Empowering Power Outage Prediction with Spatially Aware Hybrid Graph Neural Networks and Contrastive Learning
Authors: Xuyang Shen
Zijie Pan
Diego Cerrai
Xinxuan Zhang
Christopher Colorio
Emmanouil Anagnostou
Dongjin Song
Venue: Accepted by TMLR ()

Abstract: Extreme weather events, such as severe storms, hurricanes, snowstorms, and ice storms, which are exacerbated by climate change, frequently cause widespread power outages. These outages halt industrial operations, impact communities, damage critical infrastructure, profoundly disrupt economies, and have far-reaching effects across various sectors. To mitigate these effects, the University of Connecticut and Eversource Energy Center have developed an outage prediction modeling (OPM) system to provide pre-emptive forecasts for electric distribution networks before such weather events occur. However, existing predictive models in the system do not incorporate the spatial effect of extreme weather events. To this end, we develop Spatially Aware Hybrid Graph Neural Networks (SA-HGNN) with contrastive learning to enhance the OPM predictions for extreme weather-induced power outages. Specifically, we first encode spatial relationships of both static features (e.g., land cover, infrastructure) and event-specific dynamic features (e.g., wind speed, precipitation) via Spatially Aware Hybrid Graph Neural Networks (SA-HGNN). Next, we leverage contrastive learning to handle the imbalance problem associated with different types of extreme weather events and generate location-specific embeddings by minimizing intra-event distances between similar locations while maximizing inter-event distances across all locations. Thorough empirical studies in four utility service territories, i.e., Connecticut, Western Massachusetts, Eastern Massachusetts, and New Hampshire, demonstrate that SA-HGNN can achieve state-of-the-art performance for power outage prediction.

Published in Transactions on Machine Learning Research (04/2026)
Empowering Power Outage Prediction with Spatially Aware Hybrid Graph Neural Networks and Contrastive Learning
Xuyang Shen University of Connecticut
mayong.shennuucoon.edl
Zijie Pan
University of Connecticut
Diego Cerrai University of Connecticut
Xinxuan Zhang
Western Connecticut State University
Christopher Colorio
Eversource Energy
Emmanouil N. Anagnostou
University of Connecticut
Dongjin Song University of Connecticut
Reviewed OpenReview: petps://openrevieet net/ forum? id- VF5FDY+0sU
Abstract
Extreme weather events, such which exacerbated by climate change, frequently cause widespread power outages. These outages halt industrial operations, impact communiliess, damage critical infrastructuure pro- foundly disrupt economies, and have far-reaching effects across various sectors. To mitigate those effects, the University of Connecticut and Eversource Energy Center have developed an outage prediction modeling (OPM) system to provide pre-emptive forecasts for elec- trie distribution networks before such weather events occur. However, existing predictive models in the system do not incorporate the spatial effect of extreme weather events. To this end, develop Spatially Aware Hybrid Graph Neural Networks (SA-HGNN) with contrastive learning to enhance the OPM predictions for extreme weather-induced power outages. Specifically, we first encode spatial relationships of both static features (e.g., land cover, infrastructure) and event-specific dynamic features (e.g., wind speed, precipitation) via Spatially Aware Hybrid Graph Neural Networks (SA-HGNN). Next, we leverage con- trastive learning handle the imbalance problem associated with different types of extreme weather events and generate location-specífic embeddings by minimizing intra-event dis- lances between similar locations while maximizing inter-event distances across all locations. Thorough empirical studies in four utility service territories, i.e., Connecticut, Western Mas- sachusetts, Eastern Massachusotts, and New Hampshire, demonstrate that SA-HGNN can achieve state-offthe-arl performance for power outage prediction.
storms, hurricanes, snowstorms, and ice storms,

---

Published in Transactions on Machine Learning Research (04/2026)
1 Introduction
Power outages caused by severe weather events, such as hurricanes, snowstorms, and heavy rainfall, pose significant risks to modern society by disrupting critical infrastructure and essential services across sectors like healthcare, transportation, and finance. In the United States, weather-related power outages cost the oconomy an estimated $18 to $70 billion annually, with the frequency and severity of billion-dollar disasters steadily increasing over the past two decades (Campbell 2012 Smith 2020). These outages can result in significant. economic losses and, in extreme cases, loss of life (Flores et al. 2022; Dominianni et al. 2018). For instance, over 15 months between 2011 and 2012, three major storms in Connecticut caused extensive outages, affecting hundreds of thousands of people and resulting in considcrable cconomic losses. Similarly, Hurricane Sandy inflicted severe damage on New York, causing prolonged service disruptions and operal ional challenges for utility companies (Yang et al. 2020 Udeh et al. 2024). Therefore, accurate forecasting of the magnitude and spatial distribution of weather-induced power outages is essential to mitigate these impacts. Such forecasts can inform evacuation strategies, improve storm response planning, and guide investments in
reinforcing and upgrading electrical infrastructure (Baembitov et al. 2023: Cerrai et al. 2019a b D' D'Amico
et al. 2019
Although outage prediction has received increasing attention recently, existing approaches still suffer from critical limitations. Traditional machine learning methods, such as ensemble models, have shown promising
results by improving prediction accuracy and robustness (Natoghi et al.] 2014 Wanik et al. 2015 He ct al.
2017: Cerrai et al.) 2019a c Udeh et al., 2024). However, they treat each location independently and do
not explicitly model spatial relationships between geographic regions, which are crucial for understanding
the spatial effect of storm impacts. Although convolutional and recurrent neural networks, including their
advanced variants (Han et al.) 2022 Sun et al., 2022), can capture spatiolemporal dependencies in grid- structured data such as radar images weather maps, their dependency on rigid Euclidean grids limits their applicability to sensor networks or outage datasets defined on irregular geographic layouts. More recently, graph-based approaches have emerged as powerful tools for modeling non- -on-Euclddaan spatial dependencies, allowing each node to represent a spatial location. Nevertheless, existing GNN-based methods (Kipl & Welling 2016 Hamilton et al., 2017a Owerko et al.] 2018 Defferrard et al.] 2016) often consider only fixed spatial structures and lack the flexibility to model event-specilic spatial dynamics. Furthermore, most prior work overlooks the inherent imbalance in outage datasets, where low- cow-impact events dominate and high-impact events, though rare, carry greater operational significance and value. These gaps motivate the development of a more spatially adaptive and representation-disciiii
approach for power outage prediction.
To this end, we propose Spatially Aware Hybrid Graph Neural Networks (SA-HGNN) that leverage con- trastive learning to enhance outage prediction models (OPM) for extreme weather-indueed power outages. Specifically, we first construct fixed adjacency matrix to encode the spatial relationships of static features and design a dynamic graph learning module to capture and infer complex, evolving spatial dependencies across different events. We then develop SA-HGNN to integrate spatial dependencies derived from both static and dynamic features. To address the imbalance issuc associated with extreme weather events of vary- ing severity, we incorporate a contrastive learning strategy to generate location-specific embeddings. These embeddings are obtained by minimizing intra-event distances between similar locations while maximizing inter-event distances across all locations, resulting in more discriminative representations for each location. Our main contributions include:
We introduce SA-HGNN, a novel graph-based deep learning model that can effectively integrate both static and dynamic spatial dependencies to enhance outage prediction for extreme weather events.
We develop a dynamic graph learning module that can capture and infer complex, evolving spatial relationships across different locations, addressing the limitations of existing methods that rely solely on fixed spatial structures.
To tackle the imbalance issue in outage datasots, we adopt a contrastive learning stratogy that learns location-specific embeddings by minimizing intra-cvent distances between similar locations while maximizing inter-event. distances across all locations.
2

---

Published in Transactions on Machine Learning Research (04/2026)
Our studies in four utility service territories, i.e., Connectieut, Western Massachusetts, Eastern Massachusetis, and New Hampshire, demonstrate that SA-HGNN can achieve state-of-the-art per- formance for power outage prediction.
2
Related work
In recent years, machine learning methods have been incrcasingly employed to address the challenges of forecasting weather-related power outages (Watson el al.
2022
Garland et al. 2023). One widely adopted
approach is ensemble learning. For instance, (Nateghi et al.
2014
2014) utilized Random Forest (RF) to predict employed tree- based models to forecast power
outages caused by tropical cyclones, while (Wanik et al.
2015
outages in the New England region. He and Cerrai leveraged
Bayesian additive regression trees (BART)
2019a|e) whereas (Udeh et al., 2024) explored RF for predicting storm-induced power outages in the New York State region. These ensemble approaches help mitigale overfilling and enhance prediction accuracy by leveraging diverse decision paths and combining the outputs of multiple decision trees. However, they do not explicitly incorporate or exploit spatial information, which critical for outage prediction as extreme weather events (c.g., heavy rainfall, snowstorms) typically have strong spatial effects.
predict outages resulting from storm events {He et. al.
2017
Cerrai et al.
Convolutional and recurrent neural networks (CNNs and RNNs), including advanced hybrid architectures like ConVLSTM, have been widely adopted to capture spatiotemporal relationships in targeted datasets, including radar images and weather sequences. These models are particularly effective at capturing both spatial and temporal dependencies, which are critical for applications such as short-term weather forecast- ing. For instance, (Han et al.) 2022) demonstrated the use of a U-Net model for convective precipitation prediction, while (Sun et al. 2022) applied a 3D-ComYLSTM model for storm nowcasting, showcasing the strengths of these architectures in handling complex weather data. However, CNNs are inherently designed for processing data with a regular rigid structure, such as images and time scries. This makes them less suited for sensor network data used in weather and outage monitoring, with their utility in outage prediction still underexplored.
Recently, the development of graph neural networks Kipp & Welling 2016 Hamilton et al. 2017 7a provides promising sonutions to incorporate the complex spatial relationships of outage data at different locations, where each node corresponds to a spatial location and contains both static features (e.g., land cover, infras- tructure) as well as dynamic features (wind speed, precipitation, etc). (Owerko et al. 2018) explored various GNN architectures, including ChebNet (Defferrard et al., 2016), to predict brather-induccoe power outages. More broadly, recent. graph-based multitask learning studies have shown that modeling task affinity can improve representation learning and knowledge sharing across related graph prediction problems, including through higher-order task interactions and gradient- based task affinity cstimation (Li et al. 2023 2024).
These works strengthen the connection between outage forecasting and the broader graph machine learning literature. However, existing techniques stlll often fall short in simultaneously integrating static and dynamic features while modeling event-specific spatial dependencies across diverse locations.
In addition, recent advances in contrastive learning have shown promise improving robustness under data imbalance and distribution shifts. For example, Corntet-N-Contrast (Zhang et al. 2022a) encourages repre- sentations that distinguish true predictive signals from spurious correlations. This perspective is relevant to outage prediction, where rare but high-impact events may induce substantial imbalance and spurious pat- terns. However, such methods are not specifically designed for structured spatiotemporal outage forecasting with dynamic spatial dependencics.
3 Problem statement
We aim to predict location-speeific power outage counts during extreme weather events within a given ser- vice territory, i.e., different regions in New England. For each specific territory, we observe a collection of m historical extreme weather events. In every event, a fixed set of N goographical locations moni- tored, and each location is described by feature vector that combines both static and dynamic attributes. Static features capture time-invariant location characteristics, such as topography, land cover, vegetation,
3

---

Published in Transactions on Machine Learning Research (04/2026)
Traeiig Trakingg Testing
Space
Postbre Pair Negetice
Dynamic Graph Learning Module
Dynamic Knowledge
Inferred Strutural Knowledge
Contrastive Learning
Weather Gwants
DGCN
DGCN
Weather Event Feature
S00N
S0CN
Outage Prediction
Extream Weather Events
Hybrid GCN Module
Static Strutural
Knowledge
The dynamic graph learning module learns event-specific adjacency matrices guided by external structure, which used in the dynamic graph convolution. The hybrid graph convolution includes a dynamic GCN (DGCN) for capluring event-specific pallerns and static GCN (SGCN) that aggregates information from a shared graph. Their outputs are concatenated to form location- wise embeddings. Contrastive learning further refines these embeddings by aligning similar locations within events and separating dissimilar ones across events. A regression module then projects the fused embeddings predict outage values.
Figure 1: The framework of SA-HGNN.
and infrastructure properties, which remain fixed across events. Dynamic features capture event-specific metcorological conditions, such as wind speed, procipitation, temperature, and soil moisture observed dur- ing a particular extreme weather event. The complete feature description is provided in Appendix A This separation enables event conditioned representation learning by decoupling persistent spatial context from transient weather-driven effects.
Formally, for an event k, let X E NXF denote the input feature matrix, where each row corresponds to a location and is the number of features per location. The corresponding outage count vector is denoted by Ys RN, where Ye. represents the observed outage count at location i during event k. Collectively, the data for a territory can be viewed as an event-wise tensor X E R= Each event is modeled graph Gg (V, Ex), where the node set = (ui,..., uN} corresponds the fixed locations, and edges represent spatial functional dependencies between locations, and E, defines the edges based on spatial functional relationships. During training, we have access to evenl-specific adjacency matrices A₁ E RR x construeted from external structural knowledge, which are used to guide the learning of spatial relationships. At inference time, however, the adjacency matrix is not assumed to be known; instead, the model infers an event event-specific graph structure A directly from the input features X₃.-
Given an event-level input Xg, a graph neural network learns spatially informed node representations and predicts outage counts as
(1) where As denotes the learned adjacency matrix inferred from Xx. and 0 represents the learnable model parameters. The training objective to minimize the discrepancy between the prodicted outage counts Y. and the ground-truth observations Yς across events.
Y faNN Au:
4 Methodology
In this section, we introduce the general framework of our proposed model Spatially Aware Hybrid Graph Neural Networks (SA-HGNN) with dynamic graph inference and contrastive learning in detail. The overview of SA-HGNN is illustrated in Figure I SA-HGNN contains three key components: Dynamic Graph Learn- ing, Hybrid Graph Convolutional Module, and Contrastive Learning Module. To capture latent spatial relationships among locations across different events under dynamically evolving extreme weather condi- tions, the Dynamic Graph Inference Module (Subsoction 4.1} learns and infers a dynamic adjacency matrix for each event, incorporating external structural knowledge to guide the learning process. To incorporate both static and dynamic features, design Hybrid Graph Convolutional Module (Subsection 4.2 that
4

---

Published in Transactions on Machine Learning Research (04/2026)
separately processes learned static and dynamic neighbor information through two distinct branches, en- abling the model to capture more meaningful spatial dependencies and adapt to varying weather-induoed outage patterns. Lastly, the Contrastive Learning Module (Subsection 4.3) is designed to overcome the im- balance issue, enhance generalization, and improve the model's ability to distinguish outage patterns across different extreme weather events. By incorporating intra-event and inter-event contrastive learning, the module refines node embeddings by ensuring that locations with similar outage behaviors under the same weather event are closely aligned, while those experiencing different outage impacts across events remain distinct. This distinction is crucial for capturing the variability of outage patterns under different weather conditions, allowing the model to better adapt to unseen events. Projection layers are applied to the learned node embeddings to the desired output dimension for the final outage predictions. The following subsections provide details of these three key components.
4.1 Dynamic Graph Learning Module
For extreme weather events, spatial dependencies among locations vary significantly across events due to the dynamic and localized nature of weather conditions. Relying solely on a fixed, pre-defined graph constructed from static geographic proximity or infrastructure information is therefore insufficient, as such relationships may fail to reflect event-specific interactions induced by extreme weather. To accurately model outage patterns, it is crucial to account. for both static relationships, which driven by persistent geographic and infrastructural charactoristics, and dynamic spatial interactions that emerge uniquely under cach event. These dynamic interactions may arise from shared exposure to high wind fields, correlated soil moisture conditions, or aligned storm trajectories, and play a key role in shaping event-level outage propagation (Luu
ct al.
2023 Ye et al. 2022 Zhang et al. 2024
Inspired by prior work on adaptive adjacency learning (Wu et al. 2020 Shi el al., 2019 Wu el al. 2019
Bai et al., 2020 Chen et al. (021)), we introduce a dynamic graph learning module that constructs an event- specific adjacency matrix conditioned on observed node features. This formulation avoids costly and manual graph construction, which would otherwise require event-specific engineering and detailed domain knowledge for each extreme weather scenario. Instead, the learned adjacency enables the model to adaptively infer spatial dependencies that generalize across unseen events within the same service territory. During training, the learned adjacency is further guided by external structural knowledge (Pan et al. 2024 which provides a weak prior on spatial dependencies and regularizes the graph inference process (see Section 1.1.1 for details).
This module dynamically adjusts the graph structure based on the unique weather features of each event, capturing evolving spatial dependencies that critical for accurately modeling outage patterns and enhanc- ing prediction performance. Formally, the adjacency matrix As for each event k is learned via the following formulation:
A = Saf (tanh X2 W1) tanh (W] xx
for i E 21, N):
idx = arg topk (a [d]
As[i, { if E idx
0 othrewise
The learnable weight matrices W1 E Fxd and W E Fxd project the feature space into a latent dimension d. The use of tanh activation ensures bounded transformations, while the Soft operation normalizes the learned adjacency matrix, making it suitable for graph convolution. Although the subsequent top-k operation determines the final sparse graph structure, the softaax normalization plays an important role during training by constraining the adjacency scores to comparable scale, preventing uncontrolled growth of bilinear similarities, and ensuring stable gradient propagation when jointly optimizing the adjacency learning module with downstream prediction and regularization objectives. The function arg topk(-) retrieves the indices of the top-k largest values within a vector, ensuring that only the most relevant connections are retained in the learned graph structure.
The dynamic graph learning equation is reasonably designed. First, the dynamic nature of extreme weather events causes spatial relationships to evolve, making static adjacency matrix insufficient. By constructing
5

---

Published in Transactions on Machine Learning Research (04/2026)
Ag dynamically for each event, the model can capture how weather features, like wind speed and soil moisture, influence spatial dependencies specific to that event. For instance, during storm, geographic locations in the path of high wind speeds may form stronger dependencies, which are dynamically reflected in As. Additionally, the bilinear operation tanh(X, Wi)-tani -tanh( x encodes pairwise interactions between node Teatures. This approach effective in datasets where features vary significantly across events and locations, allowing the model to identify how one location's 's features influence another.
To guide the learning of dynamic adjacency matrices, incorporate external structural priors during train- ing. The regularization is applied to the contimuous adjacency scores produced before top- sparsification, allowing the prior to directly shape the learned affinities through gradient-based optimization. Unlike static geographic relationships, these priors reflect how spatial dependencies evolve under varying weather condi- tions. Encouraging alignment between the inferred graph structure and event-specific priors helps mitigate the risk of learning spurious connections and improves the model's adaptability to diverse extreme weather scenarios. To achieve this, we impose a regularization loss that minimizes the mean squared error between the learned adjacency matrix Ås and the prior adjacency matrix Ag:
Ladj
1 N2
Σ
Ac[i, - Ar(t.01| (
(2)
Furthermore, the integration of this module into the graph convolutional network allows for end-to-end learning. The parameters Wi and W2 are jointly trained with the model's other components, ensuring that the learned adjacency matrix aligns with the outage prediction task. This alignment is critical maximizing the utility of the graph structure for capturing spatial dependencies that directly impact outages.
4.2 Hybrid Graph Convolutional Module
We adopt multi-layer Graph Convolutional Network (Kipf & Welling, 2016 with residual connections spatial embedding block to effectively aggregate neighborhood information. GCNs capture complex relational dependencies between nodes by leveraging message passing and neighborhood aggregation, following the layer-wise propagation rule: H = (D 1/2 1/2 H WW)).
(3)
where = A + IN the adjacency matrix with added self-connections, D==E, Au is the degree matrix, W()) is the trainable weight matrix at layer I, and a--) a non-lincar activation function such as ReLU, The initial node representation is ( X, where X denotes the input. feature matrix.
Next, we design novel hybrid encoding architecture tailored for extreme weather-induced outage prediction based on the standard GCN spatial embedding block. Unlike traditional graph-based based approaches that treat all input features uniformly (Kipf & Welling, 2016 Velickovic et al., 2017). our framework separates the processing of static and dynamic features to capture distinct spatial relationships. Specifically, we employ two parallel GCN embedding channels:
The static channel uses a fixed adjacency matrix across all events, modeling persistent goographic or infrastructural relationships. It takes as input the static feature matrix (s).
The dynamic channel constructs an event-specific adjacency matrix Å to reflect the evolving spatial dependencies under different weather conditions. It. processes the dynamic feature matrix x(d) for each event k. k
The outputs of both channels are concatenated to form a unified node embedding, which is then passod through a two-layer MT.P to generate the final prediction. This hybrid structure enables more context-aware message passing and improves model performance scenarios characterized by heterogeneous and evolving spatial dependencies.

---

Published in Transactions on Machine Learning Research (04/2026)
4.3 Contrastive Learning Across Intra and Inter-Event
Accurale power outage prediction during extreme weather events further requires modeling robust and gener- alizable spatial representations that capture both local dependencies and global variations across events (Sun ett al., 2020 Hassani & Khasahmadij 2020). However, due the inherent imbalance in outage datasets, the learned representations may become biased toward dominant outage patterns, limiting the model's ability to generalize. To consider this, we develop a contrastive learning module that enhances the spatial repre- sentations learned by the hybrid GCN module to further distinguish similar and dissimilar locations within individual events and across different events (Zhou et al., 2020 Zhang et al. 2023 Velickovic et al. 2019; Zhang et al. 2022b Xie et al. 2022). By leveraging both intra-event and inter-event contrastive learning strategics, this module improves the quality of the learned representations and ensures the modcl's ability to generalize across diverse weather conditions. To caplure meaningful spatial dependencies within and across different events, we adopt contrastive learning framework that integrates intra-event and inter-event objectives.
Intra-event contrast. Within each event. k, the learned dynamic adjacency matrix Å defines the spatial relationships among different locations. We treat node pairs connected by an edge in As as positive pairs, reflecting strong local dependencies under specific weather conditions. In contrast, unconnected node pairs within the same event are considered negative pairs. Let 2 denote the embedding of node i in event k. The intra-event contrastive objective encourages embeddings of positive pairs (2k,i, =kg) to be closer in the representation space, while pushing negative pairs apart. This promotes spatial coherence and localized discriminative learning.
Inter-event contrast. Extreme weather events often exhibit distinct spatial patterns. To improve general- ization across events, we introduce an inter-event contrastive objective that explicitly contrasts embeddings of nodes from different events. Specifically, for each node Ækyú, we randomly sample a node a from an- other event k' * k form an inter-event negative pair. This encourages the model to distinguish between structurally different events and avoid overfitting event-specific noisc
Overall contrastive objective. The final contrastive loss integrates both intra-event and inter-event components and is defined as:
exp (sim =k.i)/T) L. = - log ElEPLUN UN exp (sim (2k, (2k,i 2/)T)
(4)
where sim(...) denotes cosine similarity between two embeddings; p is the set of positive indices for an- chor node žk,ii Nintra and Winter denote intra-cvent and inter-event negative scts, respectively, and is a lemperature scaling parameter.
By optimizing this contrastive loss, the model learns spatially aware and event-generalizable representations, ultimately improving the robustness and accuracy of outage forecasting across diverse extreme weather scenarios.
4.4 Optimization Objectives
To effectively optimize the designed model, we adopt the Huber loss (Barron 2019) between predicted outage counts Yr, and ground truths Yv,; the main learning objective Ep. The Huber loss is defined
1 (Ye, PE,))
if |Y -Y., <
(v. = 2 0. ((Yr, - Pr.il 18). otherwise
(5)
where a threshold parameter that balances the sensitivity to outliers. The Huber loss allows us to effectively handle predictions across wide range of weather scenarios. The total lcarning objective function
for this regression (ask consists of the forecasting objective Lpp the contrastive learning objective Ce, and the learning dynamic adjacency matrix objective Ladji
Liotal Lp + XL, + +-aadj
(6)
where À 2 0 and 7 2 0 are hyperparameters determined by grid search the training set.
7

---

Published in Transactions on Machine Learning Research (04/2026)
5 Experiment
5.1
Experiment Setup
5.1.1
Datasets and Preprocessing
Table 1: The detailed statistics of four datasets
Datasets
Events
Locations
Feature Length
Output Length
Connecticut
294
815
390
New Hampshire
227
1022
390
Western Massachusetts
271
312
390
Eastern Massachusetts
231
383
390
To evaluate the effectiveness of the proposed SA-HGNN to predict power outages during extreme weather events, we compare SA-HGNN with bascline methods over four utility service territorics of Eversource, i.e., Connecticut, Western Massachusetls, Eastern Massachusetts, and New Hampshire. The detailed statistics of benchmark datasets are summarized in Table
The datasets include weather variables, utility infrastructure, land cover, vegetation, and historical outage data for each storm, modeling power disruptions across uniformly distributed locations within each state. Details feature sources provided below.
Weather: Weather imput is the largest source of uncertainty in the outage predictions (Gikemaa 2018
The weather data is obtained from 48-hour simulations using version 3.8.1 of the Advanced Weather Research and Forecasting (WRF) model (Powers et al., 2017 Skamarock et al., 2008), with a 4-km horizontal grid spacing over the northeastern United States. Initial and lateral conditions were derived from the North American Mesoscale (NAM) Forecast System at 12-km spatial resolution.
Utility Infrastructure: The utility infrastructure information of Eversource Energy contains multiple lypes of assets, including electric fuses, reclosers, and poles. These serve as key explanatory variables because outages are recorded at the asset level, and the risk of having a reported outage is directly proportional to the number of assets.
The U.S. Geological Survey (USGS) provided National Land Cover Database (NLCD) prod- ucts, detailing vegetation and urbanization patterns. Since tree interaction with overhead lines during storms is a major cause of outages, we incorporated tree-related land cover variables, including the percentages of miscellaneous forests, deciduous forests, and developed areas.
Land Cover:
The complete extreme weather database contains 390 distinct numerical features associated with outage occurrences. Incorporating all features in a higl-dimensional space introduces challenges that degrade model performance and interpretability. The curse of dimensionality leads to data sparsity, poor generalization, and overfitting, while redundant or irrelevant features add noise, increase computational costs, and complicate model training (Rice et al., |2000] Bejani Ghatee 2021). To address these issues and enhance model efficiency, applied the Pearson correlation coeflicient to quantify the linear relationship between each feature Xm and the outage count Y. The Pearson correlation coefficient rx..Y y is defined
TX..Y ΣN (Xm.s - -mm) (Y, (Y,- -8)
(7)
VIN (Xms -xm)= 12VV' E (Yr 2)
where Xm.i is the value of feature Xm for location i, Xm, the mean of feature Xm across events, Y is the outage count for location i, and Y is the mean outage count. Based on the computed correlation values, we selected the top 50 features with the highest corrclation to outage counts. Among the selected variables, 20 features are static, representing location-specific characteristies that remain static over time, while the remaining 30 features are dynamic, capturing temporal variations across different. events. The
8

---

Published in Transactions on Machine Learning Research (04/2026)
complete selected feature description is provided in Appendix A We construct two adjacency matrices based these two types of features and use them external structural knowledge. The static adjacency matrix is derived from geographic distances, where each location is connected to its eight nearest neighbors, forming a fixed graph structure that remains consistent across all events. In contrast, the dynamic adjacency matrix caplures event-specific spatial relationships that may vary under different weather conditions. To construct this matrix, we compute the Pearson correlation coefficients between dynamic features mcasured during each event. For given location, identify the eight locations with the highest Pearson correlation coefficients and establish eight edges between them. As result, each event in our dataset is associated with unique dynamic adjacency matrix, which serves as external structural knowledge to guide the dynamic. graph learning module in Section 4.1
5.1.2 Evaluation Protocols and Metrics
Given the critical importance of every extreme weather event, we adopt a leave-one-out evaluation strategy to assess model performance (Yang al.] 2021). For example, in the Connecticut dataset, which consists of 294 extreme weather events, we conduct 294 training and evaluation loops, cach time leaving out single event for evaluation while training on the remaining 293 events. A similar leave-one-out procedure is applied to datasets from Western Massachusetts, Eastern Massachusetts, and New Hampshire.
We evaluated the performance of outage prodictions by using absolute error (AE), absolute percentage error (APE), mean absolute percentage error (MAPE), centered root mean square error (CRMSE), and R-square (r²). The definitions of evaluation metrics are detailed in Appendix B
5.1.3 Baseline Model
To establish a comprehensive bascline for our proposed method, we conducted a thorough comparison against
7 models, which we have categorized into three groups: traditional machine learning methods: Random Forest
[Breiman 2001): XGBoost (Chen & Guestrin 2016); GNN-based methods: ChebNet (Tang et al.
2024
Graph Attention Networks (GAT) (Velickovic et al. 2017), GraphSAGE (Hamilton et al. 2017b),
Graph
Isomorphism Network (GIN) (Xu al.) 20188: tabular foundation model: TabPFN (Hollmann et al.
2025
We provide detailed descriptions of each baseline below:
Random Forest (Breiman 2001): This method combines multiple decision troes using bagging
lo improve predictive performance and reduce overfitting, making it robust for handling high- dimensional data and capturing complex relationships.
XGBoost (Chen & Guestrin 2016):
This is a gradient boosting framework that builds decision trees sequentially, optimizing for speed and accuracy.
Graph Attention Networks (GAT) (Velickovic et al. 2017 It leverages attention mechanisms to dynamically assign weights to neighboring nodes, enabling the model to focus on the most relevant parts of the graph for learning node embeddings.
GraphSAGE (Hamilton et al. 2017b): The method generates node embeddings by sampling and aggregating features from a fixed-size neighborhood, enabling efficient and scalable learning on large graphs.
Graph Isomorphism Network (GIN) Xu et al. 2018 GIN achieves strong expressive power by using a sum aggregation function and learnable weights, making it capable of distinguishing different graph structures more effectively than traditional GNNs.
TabPFN (Holmman et al. 2025 It is pre-trained transformer-baser deep learning foundation model for regression and classilication on tabular data.
9

---

Published in Transactions on Machine Learning Research (04/2026)
Table 2: Extreme weather outage prediction results. Best results are highlighted in bold, and the second best results are underlined.
Datasets
Metric
SA-HGNN
Random Forest
XGBoost
GAT
GIN
GraphSAGE
TabPFN
AE q25
25.00
84.50
48.00
31.50
33.00
32.00
31.25
AE q50
62.50
199.00
136.00
78.00
63.50
77.50
74.00
APE q25
23.09
45.75
32.10
29.65
24.73
28.57
24.97
CT
APE q50
49.36
109.62
64.61
55.32
52.72
54.69
52.48
MAPE
52.77
127.15
155.87
65.52
65.98
67.87
79.41
CRMSE
851
1726
1323
1598
1755
1761
1590
Ra
0.79
0.23
0.49
0.25
0.10
0.12
0.26
AE q25
12.50
37.00
26.00
15.00
12.00
13.00
13.00
AE q50
29.00
83.00
58.00
27.00
32.00
31.00
31.00
APE q25
23.75
41.42
28.34
20.14
21.29
22.16
23.40
NH
APE q50
40.70
88.94
70.24
41.30
46.75
42.31
48.45
МАРE
45.66
190.77
142.54
52.34
51.38
59.89
51.51
CRMSE
364
359
360
388
389
379
395
R²
0.09
0.11
0.11
0.04
0.04
0.01
0.07
AE q25
5.00
10.00
4.00
4.50
4.00
5.00
AE q50
9.00
26.00
9.00
10.00
9.00
10.00
APE q25
25.54
32.44
31.15
25.00
26.79
25.89
25.90
WMA
APE q50
48.65
90.91
69.23
47. .6
50.00
46.67
48.28
MAPE
55.87
177.64
143.29
55.76
54.52
51.81
54.98
CRMSE
92
116
110
111
116
116
112
R2
0.32
0.09
0.02
0.10
0.08
0.08
0.02
AE q25
11.00
28.00
21.00
12.00
11.00
12.00
12.50
AE q50
21.00
55.00
25.00
25.00
25.00
23.00
APE q25
22.02
28.87
23.75
21.21
20.24
22.78
EMA
APE g50
39.02
91.76
43.96
41.67
45.16
40.91
MАPE
50.19
170.57
144.31
60.09
56.61
64.14
54.33
CRMSE
433
566
564.26
550
575
547
522
R²
0.43
0.03
0.04
0.09
0.10
0.09
0.17
5.2 Main Results
Table shows the full outage prediction results on all four datasets: Connecticut, New Hampshire, Western Massachusetts, and Eastern Massachusetts. While SA-HGNN consistently achieves competitive or superior performance across all four datasets, the magnitude of improvement varies across regions. In particular, the most significant gains are observed in Connecticut, whereas improvements in other regions are more moderate. This variation is closely related to differences in spatial dependency structures across regions, which directly affect the extent to which spatial modeling can improve prediction performance. In particular, Connecticut exhibits stronger and more coherent inter-location dependencies during extreme weather events, allowing SA-HGNN to effectively leverage dynamic graph structures. Thus the improvement of SA-HGNN in terms of MAPE is the most significant, improving by 19. 19.45% compared to the second best method. Meanwhile, it achieves the best (lowest) AE Q50 and APE Q50, showcasing clear advantage over three other bascline models in Figure 2 In contrast, other regions tend to exhibit more localized or fragmented oulage patterns, which reduce the benefit of modeling long-range spatial interactions. Importantly, even in these cases, SA-HGNN remains competitive with existing approaches and does not degrade performance, demonstrating robustness across diverse regional characteristies. SA-HGNN outperforms ensemble learning methods methods such Random Forest and XGBoost, graph- models including GAT, GIN, and GraphSAGE, well the state-of-the-art tabular foundation model TabPFN. The model achieves the
10

---

Published in Transactions on Machine Learning Research (04/2026)
Actual vs Predicted
Actual vs Predicted
Actual vs Predicted
Actual vs Predicted
y=x
yex
y=x
Prodicted Outage
Predicteo Outage
Predicted Outage
101
39
13
19
330
30"
Actual Outage
Actual Outage
Actual Outage
Actual Outage
(a) XGBoost
(b) GraphSage
(c) TabPFN
(c) SA-HGNN
Figure 2: Actual outages vs. predicted outages comparison of four models on Connectieut extreme weather data.
highest R² scores in multiple regions, reaching 0.79 in Connecticut and 0.43 in Eastern Massachusetts, indicating superior predictive accuracy, Additionally, SA-HGNN demonstrates the lowest CRSME values, showing improved robustness in capturing outage patterns. These results confirm that SA-HGNN effectively models spatial dependencies and dynamic weather impacts, leading to more accurate outage forecasts.
Our experimental results show that ensemble learning methods, such as Random Forest and XGBoost, yield suboptimal performance in outage prediction. This is primarily because they treat each location independently, ignoring critical spatial correlations and dynamic interactions that shape outage patterns during extreme weather events. In contrast, graph-based models like GAT and GIN generally perform better by leveraging graph structures to model spatial dependencies. However, their aggregation mechanisms are often fixed, and their adjacency matrices are typically predefined, limiting their adaptability to event-specific spatial dynamics. For instance, while GAT assigns attention- based weights to neighboring nodes, it does not dynamically adjust the graph structure to reflect evolving event-specific relationships.
SA-HGNN improves outage prediction by effectively capturing the unique spatial dependencies and event- specific dynamics of extreme weather data. Unlike traditional models, SA-HGNN processes static and dynamic features separately, ensuring better representation of both constant infrastructure-relatee attributes and evolving weather conditions, dynamic adjacency matrix, which adapts to each event and captures event-specific spatial relationships crucial for predicting outages under varying weather conditions. Additionally, the contrastive learning module enhances the model's ability distinguish intra-event neighbors from inter-event non-neighbors, leading more robust and generalizable node embeddings. This evident in the t-SNE visualization, where embeddings with similar outage counts form well-defined clusters after contrastive learning, highlighting its effectiveness in learning meaningful representations as shown in Figure 3l And observe that regions with stronger inter-location correlations tend to benefit more from spatially adaptive modeling, which is consistent with the design of SA-HGNN and explains the variation in performance gains across datasets.
demonstrated in Section 5.3 A key advantage of SA-HGNN is its
5.3 Ablation Study
In this section, conduct an ablation study the Connecticut extreme weather dataset to assess the impact of key components on model performance as shown in Table Our analysis highlights three critical modules that contribute to SA-HGNN's effectiveness:
w/o HGNN: SA-HGNN without the hybrid graph convolution module, which separates the processing of dynamic and constant neighbor information into two distinct branches. In this configuration, the module is replaced with a single graph convolution branch that exclusively considers static neighbor information. With this setting, the performance consistently perform worse than SA-HGNN. This is because during extreme
11

---

Published in Transactions on Machine Learning Research (04/2026)
Octage
Gutape Counts
Outege Counts
(5.53
100
210
(a) GraphSAGE
(b) GAT
(0) SA-HGNN
Figure 3: Comparison of learned location embeddings across different methods on the Connecticut dataset.
weather events, the outage of one location only only rely on its geographical neighborhood locations but also depend on the dynamic weather conditions across different locations.
w/o DSK: SA-HGNN without dynamic structural knowledge (DSK) guiding the learning process of the dynamic adjacency matrix. Instead, the model derives the dynamic adjaceney matrix directly from each weather event's data, without incorporating external prior information. The absence of external dynamic structural knowledge for cach weather event restricts the model's ability to effectively capture the complex and evolving spatial dependencies that arise under different extreme weather conditions. Without dynamic graph learning module, the graph learning process struggles to generalize to new weather events. Conse- quently, the learned dynamic graphs are less informative, leading to suboptimal performance.
w/o CL: SA-HGNN without contrastive learning, where the SA-HGNN trained to generate loca- tion embeddings without explicitly grouping similar location pairs or enforcing discrimination between different types of locations. The results show that removing contrastive learning degrades model per- formance, underscoring its role in enhancing out- age prediction. addition, we visualized the em- beddings of the learned locations in eight extreme weather events using t-SNE, as shown in Figure 1 where each event. contains 815 locations. After ap- plying contrastive learning, the embeddings exhibit clear scparability and are grouped with similar out- age counts. However, the absence of contrastive learning significantly degrades the embedding structure, resulting in less distinguishable representations. By minimizing intra-event distances between similar locations while maximizing inter-event distances across all locations, contrastive learning can help overcome potential imbalance issues and improve the model's capability to capture meaningful spatial patterns.
D.1
SA-H-NNN
SA-HGNN
Figure 4: SA-HGNN CL representation comparison
5.4 Case Study
We conduct case studies two representative extreme weather events further demonstrate the effective- ness of the proposed SA-HGNN model, illustrated in Figures and Figure 5 visualizes the predicted outage distribution across the Connecticut service territory during Hurricane Irene (August 28, 2011). While GAT partially captures spatial outage patterns, GIN fails to accuralely predict high-outage locations, and XGBoost tends to overestimate outage counts in low-impact areas, resulting in notable deviations from the observed outage distribution. The outage prediction patterns indicate that SA-HGNN effoctively captures local outage patterns and aligns most closely with the ground truth distribution in Figure a)) highlighting the advantages of the proposed SA-HGNN.
12

---

Published in Transactions on Machine Learning Research (04/2026)
Table Ablation study of our proposed SA-HGNN.
Methods
SA-HGNN w/o HGNN w/o DSK
w/o CL
AE Q25
25.00
30.50
31.00
34.00
AE Q50
62.50
68.00
67.50
77.50
APE Q25
23.09
30.18
30.53
36.92
APE Q50
49.36
55.18
49.85
57.46
MAРE
52.77
53.46
52.11
56.80
CRMSE
851
1565
1405
1378
R
0.79
0.29
0.42
0.45
Figure 6 presents & second case study for severe storm event in Eastern Massachusetts (October 29, 2017). Compared Connecticut, this event exhibits sparser and more fragmented outage patterns. Despite the weaker spatial signal, SA-HGNN remains more consistent with the ground truth distribution than the baselines, demonstrating robustness across regions with differing outage characteristics.
(a) Actual Outage Distribation
(b) SA-HGNN Prediction
(c) XGBoost Prediction
(d) GIN Prediction
GAT Prediction
Figure 5: Outage prediction distribution of Hurricane Trene (August 28, 2011) in Connecticut. The ground truth total outage count is 16022 (a). SA-HGNN (b) produces the closest total prediction (14512) compared XGBoost (21385), GIN (11273), and GAT (13742).
(a) Actual Outage Distribution
(b) SA-HGNN Prediction
(c) XGBoost Prediction
(d) GIN Prediction
GAT Prediction
Figure 6: Outage prediction distribution of Storm (October 29, 2017) in East Massachusetts. The ground truth total outage count is 2520 (a). SA-HGNN (b) produces the closest total prediction (2673) compared to XGBoost (3052), GIN (2087), and GAT (2201).
5.5 Hyperparameter Sensitivity
We further examine the sensitivity of SA-HGNN the weighting coefficients À and y in Eq. (6), which control the relative contributions of the contrastive objective and the dynamic adjacency regularization, respectively. As shown in Figure 6, the model demonstrates stable performance over wide range of values for both hyperparameters. In particular, moderate values of lead to consistently low MAPE, AEg25, and APEq25, indicating that the contrastive objective enhances representation learning without overwhelming the forccasting loss. The performance also relatively insensitive to 7, and based on this analysis, we À 0.01 and y = 0.5 in the experiments, which achieve good balance between accuracy and stability. Overall, these results show that the proposed framework is robust and does not rely fine-grained hyperparameter tuning.
13

---

Published in Transactions on Machine Learning Research (04/2026)
05.0
05.0
02.5
62.5
60.0
60.0
MAPE
MAPE
52.5
52.5
50.0
50.0
AE q25
q25
30
28
APE q25
26
APE
24-
22
22-
20
10-3
10-2
30"1
10a
10a1
10-
10-1
10a
Lambda (A)
Gamma (Y)
(a) Sensitivity to
(b) Sensitivity to T
Figure Hyperparameter sensitivity analysis. We report MAPE, AE q25, and APE q25 under different values of \ and y. The x-axis is shown in log scale.
6 Limitations and Future Work
Although proposed framework SA-HGNN demonstrates promising performance in modcling both static infrastructure features and dynamic storm-level spatial dependence, several limilations remain that motivate future research.
One limitation of the current framework is that data from different service territories are treated indepen- dently, with separate models trained for each region. Although the data are collected from multiple real-world service territories, these regions exhibit inherent distributional differences in infrastructure, vegetation, and climatic conditions, lcading to feature drift across territorics. Training region-speeific models avoids informa- tion leakage and allows the model to capture local characteristics, but it does not explicitly leverage shared structure across regions, nor does it enable systematic evaluation of cross-region generalization. As result, the model's portability to utilities or service territories with substantially different characteristics has not yet been studied. Addressing such cross-region heterogeneity an important direction for future work, and recent advances in domain generalization and distribution shift modeling (Zhou et al., 2022 Long et al., 2023) could be explored to improve robustness and generalizability across heterogencous service territorics and utility systems.
Another challenge arises from the temporal granularity of the available data. Each extreme weather event in our datasct is represented by a single aggregated snapshot of metcorological and infrastructure variables, rather than temporally continuous sequence that tracks storm evolution. As a result, the constructed dynamic adjacency matrix varies across events but remains static within each event, limiting the model's ability capture the evolving propagation of storms and cascading outage dynamics over time. Recent work on spatio-temporal graph learning emphasizes the importance of jointly modeling spatial and temporal dependencies through dynamic edge adaptation (Corradini et al. 2025 In addition, recent surveys
14

---

Published in Transactions on Machine Learning Research (04/2026)
multi-modal time series analysis highlight the importance of temporally resolved and multi-source signals for modeling complex real-world systems (Jiang et al. 2025). Incorporating temporally resolved observations, such as hourly wind fields or sequential outage reports, would enable future extensions toward fully spatio- temporal graph formulations, where both node states and edge connections evolve contimuously to reflect the real-time progression of extreme weather systems.
Finally, the contrastive learning strategy improves representation discriminability, but the selection of pos- itive and negative pairs is heuristic and may not fully reflect complex inter-event dependencies. Recent advances in sulf--uper and contrastive learning for structured data have explored more adaptive sam- pling strategies and robust objectives (Jiang et al. 2024). Future rescarch could explore adaptive contrastive sampling or curriculum-beee based contrastive learning to better capture hierarchical relationships among events of varying severity.
7 Conclusion
In this study, we introduced SA-HGNN, a spatially aware hybrid graph neural network to predicter outages caused by extreme weather events. By integrating dynamic graph inference, hybrid graph convolution, and contrastive learning, SA-HGNN effectively captures both static and evolving spatial dependencies. Exper- imental results on four utility service lerritories show that SA-HGNN outperforms existing ensemble and graph-based models by adapting to event-specific graph structures and refining node embeddings.
Beyond outage prediction, this research contributes to the broader field of graph-based forecasting under dynamic conditions, with potential applications in disaster response, climate impact modeling, and resilient infrastructure planning.
Acknowledgements
This work was supported in part by the National Science Foundation under Grant No. 2338878, the NSF WISER IUCRC, and the UConn Eversource Energy Center.
References
Rashid Bacmbitov, Mladen Kezunovic, Keith A Brewster, and Zoran Obradovic. Incorporating wind mod- eling into electric grid outage risk prediction and mitigation solution. IEEE Access, 11:4373 4380, 2023.
Lei Bai, Lina Yao, Can Li, Xianzhi Wang, and Can Wang. Adaptive graph convolutional recurrent network for traffic forecasting. Advances in neural information processing systems, 33:17804-17815, 2020.
Jonathan T Barron. general and adaptive robust. loss function. Proceedings of the IEEE/CVF conference on computer vision and pottern recognition, pp. 4331 4339, 2019.
Mohammad Mahdi Bejani and Mehdi Ghatee. A systematic review on overfitting control in shallow and deep neural networks. Artificial Intelligence Review, 54:6391 6438, 2021. URL https://api.
semanticscholarr org/ Corp/ooI:p 2333356253
Leo Breiman. Random forests. Mach. Learn., 45(1):5 32, October 2001. ISSN 0885-6125. doi: 10.1023/A: 1010933404324. URL https::/doi. /0010000111 1023 / 1011///:110193344322
Richard J. Campbell. Weather-related power outages and electric system resiliency. Technical Report, :rt.aaarrrrrrrooorDDDDDD 108180774
Congressional Research Service, 2012. URL httpppp://pp...emmaaiiccoo
Diego Cerrai, Md Abul Ehsan Bhuiyan, Xinxuan Zhang, Jaemo Yang, Maria Frediani, and Emmanouil Anagnostou. Predicting storm outages through new representations of weather and vogetation. JEEE Access, PP:1 1, 03 2019a. doi: SAL00//ACCSS.2019.....
Diego Cerrai, Marika Koukoula, Peter Watson, and Emmanouil Anagnostou. Outage prediction models for snow and ice storms. Sustainable Energy, Grids and Networks, 21:100294, 12 2019b. doi: 10.1016/j.segaa
15

---

Published in Transactions on Machine Learning Research (04/2026)
Diego Cerrai, Peter Watson, and Emmanouil N. Anagnoston. Assessing the effects of a vegetation manage- ment standard on distribution grid outage rates. Electric Power Systems Research, 175(105909), 2019c. doi: https://doi.org// /ttp://orrr....0000//epppe000000 2019..0999.1..
Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting system. In Proceddings of the 22nd ACM SIGKDD International Conference Knowledge Discovery and Data Mining, KDD '16, pp. 785-794, New York, NY, USA, 2016. Association for Computing Machinery. ISBN 9781450342322. doi: 10.1145/200 00.114/2939672. 2939672. 2939785. URL https://doi. org/10 01155/293677.2239999
Yuzhou Chen, Ignacio Segovia, and Yulia R Gel. Z-genets: Time zigzags at graph convolutional networks for time series forecasting. In International Conference on Machine Learning, pp. 1684-1694. PMLR, 2021.
Flavio Corradini, Flavio Gerosa, Marco Gori, Carlo Lucheroni, Marco Piangerelli, and Martina Zannotti. A systcmatic literature review of spatio-temporal graph neural network models for time series forccasting and classification. arXie preprint wrXbu:2410.22877 2025.
Daniel D' D'Amico, Steven Quiring, Christopher Maderia, and D. McRoberts. Improving the hurricane outage prediction model by inchuding tree species. Climate Risk Management, 25:100193, 06 2019. doi: 10.1016/ 1.crm.019..001999
Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst. Convolutional neural netsorks on graphs with fast localized spectral filtering. Advances in neural information processing systems, 29, 2016.
Christine Dominianni, Kathryn Lane, Sarah Johnson, Kazuhiko Ito, and Thomas Matte. Health impacts of citywide and localized power outages in new york city. Environmental Health Perspectives, 126, 06 2018. doi: 10. 2554
Nina Flores, Heather McBrien, Vivian Do, Mathew Kiang, Jeffrey Schlegelmilch, and Joan Casey. The 2021 texas power crisis: distribution, duration, and disparities. Journal of Exposure Science Environmental Epidemiology, 33:1-11, 08 2022. doi: 10. 101108/44447770002-4444444
Jasmine Garland, Kyri Baker, and Ben Livneh. Weather-induced power outage prediction: A comparison of machine learning models. In 2023 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridCommm) pp. 1-6. IEEE, 2023.
S.D. Guikema. Power oulage forecasting: Methods, resulls, and uncertainly, pp. 2811 2816. 06 2018. ISBN 9781351174664. doi: 00.1201/9781331114666-333
Will Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning large graphs. In Advances in Newral Information Processing Systems, pp. 1024-1034, 2017a.
William L. Hamilton, Zhitao Ying, and Jure Leskovec. Inductive representation learning on large graphs. In Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman Garnett (eds.). NIPS, pp. 1024-1034, 2017b. URL http://ablp. uni triir de/db/ confo nips/nips2017 HammlHHamiltonI..
Lei Han, He Liang Haonan Chen, Wei Zhang, and Yurong Ge. Convective precipitation nowcasting using u-net model. IEEE Transactions on Geoscience and Remote Sensing, 60:1- 8, 01 2022. doi: 10.1109/
TGRS.2021.310884
Kaveh Hassani and Amir Hosein Khasahmadi. Contrastive multi-view representation learning on graphs. In Hal Daumé III and Aarti Singh (ods.), Proceedings of the 37th International Conference on Machine Learning, volume 119 of Proceedings of Machine Leorning Research, pp. 4116-4126. PMLR, 13-18 Jul
2020. URL httpps://proceedingg. mlr. www.pprressvviee 1ttaas///11/haaaaa222aa htmll
Jichao He, David W. Wanik, Brian M. Hartman, Emmanouil N. Anagnostou, Marina Astitha, and Maria E. B. Frediani. Nonparametric Tree-Based Predictive Modeling of Storm Outages on an Elec- tric Distribution Network. Risk Analysis, 37(3):411-455 March 2017. doi: 10.1111/risa.1266 12652. URL
https://ideas.reet repec. htt.://.ww.................aaata
16

---

Published in Transactions on Machine Learning Research (04/2026)
Noah Hollmann, Samuel Müller, Lennart Purucker, Arjum Krishnakumar, Max Körfer, Shi Bin Hoo, Robin Tibor Schirrmeister, and Frank Hutter. Accurate predictions on small data with a tabular foun- dation model. Nature, 01 2025. doi: 10.000///$11566-2440022226 URL httpe://ww.nnttrre.com nature.com/
Peticles/s41885 -00-0 08328-
Haojun Jiang, Jiawei Sun, Jie Li, and Chentao Wu. Localgel: Local-aware contrastive learning for graphs. arXiv preprinl ar Xiv:2440 1 17945, 2024.
Yushan Jiang, Kanghui Ning, Zijie Pan, Xuyang Shen, Jingchao Ni, Wenchao Yu, Anderson Schneider, Haifeng Chen, Yuriy Nevmyvaka, and Dongjin Song. Multi-modal time series analysis: A tutorial and survey. In Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '25), pp. 0043-6053, 2025. doi: 10. /11111////1166.3386007
Thomas N Kipl and Max Welling. Semi-supervised classification with graph convolutional networks. arv preprint ar xrx: 02907, 2016.
Dongyue Li, Haotian Ju, Aneesh Sharma, and Hongyang R. Zhang. Boosting multitask learning on graphs through higher-order task affinities. In KDD, 2023.
Dongyue Li, Ancesh Sharma, and Hongyang R. Zhang. Scalable multitask learning using gradicnt-basse estimation of task affinity. In KDD, 2024.
Haiyang Liu, Chunjiang Zhu, Detian Zhang, and Qing Li. Attention-based spatial-temprra graph convo- lutional recurrent networks for traffic forecasting. In International Conference on Advanced Data Mining and Applications, pp. 630 645. Springer, 2023.
Shaocong Long, Qianyu Zhou, Chenhao Ying, Lizhuang Ma, and Yuan Luo. Rethinking domain generaliza- tion: Discriminability and generalizability. arXiv preprint arXiv:2309. 16483, 2023.
Roshanak Nateghi, Seth Guikema, and Steven M. Quiring. Power outage estimation for tropical cyclones: Improved accuracy with simpler models. Risk Analysis, 34(6))1069-1078, June 2014. doi: 10.1111/risa 12131. URL https://ideas: http:://dddaarrepe..... ott.////////.aaa//////////411110
html
Damian Owerko, Fernando Gama, and Alejandro Ribeiro. Predicting power outages using graph neural networks. In 2018 ieee global conference on signal and information processing (globalsip). pp. 743 743-747. 747.
TEEE, 2018.
Zijie Pan, Yushan Jiang, Dongjin Song, Sahil Garg, Kashif Rasul, Anderson Schneider, and Yuriy Nevmy- vaka. Structural knowledge informed continual multivariate time series forecasting. arXiv preprint 2rxiv:2402. 12722, 2024.
Jordan Powers, Joseph Klemp, William Skamarock, Christopher Davis, Jimy Dudhia, David Gill, Janice Coen, David Gochis, Ravan Ahmadov, Steven Peckham, Georg Grell, John Michalakes, Samuel Trahan, Stanley Benjamin, Curtis Alexander, Geoffrey Dimego, Wei Wang, Craig Schwartz, Glen Romine, and Michael Duda. The weather research and forecasting (wrf) model: Overview, system efforts, and future directions. Bulletin of the American Meteorological Society, 98, 01 2017. doi: 10.1175 /LL155/BAMS-- B-0//BAA-S--------0---- 15-0008. 1.
Leslic Rice, Eric Wong, and Zico Kolter. Overfitting in adversarially robust deep learning. In International conference on machine learning, pp. 8093 8104. PMLR, 2020.
Lei Shi, Yifan Zhang, Jian Cheng, and Hanqing Lu. Two-Stream Adaptive Graph Convolutional Networks for Skeleton- -aaeed Action Recognition In 2019 IEEE/CT /CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 12018 12027. IEEE Computer Society, June 2019. doi: 10.1109/CVPR.2019, 01230. URL https:///oi. htw.ppptceeecccpppeooooooeeeeeee 10/./////.//..../// 2019. 2019.01230
W.C. Skamarock, J. Klemp, Jimy Dudhia, D.O. Gill, Dale Barker, Wei Wang, and J.G. Powers, A description of the advanced research wrf version 3. 27:3 27, 01 2008.
17

---

Published in Transactions on Machine Learning Research (04/2026)
A.B. Smith. U.s. billion-dolaar weather and climate disasters (2025). NOAA National Centers for Environ- mental Information (NCET), 2020. URL httph::////wtt htweiwww.cciii...ooooo.eo..mm..e noaa. /ot/://ceess/iillloo///eeeeeerse
Fan-Yun Sun, Jordan Hoffmannn Vikas Verma, and Jian Tang. Infograph: Unsupervised and semi-supervised graph-level representation learning via mutual information maximization. In ICLR. OpenReview.nee net, 2020.
URL http://bblp.... maierrier... hts/dddcoofff http:///oooofcccr/////eee/ iclor//rror///.22000.... htm1#SunHV020
Nengli Sun, Zeming Zhou, Qian Li, and Jinrui Jing. Three-dimensional gridded radar echo extrapolation for convective storm nowcasting based on 3d-convlstm model. Remole Sensing, 14:4256, 08 2022. doi:
10.3390/rs141142556
Shanshan Tang, Bo Li, and Hajjun Yu. Chebnet: efficient and stable constructions of deep neural networks with rectified power units via chebyshev approximation. Communications in Mathematics and Statistics, pp. 1-27, 2024.
Kingsley Udeh, David W. Wanik, Diego Cerrai, Emmanouil N. Anagnostou, and Derek Aguiar. Probabilistic storm and electric utility customer outage prediction. IEEE Access, 12:126285 126295, 2024. doi: 10.1109/ ACCESS 210BSS..02443446311..
Petar Velickovic, Guillem Cucurull, Arantxa Casanova, Adriana Romcro, Pictro Lio, and Yoshua Bengio. Graph attention networks. 6th International Conference on Learning Representations, 2017.
Pelar Velickovic, William Fedus, William L Hamilton, Pietro Liò, Yoshua Bengio, and R Devon Hjelm. Deep graph infomax. ICLR (Poster), 2(3):4, 2019.
D. Wanik, E. Anagnostou, B. Hartman, M. Frediani, and M. Astitha. Storm outage modeling for an electric distribution network in Northeastern USA. Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hozards, 79(2):1359-1333 1384, November 2015. doi: 10.1007/ s11069-015-1908 URL htthh:://///eei reper. httppp........//s.aaaaaaaaa///aa 13845999131...1 html
Peter Watson, Aaron Spanlding, Marika Koukoula, and Emmanouil Anagnostou. Improved quantitative prediction of power outages caused by extreme weather events. Weather and Climate Extremes, 37:100487, 07 2022. doi: ww..1////...e..2222..0000.
Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, and Chengqi Zhang, Graph wavenet for deep spatial- temporal graph modeling. International Joint Conferences Artificial Intelligence Organization, pp. 1907-1913, 2019. URL https://do1.org///
14963/1jcai. 2019922222.11
Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, Xiaojun Chang, and Chengqi Zhang. Connecting the dots: Multivariate time series forecasting with graph neural networks. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, KDD 20, pp. 753-766 New York, NY, USA, 2020. Association for Computing Machinery. ISBN 9781450379984 doi: 10.1145/339448 3403118. URL https://aci..rrg//1 11w..0.111113334188..1 340311
Yaochen Xie, Zhao Xu, Jingtun un Zhang, Zhengyang Wang, and Shuiwang Ji. Self-supervised learning of graph neural networks: A unified review. IEEE transactions on pattern analysis and machine intelligence, 45 (2):2412-244) 24212222299222 2022.
Keyulu Xu, Waihua Hu, Jure Leskovee, and Stefanic Jegelka. How powerful are graph neural networks? CoRR, abs//810.0 hts//880.00826, 2018. URL http:://blpp..... htt///bll...nittee uni-trier httpa///oooaaaa/ooooooorrr.r.... 1tt.1..1..mm....mmmmmmmmmmm.....
abs- 111000000086
Feifei Yang, Peter Watson, Marika Koukoula, and Emmanouil N. Anagnostou. Enhancing weather-related power outage prediction by event severity classification. IEEE Access, 8:60029 60042, 2020, doi: 10.1109/
Feifei Yang, Diego Carrai, and Emmanouil N Anagnostou. The effect of lead-time weather forecast uncer- tainty on outage prediction modeling. Forecasting, 3(3):501-516 2021.
18

---

Published in Transactions on Machine Learning Research (04/2026)
Junchen Ye, Zihan Liu, Bowen Du, Leilei Sun, Weimiao Li, Yanjie Fu, and Hui Xiong. Learning the evolutionary and multi-scale graph structure for multivariate time series lorecasting. In Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining, pp. 2296 2306, 2022.
Jiaxing Zhang, Zhuomin Chen, Hao Mei, Dongsheng Luo, and Hua Wei. Regexplainer: Generating expla- nations for graph neural networks in regrossion task. arXiv preprint arXiv:2307008840 2023.
Michael Zhang, Nimit S. Sohoni, Hongyang R. Zhang, Chelsea Finn, and Christopher Ré. A contrastive approach for improving robustness to spurious correlations. In International Conference on Machine Learning (ICML), 2022a.
Rui Zhang, Yunxing Zhang, Chengjun Lu, and Xuelong Li. Unsupervised graph embedding via adaptive graph learning. IEEE Transactions on Pottern Analysis and Machine Intelligence, 45(4):5329- 53339-333,--- 2022b.
Xikun Zhang, Dongjin Song, and Dacheng Tao. Continual learning on graphs: Challenges, solutions, and opportunities. arXiv preprint arXie:2402.1150 2024.
Jie Zhou, Ganqu Cui, Shengding Hu, Zhengyan Zhang, Cheng Yang, Zhiyuan Liu, Lifeng Wang, Changcheng Li, and Maosong Sun. Graph neural networks: A review of methods and applications. AI open, 1:57-81, 2020.
Kaiyang Zhou, Ziwei Liu, Yu Qiao, Tao Xiang, and Chen Change Loy. Domain generalization: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(4):4396 141489666411,,,,-1111111111-4451 2022. doi: 10.1109/ TPAML 2P2.M..222.3195552
19

---

Published in Transactions on Machine Learning Research (04/2026)
A Selected Feature Information
This section provides a comprchensive list of all the selected features along with their explanations. Each feature described in detail to clarify its significance and relevance to the analysis. These features encompass various environmental, meteorological, and infrastructure-reltted factors essential for understanding outage patterns.
land21: Land Area Developed, Open Space
stdPOTT: Standard Deviation Potential Temperature at 2 m
land22: Land cover Area Developed, Low Intensity
peakSPFH: Peak Specific Humidity
land23:
Land cover Area Developed, Medium
HGT: WRF elevation
Intensity
coggt17: Duration of Continuous Gusts above 17 m/s
land24: Land cover Area Developed High
Intensity
coggt27: Duration of Continuous Gusts above 27 m/s
land43: Land cover Area Mixed Forest
lotalotal: Land cover Area Total
coggt22: Duration of Continuous Gusts above 22 m/s
prec81: Percentage of land81 (Land cover Pasture/Has Hayy)
ggt17: Hours of Wind Gusts above 17 m/s
soilDepth: Mean Soil Depth
ggt22: Hours of Wind Gusts above 22 m/s
avgSMOIS3: Average Soil Moisture (40-100 cm deep)
ggt27: Hours of Wind Gusts above 27 m/s
peakGUST: Peak Wind Gust Speed
stdSM0IS4: Standard Deviation Soil Moisture (100-200 cm deep)
maxGUST: Max Wind Gust Speed
stdGUST: Standard Deviation Wind Gust Speed
avgTPA: Trees per avgLFSH: Leaf Stress
peakW850: Peak Wind Speed above 850 mb
avgCIN: Average Convective Inhibition
max maxW850: Max Wind Speed above 850 mb
stdCIN: Standard Deviation Convective Inhibition
stdW850: Standard Deviation Wind Speed at 850
avgDPT: Avearage Dew Point Temperature at m
mb
stdDPT: Standard Deviation Dew Point
stdTDIF: Standard Deviation of Temperature Difference (850 mb to 1000 mb)
Temperature m
hydNo: Percent Not Hydric Soils
max WSPD: max Wind Speed at 10m
avgSDI: Average Total stand density index
peakLLWS: Low Level Wind Shear
avgHardBA: Average Hardwood basal area
avgCAPE: Convective Available Potential Energy
stdHardBA: Standard Deviation Hardwood basal area
maxCAPE: Max Convective Available Potential
Energy
avgHardSDI: Average Hardwood stand density
stdTURB: Standard Deviation Turbulence
index
maxTURB: Max Turbulence
stdHardSDI: Standard Deviation Hardwood stand density index
poleCount: Number of poles
fuseCount: Number of fuses
peakPSFC: Peak Surface Pressure
ohLength: Length of overhead lines
minPSFC: Minimum Surface Pressure
reclrCount: Number of reclosers
peakPOTT: Peak Potential Temperature at m
20

---

Published in Transactions on Machine Learning Research (04/2026)
B
Evaluations
AE is used to measure the difference between the total predicted (p:) and actual (o:) outage counts from event i. AE Q25 and AE Q50 mean the 25th and 50th quantile value of all events' AE. And AE is calculated as:
AE = lp; -,l,
(8)
Also APE Q25 and APE Q50 represents the 25th and 50th quantile value of all events' APE, which is caleulated as:
APE p; oil O2
(9)
MAPE is utilized to mean relative error a percentage and is defined as:
MAPE 100%
05 Pi
(10)
CRMSE to measure the deviation of predictions from the actual values while removing systematic biases. The lower this value, the better the performance of the model.
n
Ei (p: 0;) 2
CRMSEE
Pt U2
(11)
n
nf2 shows the goodness of of the various model predictions to the actual outages. The higher this value, the better the performance of the model.
1= 02 n
Pi
n
R²
(12)
71
OgPi
21


Reviews:
[{"review_id": "gqlJ3SIbom", "reviewer": "Reviewer_MRHa", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors introduce a novel GNN-based architecture designed to improve the prediction of power outages during extreme weather events. Their key contribution lies in better capturing the spatial dependencies between locations affected by such events. To do this, they propose a dual-channel embedding mechanism: one channel processes static features using a fixed adjacency matrix, while the other processes dynamic features using a learnable adjacency matrix that the model estimates during training.\nThe model is trained with a combination of contrastive loss, which encourages closer representations for positive intra- and inter-event node pairs, and regression objectives - i.e., estimate of dynamic adjacency matric; prediction of the actual number of outages. The authors evaluate the approach using simulated datasets based on four geographical regions. Their method outperforms existing approaches, with particularly strong improvements observed in the Connecticut case.", "claims_and_evidence_yn": "No", "claims_explanation": "The work is interesting and has clear potential. However, the current results appear somewhat limited: performance gains are particularly strong in the Connecticut case, but are only comparable to the baselines in the other regions. Since most of the subsequent analysis focuses on the Connecticut scenario, my main concern is: why are the improvements smaller in the other settings? Could this be related to the simulation parameters (e.g., a higher number of outages per event, which might amplify errors and thus affect performance)?\n\nFrom Figure 2, when comparing your method to other approaches (e.g., TabPFN), it also seems that your model handles high-outage events better, while underestimating the distribution in cases with fewer outages. Is this interpretation correct?\n\nMore generally:\n- It would be interesting to better understand how the model learns the different objectives. Have you monitored the loss components separately during training? What does the model learn first? Are the tasks learned jointly, or does the optimization plateau for one component while continuing for others? At the moment, the ablation study on the Connecticut dataset shows that all components contribute, but it does not reveal how the model uses the learned representations.\n- The t-SNE visualizations are mainly qualitative. While Figure 3 is promising, I am not fully convinced that GAT behaves dramatically differently from your proposed method based on this alone.\n- Similarly, Figure 5 provides useful intuition, but it would be more convincing to complement it with numerical metrics.\n- As you already acknowledge, relying solely on simulated datasets is a significant limitation - especially when the simulation design itself may influence the behavior and apparent advantages of the proposed model.", "audience_yn": "Yes", "audience_explanation": "I find the idea of dynamically estimating the adjacency matrix particularly compelling for this application. Manually determining such relationships typically requires (i) detailed knowledge of the geographical and infrastructural context, and (ii) expert involvement to define and validate the relevant features. Your approach suggests a promising alternative: (i) use data from well-understood scenarios to (ii) train a model capable of inferring these spatial dependencies automatically, and (iii) deploy the trained model in new regions where such expert knowledge is not yet available.\n\nTo strengthen this contribution, the authors should elaborate further on this aspect by:\n1) Clarifying the practical meaning of the learned adjacency matrix - for example, explaining how it relates to real-world phenomena such as how wind-induced failures might propagate from one location to another.\n2) Motivating why automatic estimation is valuable in practice, including considerations such as cost, required expertise, and time constraints associated with manually constructing these matrices.\n3) Show examples in which the knowledge learned for a set of locations \"transfer\" to others (at a different time, for different places, etc.)\n\nHighlighting these points more explicitly would significantly enhance the practical relevance and impact of the proposed approach.", "requested_changes": "- Clarify feature definitions with concrete examples (critical): Clearly distinguish static features (e.g., topography, presence of mountains) from dynamic features (e.g., wind speed at a given timestamp). Introducing examples early would significantly improve conceptual clarity.\n- Strengthen motivation for learning a dynamic adjacency matrix (critical): Explain why manual construction is costly and often infeasible, and how learned adjacency supports generalization across regions (e.g., training in Connecticut, deploying in Western Massachusetts). Provide practical intuition for what the dynamic adjacency represents.\n- Improve description of graph construction (Recommended): Clarify how nodes (locations) are grouped into events, the criteria used, and the typical graph size. How long these events last? \n- Revise Figure 1 for clearer model flow (Recommended): Make explicit what the inputs and outputs of each module are. Consider separating the pipeline into phases (e.g., learning A^, creating embeddings, downstream prediction).\n- Fix or clarify notation inconsistencies (critical): In Section 3, you use A to derive A(~). Should this instead be A^? If the model relies on A during training but not during testing, please clarify how inference works.\n- Provide insights into learning dynamics (recommended): Report how different loss components evolve during training (e.g., adjacency learning, contrastive separation, outage regression). This would show what the model learns first and how tasks interact.\n- Explain region-dependent performance differences (critical): The model performs best in Connecticut but shows marginal gains elsewhere. Explain why - e.g., simulation parameters, event severity distributions, or structural differences. This is central to evaluating robustness.\n- Expand analysis beyond the Connecticut scenario (critical): Current qualitative analyses (e.g., adjacency visualizations, ablations) rely almost exclusively on the region where the model performs best. Provide at least partial analyses for another region.\n- Add more detail on simulation procedure and limitations (critical): Provide stronger justification for lacking real-world validation or at least discuss challenges and planned future steps.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "OViU6HtMb9", "reviewer": "Reviewer_QaSo", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper is concerned with the prediction of power outages using graph neural networks. The setting is thus: each prediction query is formed by a weather event over there are $N$ locations within a geographic area. Each location offers measurements of $F$ meteorological (or other) features, yielding an instance $X \\in \\mathbb{R}^{N \\times F},$ and the goal is to predict a vector of the number of outages at each location, denoted $Y$. Each event is further modeled by a graph on the $N$ locations, with adjacency matrix $A$, which captures spatial or functional relationships introduced by the weather event. Given that the structural role of the underlying graph, the paper proposes a graph neural network approach to address this task. A significant detail is that the features $X$ are decomposed as static and dynamic features $(X^s, X^d),$ where the former do not change with events, while the latter do.\n\nThe paper considers a setting where the training data is composed of triples $(X_k, A_k, Y_k)$, while at test time $Y_k$ must be predicted from the features. The main contribution is a setup for modeling this data where the static and dynamic features are treated together. Specifically, what is effectively a shallow net is constructed for learning a dynamic adjacency matrix on the dynamic data, while the static data is crunched into a static adjacency matrix that is also given as input to the system (following the design proposed in certain recent work). Both are fed into two separate graph convolutional network, and their final representations are concatenated and then passed through an MLP. These representations are further tuned with a softmax contrastive loss thus: 1) within any event, the embeddings of adjacent nodes are treated as positive pairs, and those of non-adjacent nodes as negative pairs. 2) the embeddings of any two nodes across different events are treated as negative pairs. This contrastive loss is added to handle imbalance in outage data (the nature of which is not specified, but presumably outages are fairly rare in, say, new england). Finally, the output $\\hat{Y}$ is penalised with a Huber loss, giving a three term (adjacency, contrastive, Huber) loss that is optimized.\n\nFinally, this modeling pipeline is implemented for four outage datasets, and compared to six other methods. Two of these are classical decision forests (random forest, and XGboost), one is a foundation model for tabular data (TabPFN), and three graph neural network architectures. The main observation is that across a number of error metrics, the proposed models are either better than all competitors, or perform similarly to the best competitor.", "claims_and_evidence_yn": "No", "claims_explanation": "Before offering subjective criticisms, I want to explicitly note that I am neither an expert in modeling of power outages, not in graph neural networks. As such, I have little ability to judge the novelty of the work in its proper context.\n\n----\n\n\n\n\nI think the paper suffers from muddled evaluation, and find that the writing is quite unclear in that even the problem is not completely specified in one place, but instead is drip fed to the reader. \n\n- The evaluation is muddled. In particular, sectiion 5.1 does not seem to align well with the structure proposed, and appears to take the modular use of GCNs to be something essential to the architecture.\n\n    I understand that the boosted decision trees are being compared to because prior power outage modeling work (in non-ML venues) studied these. These are not particularly compelling for this setting, although it is interesting that they often work very well. Similarly, a tabular that ignores the dependency structure is also not particularly compelling. My understand is that these comparisons show that attempting to incorporate the underlying graph into the predictions is a good idea.\n \n    However, I do not understand how the competing graph neural networks are a valid comparison. Indeed, to my understanding, the contribution is a way of setting up the prediction model wherein the dynamic and static parts of the graph are both used to inform the representation. Here, the GCN forms just one part of the design, and as such it should be entirely possible to replace the use of the GCN in the architecture with any of the other GNN methods (like GAT or GIN or GraphSAGE as described in the paper). \n\n    As such, then, it seems that the separated GCN architecture is being compared to unseparated GATs/GINs/GraphSAGES (henceforth OGNNs for \"other GNNs\"). But this is unnecessarily changing two things at once, and obscuring the effect of the contribution. If the claim is that the particular way of jointly incorporating the static and dynamic graphs is good, then it would be better to compare a GCN version of the SA-HGNN with a vanilla GCN, and similarly a OGNN version of SA-HGNN with a vanilla SA-HGNN. The current evidence does not thus actually tell us that the SA-HGNN method is a good idea in this problem, only that this with GCNs does better than OGNNs. This is further compounded by the fact that, presumably, the representations of the OGNNs are not supervised with the contrastive loss. \n\n    Thus, in my opinion, the actual evaluation of the architecture proposed really lies in the ablations in Table 3, which I think should be the main result instead. Here the effect seen is good, but the question of how robust this effect is across architectures is left unanswered. I think a complete evaluation would reproduce something like ablation, with GCNs being changed for OGNNs.\n\n-----\n\n- The writing is quite unclear. In particular, it was not even clear to me what the actual structure of the available data is from the section describing the problem, and instead this is fed to us piecemeal through the paper. \n\n    Let me expand upon this. Equation (1) states that $\\hat{Y} = f\\_{\\textrm{GNN}}(X, A)$. However, the entirety of the rest of the paper is about the setting where this $A$ is not known, and must instead be estimated from the features $X$, and the procedure to do this is learned by fitting a model to such adjacency matrices learned during training. Thus, at the point of, say, section 4.1, one realizes that the learning setting is one where the training data is composed of triples of the form $(X\\_k, A\\_k, Y\\_k)$, while at inference time only the features $X$ are available. However, even this is not quite true: in section 4.2 we learn that actually $X$ is composed of two pieces, a static channel $X^s$ that does not change across events, and a dynamic channel $X^d$ that does. Finally, and suddenly, instead of one graph, we have two graphs, a static one and a dynamic one. \n\n    It's totally fine to have these subtleties in the model, but this should all be made clear in the problem description, rather than dripping out one by one.\n\n---\n\nOverall, while I think that the results of section 5.3 are interesting, the writing of the paper itself makes understanding the problem hard, and muddles up the evidence of the success of the design. Further, the results of this evaluation are not quite sufficient to establish that the architectural proposals are effective in a generic way even for the outage datasets.", "audience_yn": "No", "audience_explanation": "In my opinion, as it is written, this submission falls outside the scope of this journal. Looking at the scope, the closest criterion within the ones outlined by the journal is \"accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods\". However, I think the insights about machine learning techniques that are shed by this work are not particularly deep, and instead greater insights about the structure of power outage data are gained (e.g., that it is important to enforce constrastivity between locations, or that the particular way of separating and integrating dynamic and static information is good). The techniques being employed are essentially adapted to these properties of the data, but are not shedding light on, e.g., alternative machine learning methods to address these particular concerns. Instead, these are shedding light on structural deficiencies in prior approaches to modeling this data.\n\nLet me take careful stock of the proposed method to make this case. High level, there are three important pieces: 1) dynamic and static graph relationships should be modeled separately, and integrated only at the end, in this case by concatenation; 2) a contrastive loss can be used to handle the imbalances specific to outage data, and 3) the architecture incorporating these two modeling choices works well on power outage prediction. \n\nOf these, 2, 3 are specifically claims about modeling power outages. This is certainly an important problem, but I don't know that the readers of a machine learning venue would find it particularly important from an ML perspective, and certainly the paper does not make the case that they would. 1. might be an interesting contribution form an ML perspective in that it makes a claim about how one should model certain dynamic dependencies, but it is not evaluated in sufficient generality for the case to be convincing outside of the power outage application. In particular, as I pointed out in the previous text box, I don't think that the evaluation is even sufficient to make the case that the observed effect on this data is robust to changing the architecture from using a GCN to another GNN method. \n\nAs such, in my opinion, this paper in its current state would find a more natural home in a venue dedicated to the study of power outages (or electrical engineering at large), rather than in a venue dedicated to machine learning. Indeed, one can see that bulk of the substantially discussed related work is published in such venues, whereas most of the related machine learning work is discussed in generic terms without precise contrasting with the proposed work.", "requested_changes": "If the authors do want to publish this work in an ML venue, I think it could be interesting if it were rewritten with a message of the following form, it would work better for this venue: \"When modeling data with both dynamic and static dependencies, it is a good idea to separate out the static and dynamic parts in the bulk of the network, and only integrate them at the very end.\" This would be a substancial change, not an \"adjustment\": one would have to compare to other methods explicitly modeling dynamic dependencies (including the methods cited) and compare on data across many domains, rather than only power outage data.", "broader_impact_concerns": "No concerns", "additional_comments": "I think most citations in the submission should use a \\citep command instead of \\citet. Compare \n\npage 1, current: \"... with the frequency and severity of billion-dollar disasters steadily increasing over the past two decades Campbell (2012); Smith (2020).\"\n\nwith \\citep \"...  with the frequency and severity of billion-dollar disasters steadily increasing over the past two decades (Campbell, 2012; Smith, 2020)\"\n\nI believe usually \\citep{} is what \\cite{} defaults to in natbib, but obviously I don't know the setup being used here.\n\n----\n\nIt was said that the $(\\lambda, \\gamma)$ factors (and presumably also $\\delta$??) were chosen by grid search, but it was not specified over what grid, nor how the model selection was performed.", "extra_scores": {}, "extra_text": {}}, {"review_id": "y7nE1bGa6E", "reviewer": "Reviewer_ExvQ", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper studies the problem of predicting power outages caused by extreme weather events using graph neural networks (GNNs). The issue is to incorporate the spatial effects of these weather events and the imbalance between frequent low-impact events and rare high-impact events.\n\nThe paper proposes the Spatially Aware Hybrid Graph Neural Networks (SA-HGNN) to enhance outage predictions. This framework uses a dynamic graph learning module to infer evolving spatial relationships based on event-specific weather features. It also incorporates a contrastive learning module to generate location-specific embeddings, enabling the model to distinguish between similar and dissimilar outage patterns across different events.\n\nExperiments show that SA-HGNN achieves state-of-the-art performance across four utility service territories: Connecticut, Western Massachusetts, Eastern Massachusetts, and New Hampshire. The results demonstrate that the model outperforms baseline methods, including Random Forest, XGBoost, and other graph neural networks.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The main claim is the effectiveness of the proposed method SA-HGNN. This is supported by the empirical validation on four real-world datasets. SA-HGNN outperforms traditional methods (RF, XGBoost), graph-based methods (GAT, GraphSAGE, GIN), and foundation (TabPFN) baselines with multiple metrics (AE, APE, MAPE, CRMSE, $R^2$).\n\nThe ablation study shows that each component of SA-HGNN is functional. The ablation “w/o HGNN” (single GCN on static neighbors only) yields much worse $R^2$ (0.29 vs. 0.79) and higher errors on CT, indicating that separating static and dynamic channels is essential. The ablation “w/o DSK” (no dynamic structural prior) also degrades CRMSE and $R^2$, showing that guiding the dynamic graph with event-specific priors is useful. The “w/o CL” ablation consistently worsens AE/APE/MAPE and reduces $R^2$ (0.45 vs. 0.79 on CT), indicating that the contrastive term improves the learned embeddings and final predictions.", "audience_yn": "Yes", "audience_explanation": "This paper contributes to the literature of hybrid GNN architecture and graph contrastive learning. And the application has a real-world impact.", "requested_changes": "1. In Section 4.1, the authors first use the softmax function to normalize the learned adjacency matrix, and then apply a top-k method to select the indices, after which they convert them into a binary 0/1 encoding. In my understanding, these two operations conflict with each other. If the final result is a 0/1 binary encoding, then softmax does not change the top-k ordering and therefore becomes useless.\n2. The authors do not discuss the hyperparameters.\n3. In Equation (6), the final loss is a weighted combination of the forecasting objective, the contrastive learning objective, and the learning dynamic adjacency matrix objective. In my understanding, these three objectives are highly heterogeneous. Therefore, a discussion and evaluation of $\\lambda$ and $\\gamma$ is necessary.\n\nMinor: ChebNet Tang et al. (2024) is mentioned in the subsection 'baseline model', but not reported in Table 3 or any other experiments.", "broader_impact_concerns": "N/A.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)