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EnergyMamba: An Uncertainty-Aware Graph-Enhanced Selective State Space Model for Energy Consumption Prediction

The paper introduces EnergyMamba, an uncertainty-aware spatiotemporal framework that combines a Graph-Enhanced Selective State Space Model for coupled spatial-temporal modeling with an Adaptive Sequential Conformalized Quantile Regression module for dynamic uncertainty calibration, achieving superior prediction accuracy and reliability on large-scale energy datasets compared to state-of-the-art baselines.

Original authors: Dahai Yu, Rongchao Xu, Lin Jiang, Guang Wang

Published 2026-06-02

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CC BY 4.0

Original authors: Dahai Yu, Rongchao Xu, Lin Jiang, Guang Wang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to predict how much electricity a whole neighborhood will use tomorrow. It's not just about looking at the weather forecast; it's about understanding how neighbors influence each other and how to handle the surprise of a sudden heatwave or a hurricane.

The paper introduces EnergyMamba, a new computer program designed to solve this problem more accurately and safely than previous methods. Here is how it works, broken down into simple concepts:

1. The Problem: The "Solo" vs. The "Team"

Previous prediction tools were like solo runners. They looked at the history of one specific neighborhood (or "node") and tried to guess its future based only on its own past.

The Flaw: In the real world, electricity grids are like a giant web of connected friends. If one house suddenly turns on a massive air conditioner, it affects the power flow to the houses next door. Old models ignored this "social network" of electricity.
The Second Flaw: When things get weird (like a hurricane), old models get overconfident. They give a single number as a prediction but don't tell you, "Hey, I'm not sure about this." This is dangerous for power grid managers who need to know the risk of a power surge.

2. The Solution: EnergyMamba's Two Superpowers

EnergyMamba fixes these issues with two main "superpowers":

Superpower A: The "Neighborhood Watch" (GE-Mamba)

Instead of looking at one house in isolation, EnergyMamba looks at the whole neighborhood map.

The Analogy: Imagine a U-Net (the shape of a U) acting like a drone flying over a city. It zooms out to see the big picture (weekly trends) and zooms in to see the details (hourly spikes).
The Magic: It uses a "Graph" (a map of connections) to learn how electricity flows between neighbors. It's based on a real physics rule (Kirchhoff's laws) which says that if one part of the grid changes, the connected parts must change too.
The Result: It treats the electricity grid like a team sport where every player's move affects the others, allowing it to predict how a change in one area ripples through the whole system.

Superpower B: The "Self-Correcting Safety Net" (AS-CQR)

Predicting the exact number is hard, so EnergyMamba also predicts a range (a safety net) where the real number is likely to fall.

The Problem with Old Nets: Old safety nets were rigid. If the neighborhood usually uses 100 units, the net was sized for 100. But if a heatwave hits and usage jumps to 1,000, the old net was too small and broke.
The EnergyMamba Fix: This system has a dynamic, self-adjusting net.
- Local Normalization: It realizes that big houses have bigger swings in usage than small houses, so it adjusts the size of the net based on how much energy is currently being used.
- Online Feedback: It has a "learning loop." If the real number falls outside the net (the prediction was wrong), the system immediately says, "Oops, I was too confident," and widens the net for the next prediction. If it was too wide, it shrinks it back. This happens in real-time, even during extreme weather.

3. The Results: Faster, Smarter, and Safer

The authors tested EnergyMamba on real data from Florida, New York, and California.

Accuracy: It was about 5% more accurate than the best existing tools.
Reliability: It improved its ability to estimate uncertainty (how sure it is) by 6%.
Speed: Despite being smarter, it runs efficiently. It's much faster than the massive "Large Language Model" tools that are currently popular, making it practical for real-world power grids that need quick answers.

Summary

Think of EnergyMamba as a smart grid manager who:

Talks to the neighbors: It understands that electricity flows between connected areas, not just in straight lines.
Adapts to the chaos: When a storm hits or usage spikes, it doesn't panic; it instantly recalibrates its safety margins to ensure the prediction remains reliable.

The paper claims this makes energy planning more efficient and helps prevent blackouts during extreme events by providing not just a guess, but a reliable, risk-aware forecast.

Technical Summary of "EnergyMamba: An Uncertainty-Aware Graph-Enhanced Selective State Space Model for Energy Consumption Prediction"

1. Problem Definition

Energy consumption prediction is critical for grid management, demand-side optimization, and sustainable planning. However, existing approaches suffer from two primary limitations:

Neglect of Spatial Dependencies: Most methods treat energy consumption as a purely time-series forecasting problem, failing to explicitly model the spatial dependencies and interactions between different regions or grid zones.
Lack of Reliable Uncertainty Quantification: State-of-the-art models often fail to provide reliable predictions with uncertainty estimates, particularly under abnormal conditions such as extreme weather events. This leads to overconfident predictions that can mislead decision-makers.

The authors identify two specific challenges in addressing these limitations:

Spatiotemporal Heterogeneity: Consumption patterns are highly heterogeneous across regions and time due to geographical factors, temporal dynamics, and building characteristics.
Non-Stationarity: Energy demand distributions shift dramatically during extreme events, violating the exchangeability assumptions of standard uncertainty quantification methods.

2. Methodology: EnergyMamba

The authors propose EnergyMamba, an uncertainty-aware spatiotemporal learning framework comprising two core components:

A. Graph-Enhanced Selective State Space Model (GE-Mamba)
To address spatiotemporal heterogeneity, the authors design a novel architecture that injects spatial context into temporal dynamics.

Architecture: The model is organized within a U-Net structure (encoder-decoder with skip connections) to capture multi-scale temporal patterns (from short-term fluctuations to long-term trends).
Spatial Context Extraction: A Graph Convolutional Network (GCN) extracts spatial context from the grid topology (modeled as a graph where nodes are regions and edges represent spatial proximity). This design is motivated by Kirchhoff's circuit laws, where load perturbations at one node propagate to connected nodes.
Selective State Space Model (SSM): The temporal dynamics are modeled using a bidirectional Mamba (SSM) with linear complexity $O(T)$ . Crucially, the SSM's parameters (specifically the input projection $B$ , output projection $C$ , and step size $\Delta$ ) are made input-dependent and conditioned on the spatial context $z_t$ extracted by the GCN. This allows the model to adapt its temporal processing based on the state of neighboring nodes.
Bidirectional Processing (BIP): The model processes sequences both forward and backward to capture both causal dependencies and full-sequence contextual patterns.

B. Adaptive Sequential Conformalized Quantile Regression (AS-CQR)
To address non-stationarity and heteroscedasticity (where prediction variance scales with load magnitude), the authors propose a distribution-free uncertainty quantification module.

Locally Adaptive Normalization: Unlike standard Conformalized Quantile Regression (CQR) which uses absolute residuals, AS-CQR normalizes nonconformity scores by the predicted interval width. This ensures scale-invariant calibration across regions with different load magnitudes.
Online Feedback Mechanism: The target miscoverage rate $\alpha$ is treated as a control variable. Based on recent coverage performance (whether the true value fell inside or outside the predicted interval), the effective miscoverage rate is dynamically adjusted. This allows the prediction intervals to rapidly adapt to distribution shifts caused by extreme events.
Theoretical Guarantee: Under mild regularity conditions, AS-CQR guarantees that the long-run average empirical coverage converges to the target level $1-\alpha$ , even in non-stationary environments.

3. Key Contributions

Conceptual: The paper reframes energy consumption prediction as an uncertainty-aware spatiotemporal task, explicitly modeling spatial dependencies and providing reliable uncertainty quantification, rather than treating it as a pure time-series problem.
Technical:
- Introduction of GE-Mamba, which integrates GCN-derived spatial context into a bidirectional Mamba within a U-Net structure, enabling coupled spatiotemporal modeling.
- Development of AS-CQR, a distribution-free method featuring locally adaptive normalization and online feedback calibration to handle non-stationary conditions and heteroscedasticity.
Empirical: Comprehensive evaluation on four large-scale real-world datasets (Florida, New York, California) against 15 state-of-the-art baselines (including GNNs, Transformers, LLMs, and Mamba variants).

4. Experimental Results

The authors evaluated EnergyMamba using Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Prediction Interval Width (MPIW), Interval Score (IS), and Coverage (COV).

Accuracy: EnergyMamba achieved approximately 5% improvement in prediction accuracy (MAE) compared to the best baseline across the datasets.
Uncertainty Quantification: The model demonstrated a 6% improvement in uncertainty quantification (measured by IS) and consistently achieved the target coverage (e.g., $\ge 90\%$ for $\alpha=0.1$ ), whereas many baselines failed to meet the target coverage.
Robustness: In case studies involving extreme weather events (hurricanes, heat waves), EnergyMamba maintained accurate predictions and kept ground truth values within the prediction intervals, while baselines struggled to adapt to abrupt changes.
Efficiency: EnergyMamba demonstrated favorable computational efficiency, with training times and memory footprints significantly lower than LLM-based and some Transformer-based baselines, while maintaining linear time complexity due to the Mamba backbone.

5. Significance and Claims

The paper claims that EnergyMamba advances existing research by bridging data-driven learning with physical system principles (Kirchhoff's laws) and addressing the critical gap of reliability under distribution shifts.

Physical Interpretability: By conditioning temporal dynamics on spatial context derived from grid topology, the model better simulates how load perturbations propagate through the power grid.
Reliability in Extreme Events: The adaptive nature of AS-CQR ensures that the model does not become overconfident during abnormal situations, providing decision-makers with reliable risk-aware predictions.
Scalability: The framework offers a balance between high accuracy and computational efficiency, making it suitable for frequent retraining in dynamic grid scenarios.

The authors acknowledge limitations, noting that the current implementation operates at a regional level (e.g., Census Block Groups) and does not explicitly model the fine-grained physical topology of the power grid, suggesting this as a direction for future work.