Using Self-consistency to Determine Uncertainty in Particle Accelerator Diagnostic Measurements

Control of a particle accelerator relies on interpreting input diagnostics, and tuning the accelerator settings to achieve desired diagnostic values. Particle accelerator diagnostics can fail, slowly or abruptly, and currently a human operator is tasked with evaluating this. For truly autonomous operation of particle accelerators, we must be able to determine the reliability of a diagnostic using nothing more than the set of all diagnostic data. We present a method of quantifying the scale of error in diagnostic measurements based on gaussian process (GP) regression and the intuition that each diagnostic measurement from a beam position monitor (BPM) should be predictable given the set of all other BPM measurements. 1 Autonomous Accelerator Operation Particle accelerator operation currently centers on a team of skilled human operators and some automated routines for optimizing the accelerator’s operation against a set of performance metrics. Accelerators produce a large amount of data, that data is of variable reliability, and the optimization is typically multi-objective and spans a high-dimensional configuration space. This makes particle accelerators an ideal candidate for applying machine learning techniques [2]. Autonomous control is one of the key areas for progress for machine learning applications to particle accelerators [3]. There has been much progress in applying machine learning based optimization to accelerator controls. Scheinker et al. [7] demonstrated the ability for model-independent control to adapt an accelerator to deliver a certain longitudinal phase space in a free-electron laser linac based only on a handful of control knobs and a diagnostic read-out. Duris et al. [1] have demonstrated that Bayesian optimization with Gaussian process models can reach better optima faster than simplex models in computer simulations of free electron lasers. Other recent work by Scheinker et al. [8] demonstrated that a model-independent optimization algorithm can improve the average pulse energy in the LCLS SASE FEL by automatically tuningsettings with no foreknowledge of free electron laser physics. These applications all show the capability of machine learning techniques to tune an accelerator to a desired operating point. However, they all involve human-in-the-loop operation – there are still operators in the control room. For industrial applications such as water treatment – where there might be two operators for ten accelerators, instead of ten operators for one – or for accelerators deployed for space applications – where there would be no operators present – the control systems must be truly autonomous. This means that the control system must be able to evaluate the reliability of each diagnostic measurement using only the set of all diagnostic measurements. Particle accelerator diagnostics can fail for numerous reasons, and either catastrophically or slowly, and any autonomous accelerator control system must be able to detect these and distinguish them. In this paper we present a concept for determining the reliability of a set of beam position monitor (BPM) measurements using diagnostic self-consistency. In an ideal system with no errors, the BPM Third Workshop on Machine Learning and the Physical Sciences (NeurIPS 2020), Vancouver, Canada. measurements should be highly correlated. If the measurements have some noise on top of them, then a predictive model that captures uncertainty should have the scale of that uncertainty be proportional to the level of noise on the measurements. We can therefore use the predictive uncertainty of a model fit to the BPM data to determine the scale of that uncertainty with no outside input. 2 Diagnostic Self-Consistency Consider a set of diagnostic measurements {Xi}. In many cases, there are physical reasons to believe that these measurements are correlated. For our case, where we analyze BPMs, beam dynamics suggests that the BPM measurements are very strongly correlated due to the existence of an underlying transfer map that relates the beam phase space coordinates at each BPM to each other. Given enough BPMs, we should be able to reconstruct that map in a model that allows us to predict the value measured at one BPM given all the values at the other BPMs. We refer to this as the existence of diagnostic self-consistency. Formally, we expect that for each Xα measurement, given the set of inputs {Xi 6=α}, there should be a function Xα = fα({Xi 6=α}) in an ideal case with perfect diagnostic reliability for each i. In the case that fα exists and is perfectly accurate for each α then we have diagnostic self-consistency. In reality, the diagnostics will have some noise in their readings, due to electronic noise, resolution limits, etc. Thus, each Xα will have some best fit model fα which has some uncertainty in the prediction. By quantifying that uncertainty, we can extract the uncertainty in each diagnostic measurement and ascertain the variance in a diagnostic’s measurement using only the set of all diagnostic measurements. Because we are fitting the relation between ∼ 10s of diagnostics, and need to have a variance in those predictions, we will use gaussian process (GP) regression [6] to compute the correlation. GP regression has already been used effectively for optimization [1] as well as in building physics-based models for improved optimization [5]. 3 The ATR Beamline: A Test Case To generate test data, we use MAD-X simulations of the ATR beamline at Brookhaven National Laboratory, fig. (1). The ATR beamline is used to extract beam from the Alternating Gradient Synchrotron and transport it to the Relativistic Heavy Ion Collider. This beamline has a number of vertical and horizontal bends, and a number of correctors and BPMs along the line. Figure 1: Lattice layout and Twiss parameters for the ATR beamline. For what follows, we generated a dataset of 500 different beams with randomly offset initial positions and angles to the ideal axis. To compute the fα for each BPM, we train the GP models using a training set of 400 randomly selected beams, with the additional 100 held out as a test set, which we will use to infer the error in the models.