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Climate change has exacerbated water stress and water‐related disasters, necessitating more precise streamflow simulations. However, in the majority of global regions, a deficiency of streamflow data constitutes a significant constraint on modeling endeavors. Traditional distributed hydrological models and regionalization approaches have shown suboptimal performance. While current deep learning (DL)‐related models trained on large data sets excel in spatial generalization, the direct applicability of these models in certain regions with unique hydrological processes can be challenging due to the limited representativeness within the training data set. Furthermore, transfer learning DL models pre‐trained on large data sets still necessitate local data for retraining, thereby constraining their applicability. To address these challenges, we present a physics‐informed DL model based on a distributed framework. It involves spatial discretization and the establishment of differentiable hydrological models for discrete sub‐basins, coupled with a differentiable Muskingum method for channel routing. By introducing upstream‐downstream relationships, model errors in sub‐basins propagate through the river network to the watershed outlet, enabling the optimization using limited downstream streamflow data, thereby achieving spatial simulation of ungauged internal sub‐basins. The model, when trained solely on the downstream‐most station, outperforms the distributed hydrological model in streamflow simulation at both the training station and upstream held‐out stations. Additionally, in comparison to transfer learning models, our model requires fewer gauge stations for training, but achieves higher precision in simulating streamflow on spatially held‐out stations, indicating better spatial generalization ability. Consequently, this model offers a novel approach to hydrological simulation in data‐scarce regions, especially those with poor hydrological representativeness. Plain Language Summary Climate change leads to more water shortages and disasters, requiring better streamflow predictions. Yet, a big hurdle in dealing with this issue is the lack of streamflow data across many parts of the world. Traditional physics‐based distributed hydrological models and current deep learning (DL) models have their limitations, especially for regions with unique hydrological processes and limited observations. To address these challenges, we developed a new tool combining physics‐informed DL and a traditional river routing model based on the distributed framework. The model divides the region into sub‐basins, where a physics‐informed DL rainfall‐runoff model calculates runoff generation, and a physics‐informed DL routing model computes the movement of water within each subunit toward the river. Model errors propagate downstream through the river network, thus requiring only a small amount of downstream data to optimize all sub‐basin models and effectively simulate internal unmonitored sub‐basins. When solely using the downstream‐most discharge stations for training, our model outperforms the traditional physics‐based distributed hydrological model. In addition, our approach requires less training data than transfer learning, while achieving higher spatial generalization accuracy. In summary, our model provides a new way to simulate streamflow in data‐scarce regions with unique processes. Key Points A distributed physics‐informed deep learning hydrological model was proposed for data‐scarce regions The new model outperforms the traditional distributed hydrologic model in simulating streamflow in upstream held‐out stations Our model requires less data for training but performs better than the transfer learning model in spatial generalization

We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.

The accurate prediction of gas turbine output power is critical for flexible scheduling and shipboard microgrid resilience. However, purely data-driven models suffer from poor generalization and physical inconsistency in complex marine environments, especially under unseen operation conditions. This paper proposes a condition-adaptive physics-informed long short-term memory (CAPI-LSTM) framework to ensure physical consistency across the full operation envelope. In the proposed framework, an MLP-based condition-adaptive regulator is developed to dynamically adjust the compressor air flow rate within the embedded physics-informed loss function. The proposed CAPI-LSTM model is verified using the operation data from an LM2500+ gas turbine. The comparison results demonstrate the superiority of the proposed method over traditional architectures. The CAPI-LSTM model achieves the lowest root mean square error of 0.177 MW, and its error distribution is the most concentrated near zero among all compared models. The robustness of the CAPI-LSTM model is further verified under the unseen operation conditions. The CAPI-LSTM still maintains excellent generalization capability compared to both purely data-driven models and standard physics-informed models, with an average error of only 0.218 MW and a narrow interquartile range of [0.058, 0.363]. The paired t-test results confirm that the improvement of the CAPI-LSTM model is statistically significant. The CAPI-LSTM model achieves competitive computational efficiency despite the integration of the physics-informed loss function with a condition-adaptive regulator. Furthermore, the CAPI-LSTM model achieves superior performance in noise immunity and transferability to other types of gas turbines. In summary, the proposed CAPI-LSTM model provides an effective and practical solution for marine gas turbine output power prediction.