}$	$0.0882_{\pm 0.0199}$	$0.0814_{\pm 0.0092}$	$0.0780_{\pm 0.0092}$	$0.0920_{\pm 0.0225}$	$\mathbf{0.0711_{\pm 0.0071}}$	$0.0713_{\pm 0.0057}$

Table 4: Comparison of RMSE performance across different ablation variants of CoGameReg under varying labeled-data ratios.

Panel of Figure 2 — Figure 2: Ground-truth P-wave velocity and five seismic attributes used as inputs for the synthetic experiment. Each panel is displayed with its own color scale.

Figure 3: Spatial distribution of the training, validation, and blind-test wells in the synthetic experiment.

Method	RMSE $\downarrow$	$R^{2}$ $\uparrow$	SRC $\uparrow$
XGBoost	0.4580	0.3954	0.5245
KNN	0.4805	0.3345	0.5062
TabM	0.4230	0.4841	0.5686
Avg. Ensemble	0.4149	0.5036	0.5732
Self-KNN	0.4713	0.3598	0.5183
COREG	0.4629	0.3822	0.5213

Table 5: Quantitative comparison of reservoir property prediction on the simulated 3D dataset, evaluated on blind wells.

Panel of Figure 4 — Figure 4: Qualitative comparison of P-wave velocity predictions on representative slices of the synthetic 3D dataset. From top to bottom, the rows correspond to Time = 9, Time = 110, Time = 188, and Inline = 121. From left to right, the columns show XGBoost, KNN, Self-KNN, COREG, CoGameReg, and the ground truth. CoGameReg is placed next to the ground truth for direct visual comparison. All panels use the same P-wave velocity color scale as Figure 2 (a).

Subset	Number	Anonymized well identifiers
Training	10	Well 1–Well 10
Validation	5	Well 11–Well 15
Blind test	3	Well 16–Well 18

Table 6: Well partition used in the Western Field Area experiment. The well names are anonymized for data-confidentiality reasons.

Panel of Figure 5 — Figure 5: Vertical sections of the five seismic-derived volumes used as input features for water-saturation prediction in the Western Field Area. Each panel is displayed with its own color scale.

Figure 6: Spatial distribution and data partition of the 18 anonymized wells in the Western Field Area. Well 1–Well 10 were used for training, Well 11–Well 15 for validation, and Well 16–Well 18 for blind-well evaluation. Different colors denote the three well subsets.

Panel of Figure 7 — Figure 7: Comparison of time-domain water-saturation sections predicted by (a) XGBoost, (b) COREG, (c) UCVME, and (d) CoGameReg along the same arbitrary seismic line crossing nine wells in the Western Field Area. Projected well locations and reference water-saturation logs are displayed along the sections. The line includes training, validation, and blind-test wells.

Panel of Figure 8 — Figure 8: Horizon-based water-saturation maps extracted from the three-dimensional volumes predicted by (a) XGBoost, (b) COREG, (c) UCVME, and (d) CoGameReg in the Western Field Area. All four panels show the same reservoir horizon and use the same spatial extent and water-saturation color scale. The background colors represent predicted water saturation. Colored well symbols denote Gas, Poor Gas, and Water interpretations derived from well logs at the corresponding horizon and projected onto the maps for reference. The red polyline indicates the trajectory of the vertical section shown in Figure 7 .

Figure 9: Comparison of ground-truth water-saturation curves with predictions from XGBoost, COREG, UCVME, and CoGameReg at the three blind-test wells (Wells 16–18) in the Western Field Area.

Validation wells (Wells 11–15)
Method	$N$	$R^{2}\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	Pearson $r\uparrow$	Bias
XGBoost	625	0.4456	4.8480	2.1656	0.6763	0.6556
COREG	625	0.4121	4.9923	2.1673	0.6640	0.9781
UCVME	625	0.5416	4.4086	2.2239	0.7570	0.1965
CoGameReg	625	0.5407	4.4128	1.9746	0.7807	0.6828
Blind-test wells (Wells 16–18)

Table 7: Pooled water-saturation prediction results for four representative methods in the field experiment.

Semi-Supervised Learning

Semi-supervised learning uses both labeled and unlabeled data to improve prediction when reliable annotations are scarce.

See all 164 papers

Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regression
May 30, 2026Kwangho Kim, Jisu KimKernel Ridge Regression Distributional Regression
Department of Statistics, Korea University, Seoul, Korea · Department of Statistics, Seoul National University, Seoul, Korea
Beyond Backscatter: InSAR coherence from detected SAR images
Jun 5, 2026Francescopaolo Sica, Andrea Pulella, Michael SchmittRemote Sensing Synthetic Aperture Radar
Department of Aerospace Engineering, University of the Bundeswehr Munich, Neubiberg, Germany · Microwaves and Radar Institute, German Aerospace Center (DLR), Weßling, Germany
PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction
Apr 1, 2026Brandon Yee, Pairie KohMultiphysics Simulation PDE Surrogate Modeling
Physics Lab, Yee Collins Research Group · Graduate School of Business, Stanford University

May 30, 2026J/K move · Enter open · S save

Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regression

Kwangho Kim, Jisu Kim

Department of Statistics, Korea University, Seoul, Korea · Department of Statistics, Seoul National University, Seoul, Korea

Kernel Ridge Regression Distributional Regression Semi-Supervised Learning Statistical Learning Theory

Open paper AskPDF arXiv

In many modern machine learning pipelines, abundant pretrained representations serve as noisy proxy covariates, while task-specific labels remain scarce. We study semi-supervised regression in this setting, and propose a simple two stage estimator that learns kernel eigenfeatures from all proxy covariates and fits a ridge predictor on labeled data. We derive finite sample bounds showing that fast labeled sample rates are recovered when proxy perturbation is controlled and unlabeled proxy covariates are sufficiently abundant. We also show that distribution regression is a direct special case, with analogous guarantees when the finite bag size is large enough. Experiments show consistent gains over supervised and semi-supervised baselines, especially in low label regimes.

Abstract

Semi-Supervised Learning

Explore similar work

Semi-Supervised Learning with Noisy Proxy Covariates: Generalization Bounds and Distribution Regression

Beyond Backscatter: InSAR coherence from detected SAR images

PI-JEPA: Label-Free Surrogate Pretraining for Coupled Multiphysics Simulation via Operator-Split Latent Prediction