In recent years, the Prairies have seen bigger swings in climate conditions -- very wet years followed by very dry ones. That makes an already unpredictable landscape even harder to forecast, with real consequences for flood preparedness and water quality. The challenge is the landscape itself. Much of the Canadian Prairies sit within the Prairie Pothole Region, a landscape dotted with millions of shallow wetlands and depressions. Water doesn't simply run downhill into a stream, it is stored first.

Seeded segmentation in computer vision and graph-based semi-supervised machine learning are essentially thesameproblem.

The Probabilistic Watershed isasemi-supervised learning algorithm applied on undirected graphs.

Environmental modeling faces critical challenges in predicting ecosystem dynamics across unmonitored regions due to limited and geographically imbalanced observation data. This challenge is compounded by spatial heterogeneity, causing models to learn spurious patterns that fit only local data. Unlike conventional domain generalization, environmental modeling must preserve invariant physical relationships and temporal coherence during augmentation. In this paper, we introduce Generalizable Representation Enhancement via Auxiliary Transformations (GREAT), a framework that effectively augments available datasets to improve predictions in completely unseen regions. GREAT guides the augmentation process to ensure that the original governing processes can be recovered from the augmented data, and the inclusion of the augmented data leads to improved model generalization. Specifically, GREAT learns transformation functions at multiple layers of neural networks to augment both raw environmental features and temporal influence. They are refined through a novel bi-level training process that constrains augmented data to preserve key patterns of the original source data. We demonstrate GREAT's effectiveness on stream temperature prediction across six ecologically diverse watersheds in the eastern U.S., each containing multiple stream segments. Experimental results show that GREAT significantly outperforms existing methods in zero-shot scenarios. This work provides a practical solution for environmental applications where comprehensive monitoring is infeasible.

Neural Information Processing Systems http://nips.cc/

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.

The authors prove that the probabilities they obatin are equivalent to the probabilities yielded by the Random Walker algorithm. The authors state that this result has been shown in the original Random Walker work, yet is little known, and their proof is different and more self-contained, not relying on potential theory. Excitingly, their way of proof yields a novel interpretation of the Random Walker / Probabilistic Watershed probabilities in terms of the triangle equation on effective resistances between graph nodes. Last but not least the authors relate their theory to the Power Watershed, again yielding an exciting new insight, namely that for parameters beta 2 and alpha towards infinity, the latter computes marginals over all seed-separating *maximum* spanning forests (i.e.

Predicting the spatiotemporal variation in streamflow along with uncertainty quantification enables decision-making for sustainable management of scarce water resources. Process-based hydrological models (aka physics-based models) are based on physical laws, but using simplifying assumptions which can lead to poor accuracy. Data-driven approaches offer a powerful alternative, but they require large amount of training data and tend to produce predictions that are inconsistent with physical laws. This paper studies a constrained reasoning and learning (CRL) approach where physical laws represented as logical constraints are integrated as a layer in the deep neural network. To address small data setting, we develop a theoretically-grounded training approach to improve the generalization accuracy of deep models. For uncertainty quantification, we combine the synergistic strengths of Gaussian processes (GPs) and deep temporal models (i.e., deep models for time-series forecasting) by passing the learned latent representation as input to a standard distance-based kernel. Experiments on multiple real-world datasets demonstrate the effectiveness of both CRL and GP with deep kernel approaches over strong baseline methods.

Dementia, a prevalent neurodegenerative condition, is a major manifestation of Alzheimer's disease (AD). As the condition progresses from mild to severe, it significantly impairs the individual's ability to perform daily tasks independently, necessitating the need for timely and accurate AD classification. Machine learning or deep learning models have emerged as effective tools for this purpose. In this study, we suggested an approach for classifying the four stages of dementia using RF, SVM, and CNN algorithms, augmented with watershed segmentation for feature extraction from MRI images. Our results reveal that SVM with watershed features achieves an impressive accuracy of 96.25%, surpassing other classification methods. The ADNI dataset is utilized to evaluate the effectiveness of our method, and we observed that the inclusion of watershed segmentation contributes to the enhanced performance of the models.