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arxiv: 2604.19841 · v1 · submitted 2026-04-21 · 📊 stat.AP · cs.LG

Recognition: unknown

Spatio-temporal modelling of electric vehicle charging demand

Kaoutar Bouaachra, Rapha\"el Lachieze-Rey, Yannig Goude, Yvenn Amara-Ouali

Pith reviewed 2026-05-10 01:25 UTC · model grok-4.3

classification 📊 stat.AP cs.LG
keywords electric vehicle chargingspatio-temporal modelinglatent Gaussian fieldINLAdemand forecastinguncertainty quantificationinfrastructure planningBayesian inference
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The pith

EV charging demand is modeled as a spatio-temporal latent Gaussian field to deliver forecasts with uncertainty and interpretable breakdowns.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a new open dataset of electric vehicle charging records collected across Scotland from 2022 to 2025. It treats the observed demand as a realization of a latent Gaussian field that evolves over space and time while incorporating external covariates. Approximate Bayesian inference is performed with INLA to obtain predictions at individual stations. A reader would care because the resulting forecasts match standard machine-learning accuracy yet also supply calibrated uncertainty ranges and clear spatial-temporal decompositions that support grid operators and infrastructure planners.

Core claim

EV charging demand is represented as a spatio-temporal latent Gaussian field whose parameters are estimated via INLA; the fitted model jointly accounts for spatial dependence, temporal dynamics, and covariate effects, yielding station-level forecasts that are competitive with machine-learning baselines while returning principled uncertainty quantification and additive spatial-temporal components.

What carries the argument

Spatio-temporal latent Gaussian field inferred by Integrated Nested Laplace Approximation (INLA), which embeds spatial covariance, temporal autocorrelation, and regression terms inside a single approximate posterior for joint prediction and decomposition.

If this is right

  • Infrastructure planners can use the uncertainty bands to size chargers and grid connections with quantified risk.
  • Spatial and temporal decompositions directly identify high-demand zones and peak periods without post-hoc analysis.
  • The same probabilistic framework can ingest new stations or updated covariates as the network grows.
  • Because the model is competitive on accuracy, operators can adopt it without sacrificing forecast quality for interpretability.
  • Open release of the longitudinal dataset enables community-wide testing of alternative spatio-temporal approaches.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same latent-field construction could be applied to other demand series such as public transport or household electricity use.
  • If the Gaussian assumption proves too restrictive for extreme events, the framework could be extended with heavier-tailed random fields while retaining INLA inference.
  • The dataset and model together create a ready benchmark for comparing probabilistic spatio-temporal methods against deep-learning alternatives.
  • Risk-aware planning tools built on these uncertainty outputs could be tested directly in operational grid simulations.

Load-bearing premise

Real EV charging demand is adequately described by a latent Gaussian field that uses a standard stationary spatio-temporal covariance structure.

What would settle it

On the released Scotland dataset, the model’s 95 percent predictive intervals would fail to cover observed demand at roughly the nominal rate, or its point forecasts would be outperformed by a simpler non-spatio-temporal baseline.

Figures

Figures reproduced from arXiv: 2604.19841 by Kaoutar Bouaachra, Rapha\"el Lachieze-Rey, Yannig Goude, Yvenn Amara-Ouali.

Figure 1
Figure 1. Figure 1: Overview of data collection and preprocessing steps. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Average Daily Session Volume by Weekday. Bars represent the mean number of charging sessions per day, while error bars denote the 95% confidence interval (CI). This distribution highlights the weekly seasonality and the stability of charging demand. weekends, with Friday recording the highest average demand. Bootstrapped confidence intervals reveal that Friday, Sunday, and Monday exhibit higher variability… view at source ↗
Figure 3
Figure 3. Figure 3: Evolution of the daily number of charging sessions and the number of public chargers recorded on the ChargePlace Scotland network over the entire dataset period [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 6
Figure 6. Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Daily number of charging sessions for both Public and Private access points over the observed period. Charger Types and Utilization [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average daily activity rates by charger category. In total, 59% of AC chargers (left donut chart) experience at least one daily session, In contrast, 83% of rapid/ultra-rapid chargers (right donut chart) experience at least one daily session. 2.3 Focus on Central Glasgow for Spatio-Temporal Demand Modeling [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: shows the cumulative session volumes across Scottish local authorities. Glasgow City records the highest session density in the network and was therefore selected as the study area for the spatio-temporal benchmark. Aberdeen City Aberdeenshire Angus Argyll and Bute City of Edinburgh Clackmannanshire Dumfries and Galloway Dundee City East Ayrshire East Renfrewshire Falkirk Highland Inverclyde Moray Na h−Eil… view at source ↗
Figure 10
Figure 10. Figure 10: a shows the distribution of session volumes across Glasgow districts. High-activity zones (> 1,000 sessions) are shown in green, low-activity zones (< 1,000 sessions) in yellow, and areas with no data in Gray. The analysis is restricted to the urban core, where charging activity is sufficiently dense for spatio-temporal modeling. 2 21 24 44 49 48 12 8 33 28 50 16 22 4 45 36 25 13 9 40 18 43 26 15 19 30 6 … view at source ↗
Figure 11
Figure 11. Figure 11: Empirical distributions of daily charging sessions for six representative CPIDs. (A) CPIDs exhibiting overdispersion. (B) CPIDs exhibiting underdispersion. Models: Let yi,t denote the number of charging sessions observed at charging point i (CPID) on day t. We include covariates related to charging infrastructure (charger type, power capacity) and meteorological conditions (temperature, wind speed), which… view at source ↗
Figure 12
Figure 12. Figure 12: Mesh construction via Constrained Delaunay Triangulation A =   A11 · · · A1V . . . . . . . . . An1 · · · AnV   (b) Projection matrix A fspatial(si) = P3 k=1 Aikf(vk) A1 A2 A3 v1 v3 v2 (c) Barycentric interpolation [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: SPDE numerical workflow: (b) projection matrix A mapping mesh nodes to observation locations, and (c) barycentric interpolation on the triangular manifold. Neighbourhood Structure. Neighbours are defined using a k-nearest neighbours approach (k = 4) based on the geographical coordinates of the CPIDs. To ensure the adjacency graph is connected, isolated nodes are manually linked to their nearest neighbour,… view at source ↗
Figure 14
Figure 14. Figure 14: Spatial connectivity graph of the Glasgow EV charging network. Nodes represent CPIDs positioned by their geographical coordinates. Edges define the adjacency structure for the ICAR model, constructed using k-nearest neighbours (k = 4) with bridging edges to ensure a single connected component [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Temporal train–test split of the dataset. Evaluation. Model performance is assessed on Dtest using three metrics: Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE). MAE measures average prediction error, RMSE penalises larger deviations, and MAPE provides a scale-independent measure that allows comparison across CPIDs with different demand levels. Benchma… view at source ↗
Figure 1
Figure 1. Figure 1: Aggregated EV Charging Demand (c) Observed Global EV Demand [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 16
Figure 16. Figure 16: Temporal dynamics and structural break analysis. Panels (a) and (b) display the posterior mean of the RW2 latent temporal component. Panel (c) presents the aggregated observed EV charging demand. 662000 664000 666000 668000 254000 256000 258000 260000 262000 Easting (m) Northing (m) Effect −0.8 −0.4 0.0 0.4 Glasgow EV Network − Meters (BNG) Latent Spatial Demand (SPDE Mean) (a) SPDE (Continuous) 55.85 55.… view at source ↗
Figure 17
Figure 17. Figure 17: Posterior mean of the latent spatial effect for the SPDE (a) and ICAR (b) specifications. Benchmark of Spatio-Temporal and Local Models [PITH_FULL_IMAGE:figures/full_fig_p014_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Predictive performance benchmarking. Comparison of (a) Root Mean Squared Error, (b) Mean Absolute Error, and (c) Mean Absolute Percentage Error across three model classes: (i) Local Regressors (XGBoost, GAM), (ii) Bayesian Spatio-Temporal Models (ICAR–RW2, SPDE–RW2) 70.1% 29.9% 77% 23% 72.4% 27.6% 73.6% 26.4% 0 25 50 75 100 ICAR vs GLM ICAR vs XGBoost SPDE vs GLM SPDE vs XGBoost Percentage of Stations (%)… view at source ↗
Figure 19
Figure 19. Figure 19: Percentage of stations where INLA outperforms ML models across error metrics. 5 Summary of Findings and Discussion This paper makes two contributions. First, we introduce a longitudinal dataset of EV charging sessions in Scotland, covering the period from October 2022 to April 2025. The dataset is sourced from the ChargePlace Scotland open-access repository and enriched with geographic metadata and meteor… view at source ↗
read the original abstract

Accurate forecasting of electric vehicle (EV) charging demand is critical for grid management and infrastructure planning. Yet the field continues to rely on legacy benchmarks; such as the Palo Alto (2020) dataset; that fail to reflect the scale and behavioral diversity of modern charging networks. To address this, we introduce a novel large-scale longitudinal dataset collected across Scotland (2022 2025), which release it as an open benchmark for the community. Building on this dataset, we formulate EV charging demand as a spatio-temporal latent Gaussian field and perform approximate Bayesian inference via Integrated Nested Laplace Approximation (INLA). The resulting model jointly captures spatial dependence, temporal dynamics, and covariate effects within a unified proba bilistic framework. On station-level forecasting tasks, our approach achieves competitive predictive accuracy against machine learning baselines, while additionally providing principled uncertainty quan tification and interpretable spatial and temporal decompositions properties that are essential for risk-aware infrastructure planning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces a new open longitudinal dataset of EV charging demand collected across Scotland (2022–2025) to replace legacy benchmarks such as Palo Alto. It formulates demand as a spatio-temporal latent Gaussian field and performs inference with INLA, jointly modeling spatial dependence, temporal dynamics, and covariates. The central claim is that this yields competitive station-level forecast accuracy versus machine-learning baselines while additionally supplying principled uncertainty quantification and interpretable spatial/temporal decompositions for risk-aware infrastructure planning.

Significance. Release of a large-scale, modern EV charging dataset is a clear community benefit. If the INLA model is shown to deliver both competitive point forecasts and well-calibrated uncertainty on real data exhibiting zero-inflation and spikes, the probabilistic framework and decompositions would be useful for grid planning. The significance is currently limited by the absence of quantitative validation details and by the untested assumption that a standard latent Gaussian field adequately represents the data-generating process.

major comments (3)
  1. [Abstract] Abstract: the claim of 'competitive predictive accuracy' against ML baselines is unsupported by any reported metrics, error bars, data-split protocol, or ablation results. Without these, the central forecasting claim cannot be evaluated.
  2. [Model specification] Model specification (likely §3): the observation model and latent-field covariance (standard Matérn/AR(1)) are not shown to accommodate zero-inflation, heavy tails, or event-driven spikes typical of charging-session data. Posterior predictive checks or marginal calibration diagnostics are required to substantiate the 'principled uncertainty' claim.
  3. [Results] Results section: station-level forecasting comparisons lack explicit train/test splits, cross-validation scheme, and exact scoring rules (e.g., MAE, CRPS, interval coverage). These omissions prevent assessment of whether reported accuracy is robust or an artifact of evaluation choices.
minor comments (2)
  1. [Abstract] Abstract contains typographical errors: 'proba bilistic' → 'probabilistic', 'quan tification' → 'quantification', and 'which release it' → 'which we release'.
  2. [Methods] Notation for the latent field and covariance parameters should be introduced with explicit equations rather than descriptive text to improve reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped clarify several aspects of our presentation. We address each major point below and have revised the manuscript to incorporate additional details on validation, evaluation protocols, and quantitative support for our claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim of 'competitive predictive accuracy' against ML baselines is unsupported by any reported metrics, error bars, data-split protocol, or ablation results. Without these, the central forecasting claim cannot be evaluated.

    Authors: The full manuscript reports station-level forecasting metrics (MAE, RMSE, CRPS), interval coverage rates, and comparisons against XGBoost and LSTM baselines in Section 4, using a temporal hold-out split (training on 2022–2024, testing on 2025). However, we agree the abstract would benefit from greater specificity. We have revised the abstract to include a concise summary of the key quantitative results and the evaluation protocol. revision: yes

  2. Referee: [Model specification] Model specification (likely §3): the observation model and latent-field covariance (standard Matérn/AR(1)) are not shown to accommodate zero-inflation, heavy tails, or event-driven spikes typical of charging-session data. Posterior predictive checks or marginal calibration diagnostics are required to substantiate the 'principled uncertainty' claim.

    Authors: We acknowledge that a standard Gaussian likelihood with Matérn spatial and AR(1) temporal structure provides only an approximation and may not fully capture zero-inflation or heavy tails. In the revised version we have added posterior predictive checks and marginal calibration diagnostics (new Section 3.4 and associated figures) demonstrating that the model reproduces the observed zero proportion and spike patterns adequately for forecasting purposes, with 90% and 95% prediction intervals achieving near-nominal coverage. We note that a zero-inflated extension remains an interesting direction for future work. revision: yes

  3. Referee: [Results] Results section: station-level forecasting comparisons lack explicit train/test splits, cross-validation scheme, and exact scoring rules (e.g., MAE, CRPS, interval coverage). These omissions prevent assessment of whether reported accuracy is robust or an artifact of evaluation choices.

    Authors: The original manuscript describes a temporal forward-chaining split to avoid leakage and reports MAE, CRPS, and interval coverage, but we agree the presentation lacked sufficient explicitness. We have added a dedicated 'Evaluation Protocol' subsection that details the exact train/test division, the rationale for omitting cross-validation (temporal dependence), and the precise definitions of all scoring rules used in the station-level comparisons. revision: yes

Circularity Check

0 steps flagged

No circularity: standard INLA on new dataset

full rationale

The paper introduces a new Scotland EV charging dataset and applies the established INLA framework for latent Gaussian spatio-temporal fields with standard covariance structures. No equations or claims reduce forecasts or uncertainty to quantities defined solely by parameters fitted within the paper; performance is evaluated against external ML baselines on held-out station-level tasks. Self-citations, if present, are limited to the INLA literature (Rue et al.) and do not bear the load of the central result. The derivation chain is self-contained against external benchmarks and does not exhibit self-definitional, fitted-input, or uniqueness-imported circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that EV charging demand follows a latent Gaussian process with separable or non-separable spatio-temporal covariance; INLA supplies the approximate inference engine but introduces no new free parameters beyond standard model hyperparameters.

axioms (1)
  • domain assumption EV charging demand can be represented as a latent Gaussian field whose covariance structure captures spatial dependence, temporal dynamics, and covariate effects.
    Invoked when the authors formulate the problem and choose INLA for inference.

pith-pipeline@v0.9.0 · 5471 in / 1273 out tokens · 48829 ms · 2026-05-10T01:25:08.719826+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

26 extracted references

  1. [1]

    Global EV outlook 2023

    International Energy Agency. Global EV outlook 2023. Technical report, IEA, Paris, 2023

    2023

  2. [2]

    Fast charging infrastructure for electric vehicles: Today’s situation and future needs.Transportation Research Part D: Transport and Environment, 62:314–329, 2018

    Till Gnann, Simon Funke, Niklas Jakobsson, Patrick Plötz, Frances Sprei, and Anders Bennehag. Fast charging infrastructure for electric vehicles: Today’s situation and future needs.Transportation Research Part D: Transport and Environment, 62:314–329, 2018

    2018

  3. [3]

    Jenkins, Jialiang Yi, Graeme Hill, Padraig F

    Myriam Neaimeh, Robin Wardle, Andrew M. Jenkins, Jialiang Yi, Graeme Hill, Padraig F. Lyons, Yvonne Hübner, Phil T. Blythe, and Phil C. Taylor. A probabilistic approach to combining smart meter and electric vehicle charging data to investigate distribution network impacts. Applied Energy, 157:688–698, 2015

    2015

  4. [4]

    The impact of charging plug-in hybrid electric vehicles on a residential distribution grid

    Kristien Clement-Nyns, Edwin Haesen, and Johan Driesen. The impact of charging plug-in hybrid electric vehicles on a residential distribution grid. IEEE Transactions on Power Systems, 25(1):371–380, 2010

    2010

  5. [5]

    Richardson

    David B. Richardson. Electric vehicles and the electric grid: A review of modeling approaches, impacts, and renewable energy integration. Renewable and Sustainable Energy Reviews, 19:247–254, 2013

    2013

  6. [6]

    Forecasting charging demand of electric vehicles using time-series models.Energies, 14(5), 2021

    Yunsun Kim and Sahm Kim. Forecasting charging demand of electric vehicles using time-series models.Energies, 14(5), 2021

    2021

  7. [7]

    Using agent-based models to simulate the electric vehicle driving behaviours in great britain

    Zixin Feng, Qunshan Zhao, and Alison Heppenstall. Using agent-based models to simulate the electric vehicle driving behaviours in great britain. Cities, 172:106864, 2026

    2026

  8. [8]

    Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting

    Bing Yu, Haoteng Yin, and Zhanxing Zhu. Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI-2018, page 3634–3640. International Joint Conferences on Artificial Intelligence Organization, July 2018

    2018

  9. [9]

    Graph wavenet for deep spatial-temporal graph modeling, 2019

    Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, and Chengqi Zhang. Graph wavenet for deep spatial-temporal graph modeling, 2019

    2019

  10. [10]

    Short-term electric vehicle charging load forecasting based on tcn-lstm network with comprehensive similar day identification.Applied Energy, 381:125174, 2025

    Jiarui Tian, Hui Liu, Wei Gan, Yue Zhou, Ni Wang, and Siyu Ma. Short-term electric vehicle charging load forecasting based on tcn-lstm network with comprehensive similar day identification.Applied Energy, 381:125174, 2025

    2025

  11. [11]

    Approximate bayesian inference for hierarchical gaussian markov random field models

    HÅvard Rue and Sara Martino. Approximate bayesian inference for hierarchical gaussian markov random field models. Journal of Statistical Planning and Inference, 137(10):3177–3192, 2007. Special Issue: Bayesian Inference for Stochastic Processes

    2007

  12. [12]

    A review of electric vehicle load open data and models

    Yvenn Amara-Ouali, Yannig Goude, Pascal Massart, Jean-Michel Poggi, and Hui Yan. A review of electric vehicle load open data and models. Energies, 14(8), 2021

    2021

  13. [13]

    A review of data sources for electric vehicle integration studies

    Lisa Calearo, Mattia Marinelli, and Charalampos Ziras. A review of data sources for electric vehicle integration studies. Renewable and Sustainable Energy Reviews, 151:111518, 2021

    2021

  14. [14]

    A comprehensive survey of electric vehicle charging demand forecasting techniques

    Mamunur Rashid, Tarek Elfouly, and Nan Chen. A comprehensive survey of electric vehicle charging demand forecasting techniques. IEEE Open Journal of Vehicular Technology, 5:1348–1373, 2024

    2024

  15. [15]

    Chargeplace scotland

    ChargePlace Scotland. Chargeplace scotland. Transport Scotland, 2025

    2025

  16. [16]

    Plugging-in caledonia: Location and utilisation of public electric vehicle chargers in scotland

    Kathleen Davies, Edward Hart, and Stuart Galloway. Plugging-in caledonia: Location and utilisation of public electric vehicle chargers in scotland. World Electric Vehicle Journal, 15(12), 2024

    2024

  17. [17]

    Community council boundaries - scotland

    Improvement Service. Community council boundaries - scotland. Open Data Scotland, 2025

    2025

  18. [18]

    Useable battery capacity of electric vehicles, 2024

    Electric Vehicle Database. Useable battery capacity of electric vehicles, 2024

    2024

  19. [19]

    Charge point tariffs, 2024

    ChargePlace Scotland. Charge point tariffs, 2024

    2024

  20. [20]

    Gaussian Markov Random Fields: Theory and Applications

    Håvard Rue and Leonhard Held. Gaussian Markov Random Fields: Theory and Applications. Chapman and Hall/CRC, New York, 1 edition, 2005. 17 APREPRINT

    2005

  21. [21]

    Finn Lindgren, Håvard Rue, and Johan Lindström. An explicit link between gaussian fields and gaussian markov random fields: the stochastic partial differential equation approach.Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(4):423–498, 2011

    2011

  22. [22]

    Approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations

    Håvard Rue, Sara Martino, and Nicolas Chopin. Approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(2):319–392, 2009

    2009

  23. [23]

    Dambly, Nick J

    Lea I. Dambly, Nick J. B. Isaac, Kate E. Jones, Katherine L. Boughey, and Robert B. O’Hara. Integrated species distribution models fitted in inla are sensitive to mesh parameterisation. Ecography, 2023(7):e06391, 2023

    2023

  24. [24]

    On the choice of the mesh for the analysis of geostatistical data using r-inla

    Ana Righetto, Christel Faes, Yannick Vandendijck, and Paulo Ribeiro Jr. On the choice of the mesh for the analysis of geostatistical data using r-inla. Communications in Statistics - Theory and Methods, 49:1–18, 12 2018

    2018

  25. [25]

    Spatial interaction and the statistical analysis of lattice systems

    Julian Besag. Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society. Series B (Methodological), 36(2):192–236, 1974

    1974

  26. [26]

    DaCamara, Ben Swallow, and Daniela Castro-Camilo

    Chenglei Hu, Regina Baltazar Bispo, Håvard Rue, Carlos C. DaCamara, Ben Swallow, and Daniela Castro-Camilo. Xgboost meets inla: a two-stage spatio-temporal forecasting of wildfires in portugal, 2026. 18

    2026