Zhen Liu

Accurate streamflow forecasting is essential for water resource management, yet it remains challenging due to the highly non-stationary and volatile nature of hydrological time series. This study examines an enhanced Quantum Reservoir Computing (QRC) framework for one-step-ahead monthly dischage forecasting of the Buzău River across three periods. The framework implements a dual-axis rotation encoding scheme to map scalar inputs onto the Bloch sphere, coupled with a fixed, multi-layered parametric reservoir featuring a cyclic Controlled-Z (CZ) entanglement topology. Operating under a continuous state-passing strategy, the network processes historical dependencies through a single forward pass over a static 4-qubit system, shifting all learning optimization to a lightweight classical ridge regression readout. QRC achieved test NSE values of 0.693–0.738. While QNN and VQR yielded lower MAE and RMSE values across all three configurations, QRC consistently outperformed BPNN. ESN achieved slightly lower errors throughout, whereas performance comparisons with ELM and LSTM varied by configuration. The primary empirical contribution of this study is a compact, fixed-reservoir architecture that successfully avoids the iterative optimization of quantum-gate parameters.

Pre-stack AVO inversion plays a critical role in detailed reservoir characterization, dynamic reservoir monitoring, and carbon sequestration assessment. However, conventional inversion methods often suffer from high computational costs, strong dependence on initial models, insufficient frequency matching, and vulnerability to noise. To address these challenges, we propose a Physics-Informed Neural Network (PINN) framework based on the Lambda-Mu-Rho (LMR) approximation, along with an enhanced version, iPINN, for direct and efficient one-step inversion of subsurface elastic parameters: Lamé’s first parameter (λ), shear modulus (µ), and density (ρ). The approach embeds physical constraints into the network architecture, incorporates first- and second-order lateral derivative regularization to enhance lateral continuity, and innovatively treats the central frequency of the wavelet as a learnable parameter within the loss function, thereby achieving adaptive frequency optimization and significantly improving robustness under complex geological conditions. Benchmark experiments using the Marmousi2 model demonstrate that iPINN achieves superior inversion accuracy for λ with a MAE of 0.035, RMSE of 0.050, and R² of 0.931. Compared to the traditional L-BFGS-B optimization framework, iPINN reduces inversion error by 15–23% under 5–15 dB noise conditions, while requiring only 10–30% of the training samples to reach comparable accuracy to full-data training—greatly reducing both computational and data costs. Application to real CO₂-enhanced oil recovery (EOR) monitoring data confirms that iPINN can accurately capture anomalies and the spatial extent of elastic parameter changes induced by CO₂ injection. The generated synthetic seismic data show significantly improved fidelity in amplitude, phase, and AVO effects compared to traditional methods. This study offers a novel solution for unsupervised, low-sample, and high-efficiency seismic inversion. It demonstrates strong engineering applicability and lays a solid theoretical and methodological foundation for future developments in nonlinear PINN frameworks based on the full-wave Zoeppritz equation, full-spectrum wavelet parameterization, multiphysics joint inversion, and Bayesian uncertainty quantification.

A convolutional neural network-bidirectional long short-term memory-physics-informed neural network (CNN-BiLSTM-PINN) architecture is proposed that integrates physical and numerical constraints for seismic elastic parameter inversion. Traditional seismic inversion methods often face challenges of insufficient accuracy or low computational efficiency when dealing with complex geologic conditions. To address these issues, two network architectures — convolutional neural network-physics-informed neural network (CNN-PINN) and CNN-BiLSTM-PINN — were constructed, and a hybrid strategy combining model-driven and data-driven approaches was designed. Systematic experiments using the Marmousi2 model compared the inversion performance across different network architectures and driving strategies. Results indicated that under the hybrid driving mode (model 0.3 + numerical 0.7), CNN-BiLSTM-PINN provided clearer boundaries, better structural continuity, and improved resolution for the Lamé parameter (λ) and shear modulus (μ), whereas CNN-PINN demonstrated statistically significant advantages in density (ρ) inversion (p < 0.001). Practical applications in the CO₂ flooding demonstration area of X oilfield further demonstrated that the method accurately delineated the CO₂ flow range and aligned well with well logging data. The study also found that although the CNN-BiLSTM architecture showed higher training efficiency than CNN in supervised learning, its computational complexity increased significantly within the PINN framework, primarily due to the interaction between physical constraint calculations and the recursive structure of the BiLSTM. These findings offer a novel paradigm for seismic elastic parameter inversion, enhancing inversion accuracy and stability while preserving physical reasonability, with significant implications for oil and gas exploration and carbon sequestration monitoring.

Physics-Informed Neural Networks (PINNs) enable unsupervised inversion by integrating seismic forward modeling equations directly into neural network loss functions, operating on angle-domain seismic data. The inverse PINN (iPINN) extends this framework by treating the central frequency of the Ricker wavelet as a trainable parameter, thereby enhancing adaptability to spectral mismatch and improving lateral continuity in inversion results. However, iPINN do not provide uncertainty quantification for their predictions. To address this limitation, a Bayesian Physics-Informed Neural Network (iBPINN) is proposed, incorporating Flipout-based Bayesian convolutional and fully connected layers into the iPINN architecture. Through variational inference, iBPINN enables probabilistic modeling of both network weights and wavelet frequency, yielding not only predicted physical parameters but also posterior standard deviation (std) maps for direct visualization and quantitative assessment of predictive uncertainty. Numerical experiments on the Marmousi2 synthetic model show that PINN achieves rapid convergence for large-scale stratigraphic structures, while iPINN provides more consistent inversion results for deeper layers and weakly sensitive parameters via dynamic frequency correction. iBPINN maintains comparable inversion consistency and, crucially, enables intuitive mapping of predictive uncertainty through std analysis, particularly in fault zones, high-impedance contrasts, and low-SNR regions. Field application to seismic data from a CO₂ injection site further demonstrates that the uncertainty maps provided by iBPINN offer additional insights into fluid substitution and reservoir connectivity. This methodological progression—from PINN (“statistics + logic”), to iPINN (“logic + adaptability”), and ultimately to iBPINN (“logic + reasoning”)—mirrors the broader evolution of AI in geophysical inversion: from statistical models, to logic-embedded frameworks, and finally to reasoning-enhanced architectures. The proposed iBPINN framework thus offers a unified, interpretable, and trustworthy approach for next-generation seismic inversion in complex geological environments.

Traditional seismic inversion frameworks struggle to preserve spatial structure and to quantify model reliability. We present a next-generation pathway that progresses from a convolutional Physics-Informed Neural Network (PINN) to a Bayesian PINN (BPINN) with uncertainty modeling, and culminates in a Bayesian Physics-Informed Vision Transformer (BPI-ViT) that enables structure-level uncertainty quantification. In our formulation, PINN “training data” are equation-domain samples used to minimize physical residuals—supporting physics-driven, data-agnostic generalization—while BPI-ViT integrates multi-layer self-attention and Bayesian inference to transition from pixel-level optimization to structure-aware collaboration. Consistent evaluation on the Marmousi2 benchmark and validation on field-scale CO₂ EOR monitoring data show that BPI-ViT outperforms prior methods in target-horizon recovery, fault and anomaly detection, spatial continuity, and uncertainty quantification, while maintaining physical consistency. These results establish a structural-intelligent paradigm that moves seismic inversion beyond error minimization toward structure-aware, reliable, and cognitively informed modeling, and provide a foundation for future multi-physics and complex-geology applications.

In the framework of efficient water resources management, the hydrological forecast is the basis of the pertinent management of water resources. Therefore, this study applies the variational quantum regression (VQR), a novel machine learning approach inspired by quantum computing principles, to the series of water discharges from a river in Romania. The models were evaluated against the quantum neural network (QNN) and other classic artificial intelligence (AI) outputs on the same dataset. Performance was assessed based on the coefficient of determination (R²), mean absolute error (MAE), and mean squared error (MSE). VQR outperformed classical neural networks and hybrid models with respect to MSE and MAE, demonstrating superior accuracy and generalization capability. Notably, the models exhibited exceptional skill in capturing monthly maxima—an area where other models often struggle, underscoring the potential of VQR as a powerful and reliable tool for hydrological forecasting, particularly in the context of nonlinear and high-variability data series.

Predicting the river discharge is essential for preparing effective measures against flood hazards or managing hydrological droughts. Despite mathematical modeling advancements, most algorithms have failed to capture the extreme values (especially the highest ones). In this article, we proposed a quantum neural networks (QNNs) approach for forecasting the river discharge in three scenarios. The algorithm was applied to the raw data series and the series without aberrant values. Comparisons with the results obtained on the same series by other neural networks (LSTM, BPNN, ELM, CNN-LSTM, SSA-BP, and PSO-ELM) emphasized the best performance of the present approach. The lower error between the recorded values and the predicted ones in the evaluation of maxima compared to the case of the competitors mentioned shows that the algorithm best fits the extremes. The most significant mean standard errors (MSEs) and mean absolute errors (MAEs) were 26.9424 and 4.8914, respectively, and the lowest R² was 84.36%, indicating the good performances of the algorithm.

Artificial intelligence (AI) has become an instrument used in all domains with good results. The water resources management field is not an exception. Therefore, in this article, we propose two machine learning (ML) techniques—an echo state network (ESN) and sparrow search algorithm–echo state network (SSA-ESN)—for monthly modeling of the water discharge of one of the biggest rivers in Romania for three periods (S, S1, and S2). In both models, R² was over 0.989 on the test and training sets and the mean absolute error (MAE) varied between 4.4826 and 7.6038. The performance of the SSA-ESN was similar, but the ESN had the shortest run time. The influence of anomalies on the models’ quality was assessed by running the algorithms on a series without the aberrant values, which were detected by the seasonal hybrid extreme studentized deviate (S-H-ESD) test. The results indicate that removing the anomalies significantly improved both models’ performance, but the run time was increased.

The management of water resources must be based on accurate models of the river discharge in the context of the water flow alteration due to anthropic influences and climate change. Therefore, this article addresses the challenge of detecting the best model among three artificial intelligence techniques (AI)—backpropagation neural networks (BPNN), long short-term memory (LSTM), and extreme learning machine (ELM)—for the monthly data series discharge of the Buzău River, in Romania. The models were built for three periods: January 1955–September 2006 (S1 series), January 1955–December 1983 (S2 series), and January 1984–December 2010 (S series). In terms of mean absolute error (MAE), the best performances were those of ELM on both Training and Test sets on S2, with MAE_Training = 5.02 and MAE_Test = 4.01. With respect to MSE, the best was LSTM on the Training set of S2 (MSE = 60.07) and ELM on the Test set of S2 (MSE = 32.21). Accounting for the R² value, the best model was LSTM on S2 (R²_Training = 99.92%, and R²_Test = 99.97%). ELM was the fastest, with 0.6996 s, 0.7449 s, and 0.6467 s, on S, S1, and S2, respectively.

Research on the provenance of sedimentary systems is key to better understanding the sedimentary framework and improving exploration-associated decision-making and deployment. With regard to the provenance of sedimentary systems, there is still poor understanding in the initial rifting stage due to imbalanced and insufficient exploration and a common lack of seismic data, which have seriously hindered oil exploration in the Qintong Sag, Subei Basin. This study aimed at investigating the provenance in the direction of the fault-terrace zone in the southeast part of the Qintong Sag and aimed to examine whether large-scale sedimentary systems are formed by these sediment sources. Integrated analysis of heavy minerals, sandstone petrologic maturity, drilling cutting dates, 3D seismic data, and well logs was employed to identify the provenance. This study is the first time that large-scale provenance from the direction of the fault-terrace zone has been discovered in the third member of the Paleocene Funing Formation (referred to as the third Mbr of the Funing Fm in this paper) in the Subei Basin, east China. The documentation shows that sediments from the northwest Wubao Low Uplift and the southeast Taizhou Uplift can be distinguished in the Qintong Sag, with the large-scale delta system in the central and eastern part of the Qintong Sag comprising sediments from the Taizhou Uplift, improving upon previous understanding of the sedimentary framework. The deposition formed by the Taizhou Uplift provenance system was characterized by gradual weakening of the hydrodynamic forces, a decreasing sediment supply, and shrinking of the retrogradational delta depositional systems with good reservoir qualities, which are characterized by high-quality source–reservoir–cap combinations and are likely to develop into a hydrocarbon-rich belt. The discovery of the Taizhou Uplift provenance proves that there may be major provenance and large-scale sedimentary systems from the fault-terrace zone of the rift basins in the initial rifting stage. The experience of rapid retrogradation showed that these large-scale delta systems are likely to only flourish in the initial rifting stage. This study is helpful for improving the understanding of sediment provenance and the sedimentary framework of lacustrine rift basins in the initial rifting stage.