Multi-Scale Graph Learning for Anti-Sparse Downscaling

TL;DR

This work tackles the challenge of predicting fine-scale daily stream temperatures under sparse data by introducing Multi-Scale Graph Learning (MSGL), a three-task graph framework that jointly learns coarse-scale, cross-scale, and fine-scale dynamics. A cross-scale interpolation mechanism using a cross-scale distance matrix $oldsymbol{D}$ and an asynchronous pretraining strategy (ASYNC-MSGL) enable robust downscaling even with extremely limited fine-scale labels. The approach is instantiated on Delaware River Basin data, where MSGL and ASYNC-MSGL consistently outperform single-scale and other multi-scale baselines, with particular strength in highly sparse regimes. The method offers a generalizable paradigm for irregular, sparsely observed spatiotemporal graphs in hydrology and related fields, leveraging cross-scale topology and asynchronous training to improve local predictions while capitalizing on regional data.

Abstract

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.

Figures (5)

• Figure 1: The figure illustrates the architecture of the Multi-Scale Graph Learning (MSGL) model, which comprises three parallel training streams: coarse-scale graph learning (CSL), fine-scale graph learning (FSL), and cross-scale interpolation learning (CrSL). The trade-off among these three learning tasks is managed through Multi-Scale Optimization (MSO). $\mathbf{H}$ are hidden states. $\mathbf{\hat{Y}}$ are temperature predictions. $\mathbf{c}$, $\mathbf{cr}$, and $\mathbf{f}$ denote the coarse-scale, cross-scale, and fine-scale, respectively. $\mathbf{D}_{mapping}$ is a CSL-only $\mathbf{\hat{Y}}_{c}$ mapped to fine resolution for use in asynchronous pre-training of MSGL (ASYNC-MSGL).
• Figure 2: Root mean squared error (RMSE, ° C) of modeling methods RGrN (Base), MSGL, and ASYNC-MSGL applied to four watersheds, with 0.1% of the fine-scale labels in each watershed used for training. Reaches of varying lengths are color-coded by average RMSE over all dates. (Map layers from EPA2012NHDPlus.)
• Figure 3: Robustness of spatiotemporal graph models across varying label sparsity levels (training on 0.1%, 1%, 4%, 7%, 10%, 20%, 30%, 40%, 50%, and 100% of all fine-scale reach-days) in four watersheds. Filled markers represent our new methods MSGL and ASYNC-MSGL, whereas open markers represent the methods referenced in section RQ1-Baselines.
• Figure 4: Timeline of data partitions in Lower Delaware, Neversink, Lower West Branch Delaware, and Rancocas Watersheds.
• Figure 5: Sparsity levels visualized for training and validation datasets at 0.1%, 1%, 5%, 25%, and 100% data retention. This chart demonstrates the range of conditions from minimal to full data availability.