A Novel Causal Graph-Convolutional-Network-Enhanced Mamba Framework with Proportional-Integral-Derivative-Inspired Constraint for Multistep Petroleum Production Forecasting

Summary

Production forecasting is essential for reservoir management, but crosswell multistep prediction remains challenging because production data involve nonlinear temporal dynamics, delayed intervariable dependencies, and strong heterogeneity among wells. To address these issues, we propose a temporal segment (TS)-graph convolutional network (GCN)-CausalMamba, a crosswell petroleum production forecasting framework that integrates Peter-Clark momentary conditional independence (PCMCI)-based causal discovery, GCN feature fusion, TS2Vec-assisted self-supervised representation learning, a Mamba selective state-space backbone, and a proportional-integral-derivative (PID)-inspired trajectory constraint loss. The framework combines dynamic production and operational variables with well-level geological and completion descriptors, enabling the model to capture both temporal evolution and crosswell structural heterogeneity. Causal graph modeling provides interpretable time-lagged structural priors. At the same time, the PID-inspired loss improves multistep trajectory stability by jointly constraining point-wise accuracy, cumulative trend consistency, and step-to-step smoothness. Experiments on real multiblock production data from the Daqing Oilfield, using well-based fivefold cross-validation, show that TS-GCN-CausalMamba consistently outperforms both general-purpose and petroleum-oriented baselines. Under the three-step forecasting setting, the proposed method improves coefficient of determination (R2) from 0.8838 to 0.9005 in Block A, from 0.9329 to 0.9342 in Block B, and from 0.9104 to 0.9147 in Block C. Meanwhile, it reduces normalized mean absolute error (NMAE) to 0.0583, 0.0332, and 0.0378, and normalized root mean square error (NRMSE) to 0.0942, 0.0577, and 0.0831 in Blocks A, B, and C, respectively. These results demonstrate its effectiveness, interpretability, and practical value for crosswell multistep petroleum production forecasting.