Beam Measurements and Machine Learning at the CERN Large Hadron Collider Pasquale Arpaia, Gabriella Azzopardi, Frédéric Blanc, Xavier Buffat, Loic Coyle, Elena Fol, Francesco Giordano, Massimo Giovannozzi, Tatiana Pieloni, Roberto Prevete, Stefano Redaelli, Belen Salvachua, Benoît Salvant, Michael Schenk, Matteo Solfaroli Camillocci, Rogelio Tomás, Gianluca Valentino, Frederik Florentinus Van der Veken, and Jörg Wenninger P article accelerators are among the most complex instruments conceived by physicists for the exploration of the fundamental laws of nature. Of relevance for particle physics are the high-energy colliders, such as the CERN Large Hadron Collider (LHC), which hosts particle physics experiments that are probing the Standard Model predictions and looking for signs of physics beyond the standard model. Machine Learning for Beam Studies The particle beams circulating in the colliders need to be controlled in an accurate way with beam instrumentation, the key to the performance of a collider. The amount of data generated by beam instrumentation is so large that Machine Learning (ML) is making its way into the domain of Accelerator Physics, with several laboratories worldwide devoting intense efforts in this domain. The power of these tools has been exploited for advanced analysis of colliders data for decades, but it is only in recent years that ML techniques have found applications in the field of Accelerator Physics. The first attempts to use these techniques date to a few decades ago and dealt with beam diagnostics and beam control systems [1], [2]. However, some sizeable progress has been made only recently (see, e.g., [3]-[8] and references therein). Nowadays, there is a general agreement within the Accelerator Physics community of the need for and usefulness of ML techniques, which resulted in the publication of a white paper to review the state-of-the-art and present recommendations to encourage the development of such techniques in Accelerator Physics laboratories [9]. CERN has recently started focused efforts oriented towards ML techniques for beam dynamics studies at the Large Hadron Collider (LHC). The LHC complexity, in terms of the number of operational systems, size of data collected, variety of beam dynamics configurations and beam behaviors, is such that ML becomes an efficient tool for data analysis. Indeed, a wide spectrum of applications from beam measurements and machine performance optimization to analysis of numerical data from tracking simulations of nonlinear beam dynamics December 2021 will be reviewed in this paper, paying attention to future developments related to projects like the Future Circular Collider (FCC) [10] whose complexity will far exceed that of the LHC. The process of building a mathematical model built upon sample data (training data), makes the core of ML, which aims for predictions or decisions to be made without explicit programming required [11], so appealing, in particular when there is a large amount of data. ML includes a few learning paradigms, such as Supervised Learning (SL), Unsupervised Learning (UL), and Reinforcement Learning, and deals with tasks such as classification, regression, clustering, anomaly detection, dimensionality reduction, and reward maximization [12]. To train a mathematical model to successfully achieve a particular task requires a few complex steps for ML, which include data collection and curation, feature (input) engineering, feature selection and dimensionality reduction, model hyper-parameter optimization, and model training, with performance evaluation being at the end of this process. In the SL approach, training of ML algorithms is carried out on labelled data sets where a ground-truth output exists for each input. In UL [13], however, no ground-truth output is available, and the algorithms aim to discover structure in the dataset. Reinforcement Learning is typically used in control applications where the goal is to execute a series of actions to maximize a given reward, such as achieving a given beam parameter. Overview of the LHC Ring and Optics Measurement Fig. 1 shows the schematic layout of the LHC ring (see [14] for additional detail). The eight-fold symmetry is visible, together with the main function of each long straight section. Note that the RF accelerating systems share the straight section with some key beam diagnostic devices, like transverse and longitudinal beam profile monitors and beam current transformers. During the LHC Run 2 (2015-2018), proton and ion (of atomic number Z) beams were accelerated from 450 Z GeV to a maximum of 6.5 Z TeV (see, e.g., [15]). The study and optimization of the linear optics [16] has been a priority for the tight link with the collider performance. IEEE Instrumentation & Measurement Magazine 1094-6969/21/$25.00©2021IEEE 47

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