Multi-Scale Graph Learning for Anti-Sparse Downscaling

Water temperature can vary substantially even across short distances within the same sub-watershed. Accurate prediction of stream water temperature at fine spatial resolutions (i.e., fine scales, $\leq$ 1 km) enables precise interventions to maintain water quality and protect aquatic habitats. Although spatiotemporal models have made substantial progress in spatially coarse time series modeling, challenges persist in predicting at fine spatial scales due to the lack of data at that scale.To address the problem of insufficient fine-scale data, we propose a Multi-Scale Graph Learning (MSGL) method. This method employs a multi-task learning framework where coarse-scale graph learning, bolstered by larger datasets, simultaneously enhances fine-scale graph learning. Although existing multi-scale or multi-resolution methods integrate data from different spatial scales, they often overlook the spatial correspondences across graph structures at various scales. To address this, our MSGL introduces an additional learning task, cross-scale interpolation learning, which leverages the hydrological connectedness of stream locations across coarse- and fine-scale graphs to establish cross-scale connections, thereby enhancing overall model performance. Furthermore, we have broken free from the mindset that multi-scale learning is limited to synchronous training by proposing an Asynchronous Multi-Scale Graph Learning method (ASYNC-MSGL). Extensive experiments demonstrate the state-of-the-art performance of our method for anti-sparse downscaling of daily stream temperatures in the Delaware River Basin, USA, highlighting its potential utility for water resources monitoring and management.

Foundation Models for Environmental Science: A Survey of Emerging Frontiers

Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional data-driven methods face challenges in capturing inherently complex and interconnected processes and are further constrained by limited observational data in many environmental applications. Foundation models, which leverages large-scale pre-training and universal representations of complex and heterogeneous data, offer transformative opportunities for capturing spatiotemporal dynamics and dependencies in environmental processes, and facilitate adaptation to a broad range of applications. This survey presents a comprehensive overview of foundation model applications in environmental science, highlighting advancements in common environmental use cases including forward prediction, data generation, data assimilation, downscaling, inverse modeling, model ensembling, and decision-making across domains. We also detail the process of developing these models, covering data collection, architecture design, training, tuning, and evaluation. Through discussions on these emerging methods as well as their future opportunities, we aim to promote interdisciplinary collaboration that accelerates advancements in machine learning for driving scientific discovery in addressing critical environmental challenges.

A Survey of Foundation Models for Environmental Science

Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity, interconnectedness, and limited data of such systems. Foundation models, with their large-scale pre-training and universal representations, offer transformative opportunities by integrating diverse data sources, capturing spatiotemporal dependencies, and adapting to a broad range of tasks. This survey presents a comprehensive overview of foundation model applications in environmental science, highlighting advancements in forward prediction, data generation, data assimilation, downscaling, model ensembling, and decision-making across domains. We also detail the development process of these models, covering data collection, architecture design, training, tuning, and evaluation. By showcasing these emerging methods, we aim to foster interdisciplinary collaboration and advance the integration of cutting-edge machine learning for sustainable solutions in environmental science.

Towards efficient quantum algorithms for diffusion probability models

A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as high-resolution images or audio incurs significant computational, energy, and hardware costs. In this work, we introduce efficient quantum algorithms for implementing DPMs through various quantum ODE solvers. These algorithms highlight the potential of quantum Carleman linearization for diverse mathematical structures, leveraging state-of-the-art quantum linear system solvers (QLSS) or linear combination of Hamiltonian simulations (LCHS). Specifically, we focus on two approaches: DPM-solver-$k$ which employs exact $k$-th order derivatives to compute a polynomial approximation of $\epsilon_\theta(x_\lambda,\lambda)$; and UniPC which uses finite difference of $\epsilon_\theta(x_\lambda,\lambda)$ at different points $(x_{s_m}, \lambda_{s_m})$ to approximate higher-order derivatives. As such, this work represents one of the most direct and pragmatic applications of quantum algorithms to large-scale machine learning models, presumably talking substantial steps towards demonstrating the practical utility of quantum computing.

Physics-Guided Foundation Model for Scientific Discovery: An Application to Aquatic Science

Physics-guided machine learning (PGML) has become a prevalent approach in studying scientific systems due to its ability to integrate scientific theories for enhancing machine learning (ML) models. However, most PGML approaches are tailored to isolated and relatively simple tasks, which limits their applicability to complex systems involving multiple interacting processes and numerous influencing features. In this paper, we propose a \textit{\textbf{P}hysics-\textbf{G}uided \textbf{F}oundation \textbf{M}odel (\textbf{PGFM})} that combines pre-trained ML models and physics-based models and leverages their complementary strengths to improve the modeling of multiple coupled processes. To effectively conduct pre-training, we construct a simulated environmental system that encompasses a wide range of influencing features and various simulated variables generated by physics-based models. The model is pre-trained in this system to adaptively select important feature interactions guided by multi-task objectives. We then fine-tune the model for each specific task using true observations, while maintaining consistency with established physical theories, such as the principles of mass and energy conservation. We demonstrate the effectiveness of this methodology in modeling water temperature and dissolved oxygen dynamics in real-world lakes. The proposed PGFM is also broadly applicable to a range of scientific fields where physics-based models are being used.

Modeling Continuous Spatial-temporal Dynamics of Turbulent Flow with Test-time Refinement

The precise simulation of turbulent flows holds immense significance across various scientific and engineering domains, including climate science, freshwater science, and energy-efficient manufacturing. Within the realm of simulating turbulent flows, large eddy simulation (LES) has emerged as a prevalent alternative to direct numerical simulation (DNS), offering computational efficiency. However, LES cannot accurately capture the full spectrum of turbulent transport scales and is present only at a lower spatial resolution. Reconstructing high-fidelity DNS data from the lower-resolution LES data is essential for numerous applications, but it poses significant challenges to existing super-resolution techniques, primarily due to the complex spatio-temporal nature of turbulent flows. This paper proposes a novel flow reconstruction approach that leverages physical knowledge to model flow dynamics. Different from traditional super-resolution techniques, the proposed approach uses LES data only in the testing phase through a degradation-based refinement approach to enforce physical constraints and mitigate cumulative reconstruction errors over time. Furthermore, a feature sampling strategy is developed to enable flow data reconstruction across different resolutions. The results on two distinct sets of turbulent flow data indicate the effectiveness of the proposed method in reconstructing high-resolution DNS data, preserving the inherent physical attributes of flow transport, and achieving DNS reconstruction at different resolutions.

Physics-Guided Fair Graph Sampling for Water Temperature Prediction in River Networks

This work introduces a novel graph neural networks (GNNs)-based method to predict stream water temperature and reduce model bias across locations of different income and education levels. Traditional physics-based models often have limited accuracy because they are necessarily approximations of reality. Recently, there has been an increasing interest of using GNNs in modeling complex water dynamics in stream networks. Despite their promise in improving the accuracy, GNNs can bring additional model bias through the aggregation process, where node features are updated by aggregating neighboring nodes. The bias can be especially pronounced when nodes with similar sensitive attributes are frequently connected. We introduce a new method that leverages physical knowledge to represent the node influence in GNNs, and then utilizes physics-based influence to refine the selection and weights over the neighbors. The objective is to facilitate equitable treatment over different sensitive groups in the graph aggregation, which helps reduce spatial bias over locations, especially for those in underprivileged groups. The results on the Delaware River Basin demonstrate the effectiveness of the proposed method in preserving equitable performance across locations in different sensitive groups.

Adaptive Process-Guided Learning: An Application in Predicting Lake DO Concentrations

This paper introduces a \textit{Process-Guided Learning (Pril)} framework that integrates physical models with recurrent neural networks (RNNs) to enhance the prediction of dissolved oxygen (DO) concentrations in lakes, which is crucial for sustaining water quality and ecosystem health. Unlike traditional RNNs, which may deliver high accuracy but often lack physical consistency and broad applicability, the \textit{Pril} method incorporates differential DO equations for each lake layer, modeling it as a first-order linear solution using a forward Euler scheme with a daily timestep. However, this method is sensitive to numerical instabilities. When drastic fluctuations occur, the numerical integration is neither mass-conservative nor stable. Especially during stratified conditions, exogenous fluxes into each layer cause significant within-day changes in DO concentrations. To address this challenge, we further propose an \textit{Adaptive Process-Guided Learning (April)} model, which dynamically adjusts timesteps from daily to sub-daily intervals with the aim of mitigating the discrepancies caused by variations in entrainment fluxes. \textit{April} uses a generator-discriminator architecture to identify days with significant DO fluctuations and employs a multi-step Euler scheme with sub-daily timesteps to effectively manage these variations. We have tested our methods on a wide range of lakes in the Midwestern USA, and demonstrated robust capability in predicting DO concentrations even with limited training data. While primarily focused on aquatic ecosystems, this approach is broadly applicable to diverse scientific and engineering disciplines that utilize process-based models, such as power engineering, climate science, and biomedicine.

Hierarchical Conditional Multi-Task Learning for Streamflow Modeling

Streamflow, vital for water resource management, is governed by complex hydrological systems involving intermediate processes driven by meteorological forces. While deep learning models have achieved state-of-the-art results of streamflow prediction, their end-to-end single-task learning approach often fails to capture the causal relationships within these systems. To address this, we propose Hierarchical Conditional Multi-Task Learning (HCMTL), a hierarchical approach that jointly models soil water and snowpack processes based on their causal connections to streamflow. HCMTL utilizes task embeddings to connect network modules, enhancing flexibility and expressiveness while capturing unobserved processes beyond soil water and snowpack. It also incorporates the Conditional Mini-Batch strategy to improve long time series modeling. We compare HCMTL with five baselines on a global dataset. HCMTL's superior performance across hundreds of drainage basins over extended periods shows that integrating domain-specific causal knowledge into deep learning enhances both prediction accuracy and interpretability. This is essential for advancing our understanding of complex hydrological systems and supporting efficient water resource management to mitigate natural disasters like droughts and floods.

ExoTST: Exogenous-Aware Temporal Sequence Transformer for Time Series Prediction

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. Traditional time series approaches for prediction often focus on either autoregressive modeling, which relies solely on past observations of the target ``endogenous variables'', or forward modeling, which considers only current covariate drivers ``exogenous variables''. However, effectively integrating past endogenous and past exogenous with current exogenous variables remains a significant challenge. In this paper, we propose ExoTST, a novel transformer-based framework that effectively incorporates current exogenous variables alongside past context for improved time series prediction. To integrate exogenous information efficiently, ExoTST leverages the strengths of attention mechanisms and introduces a novel cross-temporal modality fusion module. This module enables the model to jointly learn from both past and current exogenous series, treating them as distinct modalities. By considering these series separately, ExoTST provides robustness and flexibility in handling data uncertainties that arise from the inherent distribution shift between historical and current exogenous variables. Extensive experiments on real-world carbon flux datasets and time series benchmarks demonstrate ExoTST's superior performance compared to state-of-the-art baselines, with improvements of up to 10\% in prediction accuracy. Moreover, ExoTST exhibits strong robustness against missing values and noise in exogenous drivers, maintaining consistent performance in real-world situations where these imperfections are common.