Bayesian Optimization of a Free-Electron Laser

J. Duris, D. Kennedy, A. Hanuka, J. Shtalenkova, A. Edelen, P. Baxevanis, A. Egger, T. Cope, M. McIntire, S. Ermon, and D. Ratner

Phys. Rev. Lett. 124, 124801 – Published 25 March 2020

Abstract

The Linac coherent light source x-ray free-electron laser is a complex scientific apparatus which changes configurations multiple times per day, necessitating fast tuning strategies to reduce setup time for successive experiments. To this end, we employ a Bayesian approach to maximizing x-ray laser pulse energy by controlling groups of quadrupole magnets. A Gaussian process model provides probabilistic predictions for the machine response with respect to control parameters, enabling a balance of exploration and exploitation in the search for the global optimum. We show that the model parameters can be learned from archived scans, and correlations between devices can be extracted from the beam transport. The result is a sample-efficient optimization routine, combining both historical data and knowledge of accelerator physics to significantly outperform existing optimizers.

Received 13 September 2019
Revised 1 February 2020
Accepted 19 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.124801

Physics Subject Headings (PhySH)

Accelerator/storage ring control systems Beam optics correction schemes Beam optics transport Optimization problems

Free-electron lasers

Bayesian methods Machine learning

Accelerators & Beams

Authors & Affiliations

J. Duris ¹, D. Kennedy^1,2, A. Hanuka ¹, J. Shtalenkova ¹, A. Edelen¹, P. Baxevanis¹, A. Egger ¹, T. Cope¹, M. McIntire³, S. Ermon³, and D. Ratner¹

¹SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
²Department of Physics, University of California, Santa Cruz, Santa Cruz, California 95064, USA
³Department of Computer Science, Stanford University, Stanford, California 94305, USA

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Issue

Vol. 124, Iss. 12 — 27 March 2020

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Images

Figure 1
LCLS beam line showing locations of linacs, quadrupole magnets, and undulator magnets. A focusing system comprised of nearly 200 quadrupoles (upper lines denote focusing whereas lower lines denote defocusing for one plane) transports the electron beam downstream (from left to right above) and several groups of matching quadrupole magnets (shown in red) are routinely used to match the beam into the focusing system. An electron beam dump and x-ray pulse energy measurement system (not shown) are positioned downstream of the undulators. Our studies focus on eight matching quads in the third linac and four in the transport line leading to the undulators.
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Figure 2
(a) Comparison of optimization of FEL pulse energy over 12 quadrupole magnets for Bayesian optimization (red curves) vs Nelder-Mead simplex optimization (blue). Each scan was performed four times with identical starting conditions, shown with different dashing. Each step corresponds to approximately 3 to 4 seconds. (b) Simulations using the conditions of (a). 100 individual scans for each method, with means shown by thick lines, are consistent with measurements. Note occasional drops in FEL pulse energy, e.g., at step 30 in the solid red line, are caused by momentary machine glitches. It is encouraging that the optimizer is not thrown off course by such brief glitches.
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Figure 3
(a) Ground truth of a 2D multinormal test function with unit slice widths (evaluated holding all but one coordinate fixed at a time) and correlation coefficient of 0.8. (b) GP regression with isotropic kernel on noisy samples from the ground truth. (c) GP regression with correlated kernel on identical samples as (b). (d) Bayesian optimization convergence tests on a correlated ground truth with and without kernel correlations. Each bar shows the standard error about the mean for 100 trials. The correlated GP kernel (blue linear fit) performs as well as optimization of an isotropic ground truth with an isotropic GP kernel, growing linearly with the number of dimensions. Steps to convergence with mismatched kernel grows exponentially (red exponential fit).
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Figure 4
(a) Average FEL pulse energy vs two adjacent quadrupoles. The dark spot near the center of the plot was due to a momentary machine malfunction. (b) The modeled average electron beam size in the undulator vs the same quadrupoles shows the same correlations. (c) Optimization test for four quadrupoles: GP (red) vs GP with correlations (yellow). Each scan was performed twice with identical starting conditions, shown with different dashing. Each step takes approximately 3 to 4 seconds. (d) Simulations using a beam matrix model for the conditions of c. 100 individual scans for each method, with means shown by thick lines, are consistent with measurements.
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