# External Data-Enhanced Meta-Representation for Adaptive Probabilistic Load Forecasting

arXiv: https://arxiv.org/abs/2506.23201 · HTML: https://mlsanity.com/paper/2506.23201/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in MoE for time series and graphs, one of 12 directions in Mixture-of-experts.
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 29 Jun 2025.

## Placed in

- Mixture-of-experts / [MoE for time series and graphs](https://mlsanity.com/moe/moe-for-time-series-and-graphs/)

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Review of Smart Meter Data Analytics: Applications, Methodologies, and Challenges](https://mlsanity.com/paper/1802.04117/) (2018)
- [LfEdNet: A Task-based Day-ahead Load Forecasting Model for Stochastic Economic Dispatch](https://mlsanity.com/paper/2008.07025/) (2020)
- [ExARNN: An Environment-Driven Adaptive RNN for Learning Non-Stationary Power Dynamics](https://mlsanity.com/paper/2505.17488/) (2025)
- [Input Modeling and Uncertainty Quantification for Improving Volatile Residential Load Forecasting](https://mlsanity.com/paper/1905.06773/) (2019)
- [MetaEformer: Unveiling and Leveraging Meta-patterns for Complex and Dynamic Systems Load Forecasting](https://mlsanity.com/paper/2506.12800/) (2025)
- [Uncovering Dominant Features in Short-term Power Load Forecasting Based on Multi-source Feature](https://mlsanity.com/paper/2103.12534/) (2021)
- [Few-Shot Load Forecasting Under Data Scarcity in Smart Grids: A Meta-Learning Approach](https://mlsanity.com/paper/2406.05887/) (2024)

## Built on by (most cited first, 3 of 3)

- [Latent Mixture of Symmetries for Sample-Efficient Dynamic Learning](https://mlsanity.com/paper/2510.03578/) (2025)
- [Neural Predictive Control to Coordinate Discrete- and Continuous-Time Models for Time-Series Analysis with Control-Theoretical Improvements](https://mlsanity.com/paper/2508.01833/) (2025)
- [Predicting Power-System Dynamic Trajectories with Foundation Models](https://mlsanity.com/paper/2604.14991/) (2026)

## Abstract (arXiv)

Accurate residential load forecasting is critical for power system reliability with rising renewable integration and demand-side flexibility. However, most statistical and machine learning models treat external factors, such as weather, calendar effects, and pricing, as extra input, ignoring their heterogeneity, and thus limiting the extraction of useful external information. We propose a paradigm shift: external data should serve as meta-knowledge to dynamically adapt the forecasting model itself. Based on this idea, we design a meta-representation framework using hypernetworks that modulate selected parameters of a base Deep Learning (DL) model in response to external conditions. This provides both expressivity and adaptability. We further integrate a Mixture-of-Experts (MoE) mechanism to enhance efficiency through selective expert activation, while improving robustness by filtering redundant external inputs. The resulting model, dubbed as a Meta Mixture of Experts for External data (M2oE2), achieves substantial improvements in accuracy and robustness with limited additional overhead, outperforming existing state-of-the-art methods in diverse load datasets. The dataset and source code are publicly available at https://github.com/haorandd/M2oE2loadforecast.git.