Physics-enhanced Neural Operator for Simulating Turbulent Transport

The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. 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 for long-term simulation at fine spatial scales. Given the pressing need for efficient simulation, there is an increasing interest in building machine learning models for turbulence, either by reconstructing DNS from alternative low-fidelity simulations or by predicting DNS based on the patterns learned from historical data. However, standard machine learning techniques remain limited in capturing complex spatio-temporal characteristics of turbulent flows, resulting in limited performance and generalizability. This paper presents a novel physics-enhanced neural operator (PENO) that incorporates physical knowledge of partial differential equations (PDEs) to accurately model flow dynamics. The model is further refined by a self-augmentation mechanism to reduce the accumulated error in long-term simulations. The proposed method is evaluated through its performance on two distinct sets of 3D turbulent flow data, showcasing the model's capability to reconstruct high-resolution DNS data, maintain the inherent physical properties of flow transport, and generate flow simulations across various resolutions. Additionally, experimental results on multiple 2D vorticity flow series, generated by different PDEs, highlight the transferability and generalizability of the proposed method. This confirms its applicability to a wide range of real-world scenarios in which extensive simulations are needed under diverse settings.

FREE: The Foundational Semantic Recognition for Modeling Environmental Ecosystems

Modeling environmental ecosystems is critical for the sustainability of our planet, but is extremely challenging due to the complex underlying processes driven by interactions amongst a large number of physical variables. As many variables are difficult to measure at large scales, existing works often utilize a combination of observable features and locally available measurements or modeled values as input to build models for a specific study region and time period. This raises a fundamental question in advancing the modeling of environmental ecosystems: how to build a general framework for modeling the complex relationships amongst various environmental data over space and time? In this paper, we introduce a new framework, FREE, which maps available environmental data into a text space and then converts the traditional predictive modeling task in environmental science to the semantic recognition problem. The proposed FREE framework leverages recent advances in Large Language Models (LLMs) to supplement the original input features with natural language descriptions. This facilitates capturing the data semantics and also allows harnessing the irregularities of input features. When used for long-term prediction, FREE has the flexibility to incorporate newly collected observations to enhance future prediction. The efficacy of FREE is evaluated in the context of two societally important real-world applications, predicting stream water temperature in the Delaware River Basin and predicting annual corn yield in Illinois and Iowa. Beyond the superior predictive performance over multiple baseline methods, FREE is shown to be more data- and computation-efficient as it can be pre-trained on simulated data generated by physics-based models.

HOSSnet: an Efficient Physics-Guided Neural Network for Simulating Crack Propagation

Hybrid Optimization Software Suite (HOSS), which is a combined finite-discrete element method (FDEM), is one of the advanced approaches to simulating high-fidelity fracture and fragmentation processes but the application of pure HOSS simulation is computationally expensive. At the same time, machine learning methods, shown tremendous success in several scientific problems, are increasingly being considered promising alternatives to physics-based models in the scientific domains. Thus, our goal in this work is to build a new data-driven methodology to reconstruct the crack fracture accurately in the spatial and temporal fields. We leverage physical constraints to regularize the fracture propagation in the long-term reconstruction. In addition, we introduce perceptual loss and several extra pure machine learning optimization approaches to improve the reconstruction performance of fracture data further. We demonstrate the effectiveness of our proposed method through both extrapolation and interpolation experiments. The results confirm that our proposed method can reconstruct high-fidelity fracture data over space and time in terms of pixel-wise reconstruction error and structural similarity. Visual comparisons also show promising results in long-term

Reconstructing Turbulent Flows Using Physics-Aware Spatio-Temporal Dynamics and Test-Time Refinement

Simulating turbulence is critical for many societally important applications in aerospace engineering, environmental science, the energy industry, and biomedicine. Large eddy simulation (LES) has been widely used as an alternative to direct numerical simulation (DNS) for simulating turbulent flows due to its reduced computational cost. However, LES is unable to capture all of the scales of turbulent transport accurately. Reconstructing DNS from low-resolution LES is critical for many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the spatio-temporal complexity of turbulent flows. In this work, we propose a new physics-guided neural network for reconstructing the sequential DNS from low-resolution LES data. The proposed 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 further reduce the accumulated reconstruction errors over long periods. The results on two different types of turbulent flow data confirm the superiority of the proposed method in reconstructing the high-resolution DNS data and preserving the physical characteristics of flow transport.

Modeling Reservoir Release Using Pseudo-Prospective Learning and Physical Simulations to Predict Water Temperature

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.

Heterogeneous Stream-reservoir Graph Networks with Data Assimilation

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. A well-trained temporal modeling component is needed in order to use adjusted states to improve future predictions. Hence, we also introduce a simulation-based pre-training strategy to enhance the model training. 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. Moreover, we show that the proposed method using the pre-training strategy can still produce good predictions even with limited training data.

Reconstructing High-resolution Turbulent Flows Using Physics-Guided Neural Networks

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.