Relational and Sequential Conformal Inference for Energy Time Series over Graphs via Foundation Models

2026-06-30

AI Summary

Existing methods for graph-structured energy time series forecasting struggle to simultaneously achieve high-accuracy point predictions and reliable uncertainty estimates, particularly due to limitations in modeling spatiotemporal dependencies. This work proposes a novel framework that, for the first time, leverages the in-context learning capabilities of tabular foundation models for graph-based energy forecasting. The approach employs a spatiotemporal graph neural network to extract features and applies zero-shot calibration to prediction residuals, yielding prediction intervals that preserve spatiotemporal consistency. Notably, the method enables calibrated, order-preserving joint uncertainty quantification without task-specific fine-tuning. Experiments on five real-world and synthetic energy network datasets demonstrate that the proposed approach significantly outperforms existing order-preserving forecasting methods, delivering more accurate and robust uncertainty estimates.

Abstract

Accurate energy demand forecasting is essential for the reliable operation and planning of modern sustainable energy systems. Spatial-temporal graph neural networks (STGNNs) have recently achieved strong performance in point forecasting by jointly modeling temporal dynamics and relational dependencies across interconnected energy nodes. However, in real-world energy systems, accurate point forecasts alone are insufficient, as operators also require reliable uncertainty estimates to support risk-aware decision-making, grid stability, and operational planning under uncertainty. Conformal prediction provides a principled and model-agnostic framework for uncertainty quantification with statistical coverage guarantees, making it particularly attractive for safety-critical energy applications. However, existing conformal prediction approaches often fail to fully capture the complex spatial-temporal structure of energy systems. To address these limitations, we propose STOIC (Spatial-Temporal Graph Conformal Prediction with In-Context Learning), a novel framework that integrates graph-based forecasting with the zero-shot calibration capabilities of tabular foundation models. STOIC first generates point forecasts using an STGNN and subsequently reformulates spatial-temporal residuals into a tabular representation suitable for in-context learning. Leveraging a tabular foundation model, STOIC calibrates prediction intervals without task-specific retraining, effectively capturing both sequential and relational dependencies. We evaluate STOIC on five diverse benchmarks, including synthetic simulations as well as real-world electricity and district heating networks. Across all datasets, STOIC consistently outperforms existing conformal prediction baselines, delivering more reliable and robust uncertainty estimates for complex graph-structured energy time series.

Problem

• conformal prediction
• energy time series
• spatial-temporal graph
• uncertainty quantification
• graph neural networks

Innovation

• Conformal Prediction
• Foundation Models
• Spatial-Temporal Graph Neural Networks
• In-Context Learning
• Energy Time Series