pith. sign in

arxiv: 2606.25301 · v1 · pith:4WY3TBAWnew · submitted 2026-06-24 · 📡 eess.SY · cs.SY

Active Learning for Optimal Experimental Design in Machine Learning-Based Building Energy System Identification

Nam T. Nguyen , Truong X. Nghiem This is my paper

Pith reviewed 2026-06-25 20:37 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords active learningoptimal experimental designbuilding energy systemsHVAC thermal dynamicsmachine learningsystem identificationneural networksGaussian processes
0
0 comments X

The pith

Active learning for choosing training experiments outperforms random sampling when identifying building energy system dynamics with machine learning models.

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

The paper systematically tests fourteen active learning methods to select informative control inputs for training data instead of using uniform random sampling. These methods are applied to two types of models, feedforward neural networks and Gaussian processes, for capturing HVAC thermal dynamics. Evaluation occurs on the BOPTEST high-fidelity building simulator under varied initial data sizes and input constraints. Results show lower prediction errors with active learning, reaching reductions of up to 54 percent, though gains differ by acquisition function and operating condition. This approach matters because higher-quality training data can improve model accuracy for energy system prediction without relying solely on physics-based equations.

Core claim

The central claim is that optimal experimental design realized through active learning yields machine learning models of building energy systems with lower root mean square error than models trained on passively collected uniformly random data, when both are evaluated across multiple test scenarios on the BOPTEST simulator. The improvement holds for both deterministic neural networks and stochastic Gaussian processes, with the magnitude varying by the specific acquisition function category and system operating regime.

What carries the argument

Four categories of active learning acquisition functions (data space, uncertainty, information gain, and model change) used to select control inputs for collecting training data on HVAC thermal dynamics.

Load-bearing premise

The BOPTEST high-fidelity simulator accurately captures the dynamics and conditions of real building energy systems.

What would settle it

Collecting data from a physical building HVAC system using the same active learning procedures and comparing the resulting model errors to those obtained in the BOPTEST simulations.

Figures

Figures reproduced from arXiv: 2606.25301 by Nam T. Nguyen, Truong X. Nghiem.

Figure 1
Figure 1. Figure 1: In-door thermal dynamics system. Modelica Wetter et al. (2014) to model realistic HVAC dynamics derived from real-world systems. The BESTEST Case is used for the performance comparison, since it has the same structure as the indoor thermal dynamics presented in [PITH_FULL_IMAGE:figures/full_fig_p019_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Test RMSE of the GP model versus elapsed online learning time, for two initial data points and ramp constraints of 0.8 ◦C on 𝑇 𝑠 and 2% on ̇𝑚, across the 0–2 h, 0–12 h, and 0–24 h evaluation windows ( [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Test RMSE of the GP model versus elapsed online learning time, for two initial data points and ramp constraints of 2 ◦C on 𝑇 𝑠 and 5% on ̇𝑚, across the 0–2 h, 0–12 h, and 0–24 h evaluation windows ( [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Test RMSE of the GP model versus elapsed online learning time, for 10 initial data points and ramp constraints of 8 ◦C on 𝑇 𝑠 and 20% on ̇𝑚, across the 0–2 h, 0–12 h, and 0–24 h evaluation windows ( [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Test RMSE of the NN model versus elapsed online learning time, for two initial data points and ramp constraints of 0.8 ◦C on 𝑇 𝑠 and 2% on ̇𝑚 ( [PITH_FULL_IMAGE:figures/full_fig_p026_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Test RMSE of the NN model versus elapsed online learning time, for two initial data points and ramp constraints of 2 ◦C on 𝑇 𝑠 and 5% on ̇𝑚 ( [PITH_FULL_IMAGE:figures/full_fig_p027_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Test RMSE of the NN model versus elapsed online learning time, for 10 initial data points and ramp constraints of 8 ◦C on 𝑇 𝑠 and 20% on ̇𝑚 ( [PITH_FULL_IMAGE:figures/full_fig_p028_7.png] view at source ↗
read the original abstract

Machine learning (ML) techniques have been commonly adopted to identify the dynamics of building energy systems (BESs), owing to their flexibility relative to first-principles, physics-based modeling approaches. Beyond the choice of ML architecture, the quality of the training data plays an essential role in the resulting model performance. Optimal experimental design (OED), realized in this work through active learning (AL), determines which experiments to conduct in order to collect informative data, rather than relying on standard approaches such as uniformly random sampling. This paper proposes a systematic comparison of OED via AL for building energy system identification, with a particular focus on HVAC thermal dynamics. We investigate fourteen AL techniques across two ML model classes, namely a deterministic feedforward neural network and a stochastic Gaussian process, and classify these techniques into four categories: data space, uncertainty, information gain, and model change. To examine the AL algorithms under realistic conditions, we implement and evaluate them on the high-fidelity building simulator BOPTEST. The results, reported as the root mean square error across multiple test scenarios with varying initial dataset sizes and control input constraints, show that AL-based models generally outperform models trained via passive learning (PL) with uniformly random control inputs, achieving error reductions of up to 54\%, although the magnitude and consistency of this improvement vary across acquisition functions and operating regimes.

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

2 major / 1 minor

Summary. The paper claims that active learning (AL) techniques for optimal experimental design outperform passive learning (PL) with uniformly random control inputs in machine learning-based identification of building energy system (BES) dynamics. Using the BOPTEST high-fidelity simulator, fourteen AL techniques are evaluated across feedforward neural networks and Gaussian processes, categorized into data space, uncertainty, information gain, and model change. The results show error reductions of up to 54% in root mean square error, though the improvement varies across acquisition functions and operating regimes, with tests under varying initial dataset sizes and input constraints.

Significance. If the results hold with proper statistical support, this work would be significant for the field of building energy system identification by providing empirical evidence that AL can substantially improve model accuracy compared to standard random sampling approaches. The systematic comparison of multiple techniques on a realistic simulator could guide practitioners in selecting appropriate OED methods for HVAC dynamics modeling.

major comments (2)
  1. Results: The reported performance gains, including the 54% error reduction, are presented without details on statistical significance testing, the exact number of experimental runs, variance across trials, or sensitivity to initial dataset sizes, which are critical for establishing the robustness of the central claim.
  2. Methods: The manuscript does not provide sufficient details on the exact implementation of the fourteen AL techniques, data exclusion rules, or how the techniques are applied under different control input constraints, hindering reproducibility and verification of the findings.
minor comments (1)
  1. Abstract: The abstract mentions 'two ML model classes' but could benefit from briefly noting the specific architectures used for the neural network and Gaussian process.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments correctly identify areas where additional rigor and transparency will strengthen the paper. We address both major comments below and will revise the manuscript to incorporate the requested details.

read point-by-point responses

  1. Referee: The reported performance gains, including the 54% error reduction, are presented without details on statistical significance testing, the exact number of experimental runs, variance across trials, or sensitivity to initial dataset sizes, which are critical for establishing the robustness of the central claim.

    Authors: We agree that explicit statistical support is necessary. The current manuscript reports results across multiple test scenarios with varying initial dataset sizes, but does not include the number of independent trials, variance measures, or formal significance tests. In the revision we will add these: we will state that each configuration was repeated over 10 independent trials, report mean RMSE with standard deviation, and include paired t-tests (or Wilcoxon tests where normality assumptions fail) comparing AL versus PL. We will also expand the sensitivity analysis to initial dataset sizes with additional tabulated results. revision: yes

  2. Referee: The manuscript does not provide sufficient details on the exact implementation of the fourteen AL techniques, data exclusion rules, or how the techniques are applied under different control input constraints, hindering reproducibility and verification of the findings.

    Authors: We accept that the current level of implementation detail is insufficient for full reproducibility. The revision will include a new subsection (or appendix) that specifies the exact acquisition-function formulations, any hyperparameters, data-exclusion criteria (e.g., rejection of duplicate or infeasible samples), and the precise mechanism used to enforce control-input constraints (projection onto feasible sets or rejection sampling). Pseudocode for the overall active-learning loop will also be added. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical results from external simulator

full rationale

The paper performs a direct empirical comparison of active learning (AL) acquisition functions against passive learning (PL) with random inputs. Performance is measured by root-mean-square error on held-out test scenarios generated by the independent BOPTEST high-fidelity simulator. No equations, fitted parameters, or self-citations are used to derive the reported error reductions; the 54% figure is obtained by running the algorithms on the simulator and computing the metric. The central claim therefore rests on external simulation output rather than any reduction to its own inputs or prior self-referential results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work depends on the external BOPTEST simulator as a faithful proxy for real systems and on standard assumptions of neural network and Gaussian process training; no additional free parameters, axioms, or invented entities are identifiable from the abstract.

pith-pipeline@v0.9.1-grok · 5774 in / 1022 out tokens · 26475 ms · 2026-06-25T20:37:35.222741+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

28 extracted references · 20 canonical work pages · 1 internal anchor

  1. [1]

    IEEE Transactions on Robotics 35, 1071–1083

    Active learning of dynamics for data-driven control using koopman operators. IEEE Transactions on Robotics 35, 1071–1083. doi:10.1109/TRO.2019.2923880. American Society of Heating, Refrigerating and Air-Conditioning Engineers,

    work page doi:10.1109/tro.2019.2923880 2019

  2. [2]

    8927–8939

    Gone fishing: Neural active learning with fisher embeddings, in: Advances in Neural Information Processing Systems 34 (NeurIPS 2021), pp. 8927–8939. Ash, J.T., Zhang, C., Krishnamurthy, A., Langford, J., Agarwal, A.,

    2021

  3. [3]

    URL:https://arxiv.org/abs/1906.03671,arXiv:1906.03671

    Deep batch active learning by diverse, uncertain gradient lower bounds. URL:https://arxiv.org/abs/1906.03671,arXiv:1906.03671. Atkinson, A., Donev, A., Tobias, R.,

    arXiv 1906

  4. [4]

    International Journal of Control 97, 1512–1531

    A learning- and scenario-based mpc design for nonlinear systems in lpv framework with safety and stability guarantees. International Journal of Control 97, 1512–1531. URL:https://doi.org/10.1080/00207179.2023.2212814, doi:10.1080/00207179.2023.2212814,arXiv:https://doi.org/10.1080/00207179.2023.2212814. Bemporad, A.,

    work page doi:10.1080/00207179.2023.2212814 2023

  5. [5]

    Information Sciences 626, 275–292

    Active learning for regression by inverse distance weighting. Information Sciences 626, 275–292. URL:https: //www.sciencedirect.com/science/article/pii/S0020025523000282, doi:https://doi.org/10.1016/j.ins.2023.01.028. Biemann, M., Gunkel, P.A., Scheller, F., Huang, L., Liu, X.,

    work page doi:10.1016/j.ins.2023.01.028 2023

  6. [6]

    IEEE Internet of Things Journal 10, 13876–13894

    Data center hvac control harnessing flexibility potential via real-time pricing cost optimization using reinforcement learning. IEEE Internet of Things Journal 10, 13876–13894. doi:10.1109/JIOT.2023.3263261. Blum, D., Arroyo, J., Huang, S., Drgoňa, J., Jorissen, F., Walnum, H.T., Chen, Y., Benne, K., Vrabie, D., Wetter, M., Helsen, L.,

    work page doi:10.1109/jiot.2023.3263261 2023

  7. [7]

    Journal of Building Performance Simulation 14, 586–610

    Building optimization testing framework (boptest) for simulation-based benchmarking of control strategies in buildings. Journal of Building Performance Simulation 14, 586–610. URL:https://doi.org/10.1080/19401493.2021.1986574, doi:10.1080/19401493.2021. 1986574,arXiv:https://doi.org/10.1080/19401493.2021.1986574. Buisson-Fenet, M., Solowjow, F., Trimpe, S.,

    work page doi:10.1080/19401493.2021.1986574 2021

  8. [8]

    Actively learning gaussian process dynamics, in: Bayen, A.M., Jadbabaie, A., Pappas, G., Parrilo,P.A.,Recht,B.,Tomlin,C.,Zeilinger,M.(Eds.),Proceedingsofthe2ndConferenceonLearningforDynamicsandControl,PMLR.pp. 5–15. URL:https://proceedings.mlr.press/v120/buisson-fenet20a.html. Burbidge,R.,Rowland,J.J.,King,R.D.,2007. Activelearningforregressionbasedonquer...

    2007

  9. [9]

    Tissue antigens 62, 378–384

    Sensitive quantitative predictions of peptide-mhc binding by a ‘query by committee’artificial neural network approach. Tissue antigens 62, 378–384. Cai,W.,Zhang,Y.,Zhou,J.,2013. Maximizingexpectedmodelchangeforactivelearninginregression,in:2013IEEE13thinternationalconference on data mining, IEEE. pp. 51–60. Carpentier, A., Lazaric, A., Ghavamzadeh, M., Mu...

    2013

  10. [10]

    modAL: A modular active learning framework for Python

    modal: A modular active learning framework for python. URL:https://arxiv.org/abs/1805.00979, arXiv:1805.00979. Drgoňa,J.,Arroyo,J.,CupeiroFigueroa,I.,Blum,D.,Arendt,K.,Kim,D.,Ollé,E.P.,Oravec,J.,Wetter,M.,Vrabie,D.L.,Helsen,L.,2020. Allyou need to know about model predictive control for buildings. Annual Reviews in Control 50, 190–232. URL:https://www.sci...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.arcontrol.2020.09.001 2020

  11. [11]

    Applied Energy 356, 122356

    Integrating active learning and semi-supervised learning for improved data-driven hvac fault diagnosis performance. Applied Energy 356, 122356. URL:https://www.sciencedirect.com/science/article/pii/S0306261923017208, doi:https://doi.org/10.1016/j.apenergy.2023.122356. Frazier, P.I.,

    work page doi:10.1016/j.apenergy.2023.122356 2023

  12. [12]

    URL:https://arxiv.org/abs/1807.02811,arXiv:1807.02811

    A tutorial on bayesian optimization. URL:https://arxiv.org/abs/1807.02811,arXiv:1807.02811. Freund, Y., Seung, H., Shamir, E., Tishby, N.,

    Pith/arXiv arXiv

  13. [13]

    Machine Learning 28, 133–168

    Selective sampling using the query by committee algorithm. Machine Learning 28, 133–168. doi:10.1023/a:1007330508534. Gal,Y.,Ghahramani,Z.,2016.Dropoutasabayesianapproximation:Representingmodeluncertaintyindeeplearning,in:Balcan,M.F.,Weinberger, K.Q.(Eds.),ProceedingsofThe33rdInternationalConferenceonMachineLearning,PMLR,NewYork,NewYork,USA.pp.1050–1059. ...

    work page doi:10.1023/a:1007330508534 2016

  14. [14]

    URL:https: //arxiv.org/abs/1112.5745,arXiv:1112.5745

    Bayesian active learning for classification and preference learning. URL:https: //arxiv.org/abs/1112.5745,arXiv:1112.5745. Jain, A., Nghiem, T., Morari, M., Mangharam, R.,

    Pith/arXiv arXiv

  15. [15]

    Learning and control using gaussian processes, in: 2018 ACM/IEEE 9th International Conference on Cyber-Physical Systems (ICCPS), pp. 140–149. doi:10.1109/ICCPS.2018.00022. Keesman, K.J.,

    work page doi:10.1109/iccps.2018.00022 2018

  16. [16]

    URL:https://arxiv.org/abs/1412.6980,arXiv:1412.6980

    Adam: A method for stochastic optimization. URL:https://arxiv.org/abs/1412.6980,arXiv:1412.6980. Kontoudis, G.P., Otte, M.W.,

    Pith/arXiv arXiv

  17. [17]

    Advances in Applied Energy 16, 100189

    Active learning concerning sampling cost for enhancing ai-enabled building energy system modeling. Advances in Applied Energy 16, 100189. URL:https://www.sciencedirect.com/science/article/pii/ S2666792424000271, doi:https://doi.org/10.1016/j.adapen.2024.100189. Ly,A.,Marsman,M.,Verhagen,J.,Grasman,R.P.,Wagenmakers,E.J.,2017. Atutorialonfisherinformation. ...

    work page doi:10.1016/j.adapen.2024.100189 2024

  18. [18]

    Scientific Reports 14, 19894

    Active learning-based machine learning approach for enhancing environmental sustainability in green building energy consumption. Scientific Reports 14, 19894. Mania,H.,Jordan,M.I.,Recht,B.,2022. Activelearningfornonlinearsystemidentificationwithguarantees. JournalofMachineLearningResearch 23, 1–30. URL:http://jmlr.org/papers/v23/20-807.html. Mocanu,E.,Moc...

    work page doi:10.1109/tsg.2018.2834219 2022

  19. [19]

    IEEE Access 14, 6481–6500

    Physics-informed data-driven modeling of hvac systems: A systematic analysis. IEEE Access 14, 6481–6500. doi:10.1109/ACCESS.2026.3653004. Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., et al.,

    work page doi:10.1109/access.2026.3653004 2026

  20. [20]

    586–591 vol.1

    A direct adaptive method for faster backpropagation learning: the rprop algorithm, in: IEEE International Conference on Neural Networks, pp. 586–591 vol.1. doi:10.1109/ICNN.1993.298623. Roinila, T., Abdollahi, H., Santi, E.,

    work page doi:10.1109/icnn.1993.298623 1993

  21. [21]

    IEEE Transactions on Power Electronics 36, 3744–3756

    Frequency-domain identification based on pseudorandom sequences in analysis and control of dc power distribution systems: A review. IEEE Transactions on Power Electronics 36, 3744–3756. doi:10.1109/TPEL.2020.3024624. Settles, B.,

    work page doi:10.1109/tpel.2020.3024624 2020

  22. [22]

    Journal of Physics: Conference Series 2600, 132004

    Enhancing personalised thermal comfort models with active learning for improved hvac controls. Journal of Physics: Conference Series 2600, 132004. URL:https://doi.org/10.1088/1742-6596/2600/13/132004, doi:10.1088/ 1742-6596/2600/13/132004. Wang, X., Jin, Y., Schmitt, S., Olhofer, M.,

    work page doi:10.1088/1742-6596/2600/13/132004

  23. [23]

    Journal of Building Performance Simu- lation 7, 253–270

    Modelica buildings library. Journal of Building Performance Simu- lation 7, 253–270. URL:https://doi.org/10.1080/19401493.2013.765506, doi:10.1080/19401493.2013.765506, arXiv:https://doi.org/10.1080/19401493.2013.765506. Wu, D.,

    work page doi:10.1080/19401493.2013.765506 2013

  24. [24]

    Pool-based sequential active learning for regression.IEEE Transactions on Neural Networks and Learning Systems, 30(5):1348–1359, 2019

    Pool-based sequential active learning for regression. IEEE Transactions on Neural Networks and Learning Systems 30, 1348–1359. doi:10.1109/TNNLS.2018.2868649. Wu, D., Lin, C.T., Huang, J.,

    work page doi:10.1109/tnnls.2018.2868649 2018

  25. [25]

    Information Sciences 474, 90–105

    Active learning for regression using greedy sampling. Information Sciences 474, 90–105. URL:https: //www.sciencedirect.com/science/article/pii/S0020025518307680, doi:https://doi.org/10.1016/j.ins.2018.09.060. Xie, K., Bemporad, A.,

    work page doi:10.1016/j.ins.2018.09.060 2018

  26. [26]

    7202–7207

    Online design of experiments by active learning for system identification of autoregressive models, in: 2024 IEEE 63rd Conference on Decision and Control (CDC), pp. 7202–7207. doi:10.1109/CDC56724.2024.10886678. Yang, J., Xia, B.,

    work page doi:10.1109/cdc56724.2024.10886678 2024

  27. [27]

    2646–2651

    Active learning using uncertainty information, in: 2016 23rd International Conference on Pattern Recognition (ICPR), pp. 2646–2651. doi:10.1109/ICPR.2016.7900034. Yu, H., Kim, S.,

    work page doi:10.1109/icpr.2016.7900034 2016

  28. [28]

    1151–1156

    Passive sampling for regression, in: 2010 IEEE International Conference on Data Mining, pp. 1151–1156. doi:10.1109/ ICDM.2010.9. Zhang,L.,2021. Data-drivenbuildingenergymodelingwithfeatureselectionandactivelearningfordatapredictivecontrol. EnergyandBuildings 252, 111436. Zhang, L., Wen, J.,

    2010