Accurate simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields. Within the realm of turbulent flow simulation, direct numerical simulation (DNS) is widely considered to be the most reliable approach, but it is prohibitively expensive and thus has limited applicability to long-term and fine-scale simulation over various configurations. Given the pressing need for efficient simulation, there is an increasing interest in building machine learning models for simulating turbulence, either by reconstructing DNS from alternative low-fidelity simulations or sequentially predicting DNS from historical data. However, conventional machine learning models are not designed for capturing complex spatio-temporal characteristics of turbulent flows. This results in their limited performance and generalizability, especially when applied to complex flow data and various flow configurations. This paper presents a novel physics-enhanced neural operator (PENO) that efficiently models the complex flow dynamics while leveraging physical knowledge of partial differential equations (PDEs) to enhance the simulation process. We further introduce a self-augmentation mechanism to reduce the accumulated errors in long-term simulations. The proposed method is evaluated on multiple turbulent flow datasets, showcasing the model's capability to reconstruct high-resolution DNS data, maintain the inherent physical properties of flow transport, and transfer across various resolution settings and simulation configurations. These encouraging results confirm its applicability to a wide range of real-world scenarios in which extensive simulations are needed under diverse settings.

Methane (CH4) is the second most powerful greenhouse gas after carbon dioxide and plays a crucial role in climate change due to its high global warming potential. Accurately modeling CH4 fluxes across the globe and at fine temporal scales is essential for understanding its spatial and temporal variability and developing effective mitigation strategies. In this work, we introduce the first-of-its-kind cross-scale global wetland methane benchmark dataset (X-MethaneWet), which synthesizes physics-based model simulation data from TEM-MDM and the real-world observation data from FLUXNET-CH4. This dataset can offer opportunities for improving global wetland CH4 modeling and science discovery with new AI algorithms. To set up AI model baselines for methane flux prediction, we evaluate the performance of various sequential deep learning models on X-MethaneWet. Furthermore, we explore four different transfer learning techniques to leverage simulated data from TEM-MDM to improve the generalization of deep learning models on real-world FLUXNET-CH4 observations. Our extensive experiments demonstrate the effectiveness of these approaches, highlighting their potential for advancing methane emission modeling and identifying new opportunities for developing more accurate and scalable AI-driven climate models.

Understanding environmental ecosystems is vital for the sustainable management of our planet. However, existing physics-based and data-driven models often fail to generalize to varying spatial regions and scales due to the inherent data heterogeneity presented in real environmental ecosystems. This generalization issue is further exacerbated by the limited observation samples available for model training. To address these issues, we propose Geo-STARS, a geo-aware spatio-temporal modeling framework for predicting stream water temperature across different watersheds and spatial scales. The major innovation of Geo-STARS is the introduction of geo-aware embedding, which leverages geographic information to explicitly capture shared principles and patterns across spatial regions and scales. We further integrate the geo-aware embedding into a gated spatio-temporal graph neural network. This design enables the model to learn complex spatial and temporal patterns guided by geographic and hydrological context, even with sparse or no observational data. We evaluate Geo-STARS's efficacy in predicting stream water temperature, which is a master factor for water quality. Using real-world datasets spanning 37 years across multiple watersheds along the eastern coast of the United States, Geo-STARS demonstrates its superior generalization performance across both regions and scales, outperforming state-of-the-art baselines. These results highlight the promise of Geo-STARS for scalable, data-efficient environmental monitoring and decision-making.

Accurate simulation of turbulent flows is of crucial importance in many branches of science and engineering. Direct numerical simulation (DNS) provides the highest fidelity means of capturing all intricate physics of turbulent transport. However, the method is computationally expensive because of the wide range of turbulence scales that must be accounted for in such simulations. Large eddy simulation (LES) provides an alternative. In such simulations, the large scales of the flow are resolved, and the effects of small scales are modelled. Reconstruction of the DNS field from the low-resolution LES is needed for a wide variety of applications. Thus the construction of super-resolution methodologies that can provide this reconstruction has become an area of active research. In this work, a new physics-guided neural network is developed for such a reconstruction. The method leverages the partial differential equation that underlies the flow dynamics in the design of spatio-temporal model architecture. A degradation-based refinement method is also developed to enforce physical constraints and to further reduce the accumulated reconstruction errors over long periods. Detailed DNS data on two turbulent flow configurations are used to assess the performance of the model.

This paper proposes a meta-transfer-learning method for predicting daily maximum water temperature in stream networks with explicit modeling of extreme events. Accurate prediction of these extreme events is challenging because of their sparsity in the training data and their distinct responses to external drivers when compared to non-extreme observations. To overcome these challenges, we propose a sample reweighting strategy to escalate the importance of extreme events in the training process while preserving the predictive performance in normal time periods. The sample weight for each training data point is estimated as the similarity with the target test data point using contextual information and physical simulation. The obtained sample weight values are then used to fine-tune the initial model to transfer it to the test data. This method is further enhanced by an extreme value theory-based loss function to enforce the distribution of extreme data points and accelerated by a clustering algorithm based on the estimated similarities. Additionally, we introduce an online learning strategy to further refine the predictive model using newly collected observed data. The experimental results using real stream data from the Delaware River Basin over the past 36 years demonstrate that our meta-transfer-learning method produces more accurate predictions in both normal and extreme time periods when compared to baselines without the sample re-weighting scheme. The similarity learning method can reveal meaningful relationships amongst data points. We also show that the clustering algorithm can be used to accelerate the prediction while not compromising the predictive performance. The online learning strategy is shown to further improve predictive performance using recently observed data.

Physics-based groundwater flow equations are powerful tools for water resource assessment under different hydrological and climatic conditions. How these conditions affect the discharge of groundwater (i.e., base-flow) into rivers is one of the most important topics in the hydrology domain. However, due to the different environmental conditions in different basins, it is difficult to use a single physics-based equation to represent the discharge of groundwater in all river basins. Despite the promise of data-driven models in capturing complex relationships, they are also limited in learning heterogeneous baseflow patterns from multiple basins, especially with sparse training data. In this paper, we propose a new data-driven model Physics Guided MeTa Learning (PGMTL), which uses meta-learning to adapt the predictive model to multiple basins and also enhance the meta-learning process with knowledge embodied in different physics-based equations so as to improve the baseflow prediction over a large number of river basins. Experimental results show that our proposed PGMTL has a significant improvement over either physics-based equations or ML models. Moreover, our method has been shown to perform much better with sparse or localized training data. Finally, our method is able to interpret the contribution of each physics-based equation under different scenarios.

This paper introduces a new method for combining simulated data over different types of nodes in heterogeneous graphs to facilitate predictive learning. Simulation has been widely used in scientific domains to mitigate the need for a large number of observation samples. However, simulated data are often created separately for each type of physical systems while interactions amongst different types of systems remain unexplored. Our method is developed in the context of predicting water temperature in stream networks, which is critical for decision making in water management. In particular, we first develop a graph diffusion network (GDN) to model the interactions amongst stream segments and reservoirs in a heterogeneous graph. We use the GDN model to combine simulated data for both streams and reservoirs in the graph, and use the obtained composite simulations to train the GDN model in a semi-supervised manner. Then the GDN model is further fine-tuned using true observations. Since observation data are often sparse and localized, we further leverage the information from simulations to build a reweighting strategy so as to migitage the discrepancy between training and testing data. Our evaluations in the Delaware River Basin have shown the superiority of the proposed method over multiple baselines using either sparse or localized training data. The proposed GDN model also creates a better composite simulation dataset for heterogeneous graphs.

This paper proposes a graph-based meta learning approach to separately predict water quantity and quality variables for river segments in stream networks. Given the heterogeneous water dynamic patterns in large-scale basins, we introduce an additional meta-learning condition based on physical characteristics of stream segments, which allows learning different sets of initial parameters for different stream segments. Specifically, we develop a representation learning method that leverages physical simulations to embed the physical characteristics of each segment. The obtained embeddings are then used to cluster river segments and add the condition for the meta-learning process. We have tested the performance of the proposed method for predicting daily water temperature and streamflow for the Delaware River Basin (DRB) over a 14 year period. The results confirm the effectiveness of our method in predicting target variables even using sparse training samples. We also show that our method can achieve robust performance with different numbers of clusterings.

This paper proposes a new data-driven method for predicting water temperature in stream networks with reservoirs. The water flows released from reservoirs greatly affect the water temperature of downstream river segments. However, the information of released water flow is often not available for many reservoirs, which makes it difficult for data-driven models to capture the impact to downstream river segments. In this paper, we first build a state-aware graph model to represent the interactions amongst streams and reservoirs, and then propose a parallel learning structure to extract the reservoir release information and use it to improve the prediction. In particular, for reservoirs with no available release information, we mimic the water managers' release decision process through a pseudo-prospective learning method, which infers the release information from anticipated water temperature dynamics. For reservoirs with the release information, we leverage a physics-based model to simulate the water release temperature and transfer such information to guide the learning process for other reservoirs. The evaluation for the Delaware River Basin shows that the proposed method brings over 10% accuracy improvement over existing data-driven models for stream temperature prediction when the release data is not available for any reservoirs. The performance is further improved after we incorporate the release data and physical simulations for a subset of reservoirs.

Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Large eddy simulation (LES) is an alternative that is computationally less demanding, but is unable to capture all of the scales of turbulent transport accurately. Our goal in this work is to build a new data-driven methodology based on super-resolution techniques to reconstruct DNS data from LES predictions. We leverage the underlying physical relationships to regularize the relationships amongst different physical variables. We also introduce a hierarchical generative process and a reverse degradation process to fully explore the correspondence between DNS and LES data. We demonstrate the effectiveness of our method through a single-snapshot experiment and a cross-time experiment. The results confirm that our method can better reconstruct high-resolution DNS data over space and over time in terms of pixel-wise reconstruction error and structural similarity. Visual comparisons show that our method performs much better in capturing fine-level flow dynamics.

Accurate prediction of water temperature in streams is critical for monitoring and understanding biogeochemical and ecological processes in streams. Stream temperature is affected by weather patterns (such as solar radiation) and water flowing through the stream network. Additionally, stream temperature can be substantially affected by water releases from man-made reservoirs to downstream segments. In this paper, we propose a heterogeneous recurrent graph model to represent these interacting processes that underlie stream-reservoir networks and improve the prediction of water temperature in all river segments within a network. Because reservoir release data may be unavailable for certain reservoirs, we further develop a data assimilation mechanism to adjust the deep learning model states to correct for the prediction bias caused by reservoir releases. Our evaluation for the Delaware River Basin has demonstrated the superiority of our proposed method over multiple existing methods. We have extensively studied the effect of the data assimilation mechanism under different scenarios.

This paper proposes a new physics-guided machine learning approach that incorporates the scientific knowledge in physics-based models into machine learning models. Physics-based models are widely used to study dynamical systems in a variety of scientific and engineering problems. Although they are built based on general physical laws that govern the relations from input to output variables, these models often produce biased simulations due to inaccurate parameterizations or approximations used to represent the true physics. In this paper, we aim to build a new data-driven framework to monitor dynamical systems by extracting general scientific knowledge embodied in simulation data generated by the physics-based model. To handle the bias in simulation data caused by imperfect parameterization, we propose to extract general physical relations jointly from multiple sets of simulations generated by a physics-based model under different physical parameters. In particular, we develop a spatio-temporal network architecture that uses its gating variables to capture the variation of physical parameters. We initialize this model using a pre-training strategy that helps discover common physical patterns shared by different sets of simulation data. Then we fine-tune it using limited observation data via a contrastive learning process. By leveraging the complementary strength of machine learning and domain knowledge, our method has been shown to produce accurate predictions, use less training samples and generalize to out-of-sample scenarios. We further show that the method can provide insights about the variation of physical parameters over space and time in two domain applications: predicting temperature in streams and predicting temperature in lakes.