# Coherent Hierarchical Probabilistic Forecasting of Electric Vehicle Charging Demand

arXiv: https://arxiv.org/abs/2411.00337 · HTML: https://mlsanity.com/paper/2411.00337/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 42 references that are in the map.
- First posted on arXiv 1 Nov 2024.

## Builds on (most cited first, 9 of 9)

- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [Energy Demand Prediction with Federated Learning for Electric Vehicle Networks](https://mlsanity.com/paper/1909.00907/) (2019)
- [Multivariate Quantile Function Forecaster](https://mlsanity.com/paper/2202.11316/) (2022)
- [Probabilistic Charging Power Forecast of EVCS: Reinforcement Learning Assisted Deep Learning Approach](https://mlsanity.com/paper/2204.07905/) (2022)

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

- [Forecasting time series with constraints](https://mlsanity.com/paper/2502.10485/) (2025)
- [Optimizing Electric Vehicle Charging Station Placement Using Reinforcement Learning and Agent-Based Simulations](https://mlsanity.com/paper/2511.01218/) (2025)
- [Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure](https://mlsanity.com/paper/2610.13588/) (2026)

## Abstract (arXiv)

The growing penetration of electric vehicles (EVs) significantly changes typical load curves in smart grids. With the development of fast charging technology, the volatility of EV charging demand is increasing, which requires additional flexibility for real-time power balance. The forecasting of EV charging demand involves probabilistic modeling of high dimensional time series dynamics across diverse electric vehicle charging stations (EVCSs). This paper studies the forecasting problem of multiple EVCS in a hierarchical probabilistic manner. For each charging station, a deep learning model based on a partial input convex neural network (PICNN) is trained to predict the day-ahead charging demand's conditional distribution, preventing the common quantile crossing problem in traditional quantile regression models. Then, differentiable convex optimization layers (DCLs) are used to reconcile the scenarios sampled from the distributions to yield coherent scenarios that satisfy the hierarchical constraint. It learns a better weight matrix for adjusting the forecasting results of different targets in a machine-learning approach compared to traditional optimization-based hierarchical reconciling methods. Numerical experiments based on real-world EV charging data are conducted to demonstrate the efficacy of the proposed method.