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Neural Networks for Modeling and Control of Particle Accelerators

A. L. Edelen, S. G. Biedron, B. E. Chase, D. Edstrom, S. V. Milton, P. Stabile

arXiv:1610.06151v1physics.acc-ph

TL;DR

Particle accelerator control must handle complex systems and human operators face increasing difficulty as parameters and operating conditions multiply. The paper surveys neural-network applications and develops a model-predictive controller for RF-gun water-system resonance control; its benchmark substantially improves on the existing feed-forward/PI controller, with a roughly fivefold shorter setting time and virtually no overshoot.

Abstract

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We describe some of the challenges of particle accelerator control, highlight recent advances in neural network techniques, discuss some promising avenues for incorporating neural networks into particle accelerator control systems, and describe a neural network-based control system that is being developed for resonance control of an RF electron gun at the Fermilab Accelerator Science and Technology (FAST) facility, including initial experimental results from a benchmark controller.

I. INTRODUCTION

Particle accelerator control is difficult because nonlinear, interacting, time-varying systems must meet tight performance demands despite drift and changing operating conditions. The paper introduces AI/ML, especially neural networks, as a route toward these challenges and describes why human tuning becomes difficult as system complexity grows.

I. INTRODUCTION

  • Accelerators combine nonlinear, interacting dynamics, component changes, tight tolerances, and non-steady operating conditions, challenging reliable control.Differences between designs, simulations, and installed machines further complicate control; traditional techniques become inadequate in some domains as accelerator complexity increases.Source: §I · p. 1
  • Neural networks are proposed for modeling, control, and diagnostics because they can use machine data to address time variation, noise, delays, and large parameter spaces.The paper presents an overview of accelerator-control challenges and AI concepts, proposed applications, and FAST RF-gun resonance-control work.Source: §I · pp. 1–2

A. Preliminary Terminology

  • Optimization searches for operating parameters that better meet performance goals, while control maintains set points or other goals despite machine disturbances.The paper also distinguishes tuning, which combines model and policy learning, planning, and prediction, from optimization as a search process.Source: A. Preliminary Terminology · p. 2

B. Challenges for Human Operators

  • Human tuning becomes unwieldy with nonlinear dynamics, many interrelated parameters, and multiple timescales, while frequent operating changes multiply the strategies operators must learn.Operators can handle complex dynamics effectively when familiar with a machine or task, but human limits in processing, acting, timescales, and cost remain.Source: B. Challenges for Human Operators · p. 2

C. Challenges for Automated Systems

Automated accelerator control must combine sparse or numerous diagnostics, planning under delays, and system-wide adaptation. The authors frame neural-network control as a way to draw on capabilities analogous to those used by experienced operators.

C. Challenges for Automated Systems

  • Automated systems can struggle to infer machine state from limited outputs or use many diagnostics collectively, and long delays make accurate, fast planning difficult.Complexity can yield decisions designers did not anticipate, while operators may find the same planning tasks comparatively straightforward.Source: C. Challenges for Automated Systems · p. 3
  • Desired automated capabilities include adaptive models, drift compensation, system-wide optimization, rapid adjustment to new conditions, pre-emptive planning, and constraint handling.The list also includes extracting useful information from large data volumes and compensating for deviations from ideal design.Source: C. Challenges for Automated Systems · p. 3

D. Expanding the Scope: Artificial Intelligence and Neural Networks

  • Experienced operators combine model learning, memory of states and outcomes, planning, prediction, diagnostic analysis, and policy learning; the authors use these capabilities to guide NN control design.A character-recognition example illustrates that incorporating a human-like learning process can improve performance with fewer training examples.Source: D. Expanding the Scope: Artificial… · pp. 3–4

E. Some Other Recent Approaches Toward Achieving Greater Automation and Improved Performance

The paper places neural networks alongside other automation approaches, outlines basic machine-learning frameworks, and sketches reinforcement learning as an agent learning actions to maximize performance over time.

E. Some Other Recent Approaches Toward Achieving Greater Automation and Improved Performance

  • Accelerator researchers pursue stochastic online optimization, extremum-seeking control, and faster online physics-based modeling through parallelization and speed–accuracy tradeoffs.The cited examples include PSO and genetic algorithms [6, 7], extremum-seeking applications, and online modeling.Source: E. Some Other Recent Approaches Toward… · p. 4

A. Machine Learning and Artificial Intelligence

  • Machine learning improves task performance through data interaction, while common frameworks include supervised, unsupervised, and reinforcement learning.Typical tasks include classification, clustering, dimensional reduction, and regression.Source: A. Machine Learning and Artificial… · p. 4

B. Reinforcement Learning

  • Reinforcement learning trains an agent to choose actions using a policy, reward feedback, and estimates of long-term value, with some architectures also using a process model.Methods vary in how these elements are computed and related, and RL can also be framed as stochastic search over policies.Source: B. Reinforcement Learning · pp. 4–5

C. Artificial Neural Networks

Neural networks are flexible function approximators whose weighted connections and structures can be trained for desired outputs. They can be trained from simulated data, measured data, or both.

C. Artificial Neural Networks

  • Neural networks are universal function approximators tailored to particular tasks and can serve varied purposes.Their flexibility makes them applicable to many different situations.Source: C. Artificial Neural Networks · p. 5
  • A basic neural network uses functions linked by weighted connections that are adjusted through optimization to achieve desired output behavior.Training can also adjust the network structure, such as its number of nodes and layers.Source: C. Artificial Neural Networks · p. 5
  • Neural networks can be trained using simulation data, measured data, or a combination, with architectures and training methods suited to different problems.The paper points readers to introductions and overviews of NN-based control.Source: C. Artificial Neural Networks · p. 5

A. Some Proposed Use Cases

Neural networks can support accelerator modeling, faster computation, diagnostics, and both existing and newly learned control policies. The paper also situates these use cases against past deployment barriers and advances that have made more complex approaches feasible.

1) As an identified system model for control or simulation

  • Neural-network models can represent interacting, nonlinear, time-varying systems and feed model-based predictive control, especially where delays and nonlinear behavior matter.Models may be updated as behavior drifts or operating conditions change, and can be pretrained on data from an existing model or simulation.Source: A. Some Proposed Use Cases · p. 5

2) As a fast stand-in for a computation whose speed usually limits real-time deployment

  • Trained neural networks can provide faster stand-ins for physics simulations or computationally intensive control and diagnostic procedures, including model-predictive-control optimization.The proposed use is to approximate procedures whose computation time limits real-time deployment.Source: A. Some Proposed Use Cases · p. 5

3) As a way of doing fast, sophisticated diagnostic analysis and feedback

  • Neural networks can classify, select features, or reduce dimensions for diagnostics and higher-level control, including image-based early detection of developing beam instability.They may also provide bunch-to-bunch analysis and feedback, particularly in hardware or firmware for high-repetition-rate systems.Source: A. Some Proposed Use Cases · p. 6

5) As a means of improving an existing controller or optimization scheme

  • Neural networks can augment existing controllers as adaptive helpers or learn their behavior and improve it during operation, including small adjustments to otherwise adequate controllers.The paper also notes hybrid approaches that use machine learning to tune optimization-algorithm parameters.Source: A. Some Proposed Use Cases · p. 6

As a means of codifying and executing an existing policy; as part of a tool to learn and execute a new control policy

  • Neural networks could learn new control policies from action outcomes, or codify an operator’s routine tuning behavior.The learned policy may be static or adaptive; neural-network reinforcement learning can estimate continuous-valued functions and represent information efficiently in large parameter spaces.Source: A. Some Proposed Use Cases · p. 6

Historical Impediments and Recent Advances

  • Earlier real-time neural-network control attempts faced slow computation, limited architectures, and algorithmic instability; later advances have mitigated many of these barriers.Developments in computing, learning algorithms, control theory, architectures, and training methods have enabled more complicated problems to be addressed in theory and practice.Source: A. Some Proposed Use Cases · pp. 6–7

3) Some Successes in Other Science and Engineering Disciplines

The paper points to neural-network applications in scientific data analysis, tokamak monitoring, and industrial control as relevant examples beyond particle accelerators. Some tokamak applications include experimentally demonstrated real-time detection of potentially problematic features.

Scientific data analysis

  • Neural networks have been used to analyze astronomical and high-energy physics data, including object classification, artifact rejection, event selection, and particle identification.The cited high-energy physics examples address statistically improbable events in data with high backgrounds.Source: 3) Some Successes in Other Science and… · p. 7

Tokamak applications

  • Tokamak studies report neural-network modeling, instability detection, and disruption prediction, with experimental demonstrations of real-time video-frame classification for early detection of hot spots or instabilities.Source: 3) Some Successes in Other Science and… · p. 7

Industrial control

  • Industrial neural-network applications include nonlinear process regulation, manufacturing optimization, temperature control with delays, building energy savings, PID self-tuning, and operating-cost reduction.The paper also cites successful experimental and simulation studies pairing neural networks with advanced optimal control, including model predictive control.Source: 3) Some Successes in Other Science and… · p. 8

V. AN EXAMPLE APPLICATION: RESONANCE CONTROL AT FAST

The FAST electron-gun cooling system was selected as an initial candidate for neural-network resonance control because its thermal dynamics and transport delays make PI control slow to settle and prone to large overshoots. The gun’s phase-stability requirements also make tight regulation of its inlet-water temperature important.

  • Large thermal time constants, long transport delays, and recursive cooling-system behavior produce long settling times and large overshoots under PI control, motivating the FAST resonance-control application.Source: §V · p. 8
  • The FAST gun is a water-cooled 1½-cell copper RF photoinjector operating at 1.3 GHz; its resonant frequency shifts 23 kHz per °C change in cavity temperature.Existing phase-stability requirements call for inlet-water temperature regulation within ± 0.02 °C.Source: §V · p. 8

A. Water System Description and Control Challenges

The FAST water system uses heater power and a flow-control valve to regulate gun temperatures, but long delays, ambient variation, recirculating heat, and supply-temperature fluctuations complicate control. Feedback from water exiting the gun can return to the mixing chamber and produce minutes-long damped oscillations in inlet-water temperature.

Water System Description

  • The controllable inputs are the flow-control valve setting and heater power; sensors measure supply, post-mixing, cavity, and return-water temperatures.TCAV is located in the gun iris, and sensor abbreviations refer to either the sensor or its reading.Source: A. Water System Description and… · p. 8

Control Challenges

  • Long, variable transport delays separate elements of the system, and typical delays are tabulated in Table I.Source: Table I · p. 8, A. Water System Description and… · p. 9
  • Heat in water leaving the gun can recirculate to the mixing chamber, causing a minutes-long damped oscillation in inlet-water temperature; Figure 2 illustrates the open-loop response.The figure caption attributes the T02 oscillation to mixing cold supply water with returning water (TOUT).Source: A. Water System Description and… · p. 9, Figure 2 · p. 9
  • The low-conductivity-water supply is nominally regulated within ± 0.5 °C, but larger spikes occur, including when other FAST heat sources use the same supply.Source: A. Water System Description and… · p. 9
  • Uninsulated pipes cross building areas with changing ambient temperatures, and relationships among T02, TIN, TCAV, TOUT, and T06 vary with those conditions.Some steady-state temperature differences can change without corresponding ambient-sensor changes.Source: Figure 1 · p. 8, A. Water System Description and… · p. 9
  • Because TCAV reads higher than the real bulk cavity temperature under RF power, its set point for proper resonance rises with average RF power; direct resonant-frequency regulation is less circuitous.Source: A. Water System Description and… · p. 9

B. Description and Assessment of the Existing Feed-forward/PI Loop

The existing feed-forward/PI loop regulates cavity temperature through water-flow adjustments, but long delays and water recirculation produce overshoot and slow settling, while RF turn-on can raise reflected power. The section characterizes the water system and develops neural-network models, with the T02 model performing well across the tested data sets and RF-powered TCAV predictions still showing offsets.

Description and Assessment of the Existing Feed-forward/PI Loop

  • A 1-°C set-point step produces ~0.6-°C initial overshoot and takes ~23 minutes to reach steady state, with oscillations attributed to delays and water recirculation rather than PI gain tuning.The reported instance had no significant supply-temperature disturbances.Source: B. Description and Assessment of the… · p. 9, Figure 3 · p. 10
  • During RF turn-on, the PI loop overshoots TCAV by an average 0.19 °C, raising mean reflected power by 70.6 kW to 103.0 kW, above the 100-kW administrative limit.These values come from eight turn-on instances at approximately 2.33 MW forward RF power.Source: B. Description and Assessment of the… · p. 9

System Characterization

  • The water-system data sets varied in operating conditions: Set 1 used pseudo-random FCV and heater changes at low RF power with PI disabled, Set 2 characterized temperatures under RF power with PI enabled, and Set 3 used larger setting changes with the gun off.Set 5 collected several days of normal operation at a cavity gradient of 42 MV/m; sensor ADC hardware changes between sets reduced the resolution of some readings.Source: B. Description and Assessment of the… · p. 10, Figure 4 · p. 10, Figure 5 · p. 11
  • At steady state, TOUT–TIN differs significantly from TCAV–TIN, reflecting local RF heating near the gun iris; the T02–TIN difference has only a weak trend with estimated ambient temperature (slope 0.002).At steady state, cooling power balances input power, approximately the average RF power.Source: B. Description and Assessment of the… · p. 12, Figure 10 · p. 13

Neural Network Modeling

  • Training first on Set 1 and then on part of Set 3 gave the best performance, combining Set 1’s lower-noise, higher-resolution readings with Set 3’s larger changes.For TCAV models, selected Set 2 data under RF power were also used for additional training.Source: B. Description and Assessment of the… · p. 13
  • The T02 model performs well across all data sets, while TCAV models tested under RF power show steady-state offsets that require training across more RF power levels.Without RF power, the best full TCAV model outperforms the T02 model; Table II reports average absolute error, its standard deviation, and maximum error, but its values are not supplied here.Source: B. Description and Assessment of the… · p. 14, Table II · p. 14

G. Control Over the Water System

The water system is the first control target toward maintaining the gun’s resonant frequency, because long transport delays and recirculation challenge the existing controller. The planned modular design regulates water entering the gun and can be nested within a loop that targets cavity temperature or detuning.

Control Over the Water System

  • The longer-term controller aims to adjust FCV and heater settings for a desired resonant frequency or optimal detuning, and to control RF power ramp-up during turn-on.Source: G. Control Over the Water System · p. 14
  • Water-temperature control at the cavity entrance is the first step toward keeping the gun at its proper resonant frequency.The approach also permits direct comparison with the existing feed-forward/PI loop by relating water temperature at the entrance to TCAV.Source: G. Control Over the Water System · p. 14
  • The base controller adjusts FCV and heater settings to regulate water entering the gun, and can be nested in a loop targeting cavity temperature or detuning.The outer loop can minimize detuning directly or achieve an operator-specified cavity-temperature set point.Source: G. Control Over the Water System · p. 14

H. Benchmark Controller for the RF Gun

The benchmark uses model predictive control (MPC) to coordinate water-system actuators around a target T02 temperature. In an initial step test, it settled about five times faster than the existing feed-forward/PI loop with virtually no overshoot, though further testing and model improvements remain necessary.

MPC Approach

  • MPC is suited to this water-control problem because long time constants, returning water, and two controllable variables make anticipatory action useful.The scheme combines a system model with optimization to select future actions subject to constraints.Source: H. Benchmark Controller for the RF Gun · p. 14

Controller Structure

  • The controller translates an operator's TCAV set point into an approximate T02 set point, then manipulates the flow-control valve and heater power.It monitors TOUT to anticipate water-temperature changes and T01 to compensate for fluctuations in LCW supply temperature.Source: H. Benchmark Controller for the RF Gun · p. 15

Implementation

  • The benchmark linearizes the neural-network model at each time step and uses QPKWIK, with hard constraints and no desired controllable-variable trajectory.A rudimentary neural-network model translates TCAV to T02 to capture dynamic response.Source: H. Benchmark Controller for the RF Gun · p. 16

Performance

  • The benchmark MPC settled about 5x faster than the pre-existing feed-forward/PI loop, with virtually no overshoot in the target parameter.The reported test was a 1-°C TCAV set-point step; additional data is needed to characterize transient and steady-state performance fully.Source: H. Benchmark Controller for the RF Gun · p. 16, Figure 15 · p. 16

Limitations and Potential Improvements

  • Control timing remains imperfect: unmodeled command-to-actuator delays and timing mismatch for recirculating water produced small T02 oscillations.The controller also used requested rather than measured valve and heater settings; testing across the cavity's RF-power range and improving the TCAV-to-T02 component remain outstanding.Source: H. Benchmark Controller for the RF Gun · p. 17

I. Future Work and Extensions To Pure NN Control

Future work at FAST will improve the benchmark MPC and build neural-network control schemes on it. The plans include MPC-based resonance control as well as reinforcement learning directly from scratch.

Future Work

  • The future-work program has two tracks: improving the benchmark MPC and developing neural-network-centered schemes that build on it.Source: §I · p. 17

NN-Centric Schemes

  • The benchmark MPC is intended to provide an initial policy for a neural network to mimic and improve through simulated interaction before experimental testing.The group plans to extend the module to direct resonance control using another MPC or a reinforcement-learning component.Source: §I · p. 17

Resonance Control

  • A separate MPC is being developed to choose T02 and RF-power trajectories that reach requested RF power without significant increases in reflected power.The work will use resonant frequency, measured by detuning, as the reference parameter and also examine reinforcement learning from scratch and resonance control for an RFQ at Fermilab.Source: §I · p. 17

VI. CONCLUSION

Particle accelerators need reliable adaptive control as operating conditions and performance tolerances become more demanding. The paper highlights neural-network approaches and reports an encouraging FAST benchmark result, while presenting accelerator control as a useful test bed for further development.

Conclusion

  • Complex accelerator systems and increasingly stringent beam tolerances motivate reliable, adaptive control for a growing range of applications.Source: §VI · pp. 17–18
  • At FAST, a relatively simple neural-network-based MPC achieved a ~5x shorter setting time and virtually no overshoot in the target parameter than the existing feed-forward/PI controller.Source: §VI · p. 18
  • Neural networks can model system relationships, perform rapid computations, and act as controllers; accelerator experiments can guide development of techniques suited to operational challenges.Source: §VI · p. 18

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