# In-Context Residual Calibration for Uncertainty Quantification of Energy Time Series over Graphs

arXiv: https://arxiv.org/abs/2606.31804 · HTML: https://mlsanity.com/paper/2606.31804/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 74 references that are in the map.
- First posted on arXiv 30 Jun 2026.

## Builds on (most cited first, 30 of 30)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [TabPFN-2.5: Advancing the State of the Art in Tabular Foundation Models](https://mlsanity.com/paper/2511.08667/) (2025)
- [Uncertainty Quantification over Graph with Conformalized Graph Neural Networks](https://mlsanity.com/paper/2305.14535/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Statistical Foundations of Prior-Data Fitted Networks](https://mlsanity.com/paper/2305.11097/) (2023)
- [Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorial](https://mlsanity.com/paper/2305.04933/) (2023)
- [Spatio-temporal graph neural networks for multi-site PV power forecasting](https://mlsanity.com/paper/2107.13875/) (2021)
- [Physics-Enhanced Machine Learning: a position paper for dynamical systems investigations](https://mlsanity.com/paper/2405.05987/) (2024)
- [Variational Inference for Uncertainty Quantification: an Analysis of Trade-offs](https://mlsanity.com/paper/2403.13748/) (2024)
- [Relational Conformal Prediction for Correlated Time Series](https://mlsanity.com/paper/2502.09443/) (2025)
- [Spatial Conformal Inference through Localized Quantile Regression](https://mlsanity.com/paper/2412.01098/) (2024)
- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Conformal Inference for Time Series over Graphs](https://mlsanity.com/paper/2510.11049/) (2025)
- [Bayesian system identification for structures considering spatial and temporal correlation](https://mlsanity.com/paper/2305.00867/) (2023)
- [Multivariate Ensemble Forecast Framework for Demand Prediction of Anomalous Days](https://mlsanity.com/paper/1811.09339/) (2018)
- [Adversarial Disentanglement by Backpropagation with Physics-Informed Variational Autoencoder](https://mlsanity.com/paper/2506.13658/) (2025)
- [Heterogeneous Graph Neural Networks for Short-term State Forecasting in Power Systems across Domains and Time Scales: A Hydroelectric Power Plant Case Study](https://mlsanity.com/paper/2507.06694/) (2025)
- [Integrating the Expected Future in Load Forecasts with Contextually Enhanced Transformer Models](https://mlsanity.com/paper/2409.05884/) (2024)
- [Integrating Physics-Based and Data-Driven Approaches for Probabilistic Building Energy Modeling](https://mlsanity.com/paper/2507.17526/) (2025)

## Abstract (arXiv)

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 under exchangeability assumptions, 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 uncertainty quantificatiOn via In-Context learning), a conformal-inspired post-hoc residual calibration framework that integrates graph-based forecasting with the in-context learning 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 estimates feature-conditional residual quantiles without task-specific retraining of the calibration model, effectively capturing both sequential and relational dependencies. STOIC should be viewed as a conformal-inspired residual calibration method and does not by itself provide a finite-sample distribution-free coverage guarantee under arbitrary temporal dependence...