Abstract
A Machine Learning approach to scientific problems has been in use in Science and Engineering for decades. High-energy physics provided a natural domain of application of Machine Learning, profiting from these powerful tools for the advanced analysis of data from particle colliders. However, Machine Learning has been applied to Accelerator Physics only recently, with several laboratories worldwide deploying intense efforts in this domain. At CERN, Machine Learning techniques have been applied to beam dynamics studies related to the Large Hadron Collider and its luminosity upgrade, in domains including beam measurements and machine performance optimization. In this paper, the recent applications of Machine Learning to the analyses of numerical simulations of nonlinear beam dynamics are presented and discussed in detail. The key concept of dynamic aperture provides a number of topics that have been selected to probe Machine Learning. Indeed, the research presented here aims to devise efficient algorithms to identify outliers and to improve the quality of the fitted models expressing the time evolution of the dynamic aperture.
Highlights
Machine Learning (ML) represents the process of building a mathematical model based on sample data, with the goal of making predictions or decisions without being explicitly programmed [1]
The need for and usefulness of ML techniques is testified to by the publication of a white paper that reviews in detail the state-of-the-art of ML applications and lists several recommendations to encourage the uptake of such techniques in accelerator physics laboratories [19]
The results show that when the training data set is approximately balanced between abnormal and normal points, the number of True Positives (TP) is quite high, while the False Positives (FP) and False Negatives (FN) are low
Summary
Machine Learning (ML) represents the process of building a mathematical model based on sample data, with the goal of making predictions or decisions without being explicitly programmed [1]. The distribution of DA values needs to be carefully considered, in particular paying attention to the presence of outliers Another hurdle to overcome in the numerical evaluation of the DA is the huge amount of CPU time required to obtain accurate estimates of the DA. In the presence of such scaling laws, one could use the results of numerical simulations to evaluate the parameters in the scaling laws and use them to extrapolate the DA values for a much larger number of turns This goal is actively pursued, and scaling laws have been found based on general theorems of dynamical systems theory (see, e.g., [24] and references therein).
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