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Volume 14
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10.3390/computers14070287
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Article

Machine Learning Techniques for Uncertainty Estimation in Dynamic Aperture Prediction

by
Carlo Emilio Montanari
1,2,*,
Robert B. Appleby
1,
Davide Di Croce
2,3,
Massimo Giovannozzi
2,*,
Tatiana Pieloni
3,
Stefano Redaelli
2 and
Frederik F. Van der Veken
2
1
Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK
2
CERN, 1211 Geneva, Switzerland
3
Institute of Physics, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
*
Authors to whom correspondence should be addressed.
Computers 2025, 14(7), 287; https://doi.org/10.3390/computers14070287
Submission received: 8 May 2025 / Revised: 7 July 2025 / Accepted: 15 July 2025 / Published: 18 July 2025
(This article belongs to the Special Issue Machine Learning and Statistical Learning with Applications 2025)
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Abstract

The dynamic aperture is an essential concept in circular particle accelerators, providing the extent of the phase space region where particle motion remains stable over multiple turns. The accurate prediction of the dynamic aperture is key to optimising performance in accelerators such as the CERN Large Hadron Collider and is crucial for designing future accelerators like the CERN Future Circular Hadron Collider. Traditional methods for computing the dynamic aperture are computationally demanding and involve extensive numerical simulations with numerous initial phase space conditions. In our recent work, we have devised surrogate models to predict the dynamic aperture boundary both efficiently and accurately. These models have been further refined by incorporating them into a novel active learning framework. This framework enhances performance through continual retraining and intelligent data generation based on informed sampling driven by error estimation. A critical attribute of this framework is the precise estimation of uncertainty in dynamic aperture predictions. In this study, we investigate various machine learning techniques for uncertainty estimation, including Monte Carlo dropout, bootstrap methods, and aleatory uncertainty quantification. We evaluated these approaches to determine the most effective method for reliable uncertainty estimation in dynamic aperture predictions using machine learning techniques.
Keywords: surrogate modelling; uncertainty quantification; Monte Carlo dropout; bootstrap aggregation; dynamic aperture; accelerator modelling; epistemic uncertainty; LHC; HL-LHC; FCC surrogate modelling; uncertainty quantification; Monte Carlo dropout; bootstrap aggregation; dynamic aperture; accelerator modelling; epistemic uncertainty; LHC; HL-LHC; FCC
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MDPI and ACS Style

Montanari, C.E.; Appleby, R.B.; Di Croce, D.; Giovannozzi, M.; Pieloni, T.; Redaelli, S.; Van der Veken, F.F. Machine Learning Techniques for Uncertainty Estimation in Dynamic Aperture Prediction. Computers 2025, 14, 287. https://doi.org/10.3390/computers14070287

AMA Style

Montanari CE, Appleby RB, Di Croce D, Giovannozzi M, Pieloni T, Redaelli S, Van der Veken FF. Machine Learning Techniques for Uncertainty Estimation in Dynamic Aperture Prediction. Computers. 2025; 14(7):287. https://doi.org/10.3390/computers14070287

Chicago/Turabian Style

Montanari, Carlo Emilio, Robert B. Appleby, Davide Di Croce, Massimo Giovannozzi, Tatiana Pieloni, Stefano Redaelli, and Frederik F. Van der Veken. 2025. "Machine Learning Techniques for Uncertainty Estimation in Dynamic Aperture Prediction" Computers 14, no. 7: 287. https://doi.org/10.3390/computers14070287

APA Style

Montanari, C. E., Appleby, R. B., Di Croce, D., Giovannozzi, M., Pieloni, T., Redaelli, S., & Van der Veken, F. F. (2025). Machine Learning Techniques for Uncertainty Estimation in Dynamic Aperture Prediction. Computers, 14(7), 287. https://doi.org/10.3390/computers14070287

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