Frank, J.; Arlandoo, M.; Goslawski, P.; Li, J.; Mertens, T.; Ries, M.; Vera Ramirez, L.: Novel Non-Linear Particle Tracking Approach Employing Lie Algebraic Theory in the TensorFlow Environment. In: Liu Lin ... [Ed.] : IPAC 2021 : Proceedings of the 12th International Particle Accelerator Conference in Campinas, Brazil, 24–28 May 2021Geneva: JACoW, 2021. - ISBN 978-3-95450-214-1, p. TUPAB215/1-4
https://accelconf.web.cern.ch/ipac2021/papers/tupab215.pdf
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Abstract:
With this paper we present first results for encoding Lie transformations as computational graphs in Tensorflow that are used as layers in a neural network. By implementing a recursive differentiation scheme and employing Lie algebraic arguments we were able to reproduce the diagrams for well known lattice configurations. We track through simple optical lattices that are encountered as the main constituents of accelerators and demonstrate the flexibility and modularity our approach offers. The neural network can represent the optical lattice with predefined coefficients allowing for particle tracking for beam dynamics or can learn from experimental data to fine-tune beam optics.