One of the Grand Challenges in beam physics relates to the use of virtual particle accelerators for beam prediction and optimization. Useful virtual accelerators rely on efficient and effective methodologies grounded in theory, simulation, and experiment. This work extends the application of the Sparse Identification of Nonlinear Dynamical systems (SINDy) algorithm, which we have previously presented at the North American Particle Accelerator Conference. The SINDy methodology promises to simplify the optimization of accelerator design and commissioning by discovery of underlying dynamics. We extend how SINDy can be used to discover and identify underlying differential systems governing the beam’s sigma matrix evolution and corresponding invariants. We compare discovered differential systems to theoretical predictions and numerical results. We then integrate the discovered differential system forward in time to evaluate model fidelity. We analyze the uncovered dynamical system and identify terms that could contribute to the growth(decay) of (un)desired beam parameters. Finally, we propose extending our methodology to the broader community's virtual and real experiments.

The Fermilab Linac delivers 400 MeV H- beam to the rest of the accelerator chain. We are exploring several machine learning (ML) techniques for automated RF tuning, with an emphasis on time-evolving modeling that can account for parameter drift. Providing stable intensity, energy, and emittance is key since it directly affects downstream machines. To operate high current beam, accelerators must minimize uncontrolled particle loss; this ca be accomplished by minimizing beam longitudinal emittance via RF parameter optimization. However, RF tuning is required daily since the resonance frequency of the accelerating cavities is affected by ambient temperature and humidity variations and thus drifts with time. In addition, the energy and phase space distribution of particles emerging from the ion source are subject to fluctuations. Such drift is not unique to Fermilab, but rather affects most laboratories. Our methods include several variations of RF system modeling based on diagnostics data from beam position monitors (transverse positions and longitudinal phase). We will present the status of each approach and future plans.

In the commissioning and operational stage of X-ray free-electron lasers (XFELs), it is a challenging problem to efficiently tune the large-scale scientific machines which consist of hundreds and thousands of components. Here we tried to introduce several tuning algorithms to achieve automatic tuning in XFELs and compared the performance. This also paves the way for further development of intelligent online optimization schemes.

Although beam emittance is critical for the performance of high-brightness accelerators, optimization is often time limited as emittance calculations, commonly done via quadrupole scans, are typically slow. Such calculations are a type of *multi-point queries*, i.e. each query requires multiple secondary measurements. Traditional black-box optimizers such as Bayesian optimization are slow and inefficient when dealing with such objectives as they must acquire the full series of measurements, but return only the emittance, with each query. We propose using Bayesian Algorithm Execution (BAX) to instead query and model individual beam-size measurements. BAX avoids the slow multi-point query on the accelerator by acquiring points through a *virtual objective*, i.e. calculating the emittance objective from a fast learned model rather than directly from the accelerator. Here, we use BAX to minimize emittance at the Linac Coherent Light Source (LCLS) and the Facility for Advanced Accelerator Experimental Tests II (FACET-II). In simulation, BAX is 20x faster and more robust to noise compared to existing methods. In live LCLS and FACET-II tests, BAX performed the first automated emittance tuning, matching the hand-tuned emittance at FACET-II and achieving a 24% lower emittance at LCLS. Our method represents a conceptual shift for optimizing multi-point queries, and we anticipate that it can be readily adapted to other similar problems commonly found in particle accelerators and beyond.

Sparks in TRIUMF's main cyclotron have to dissipate a lot of energy due to the large volume of the RF cavity, causing a trip of the system, resulting in down time of the machine and provide a risk of damaging the system if not reacted to immediately. A spark detection system evaluating the rate of change of the reversed power signal within the cyclotron when a spark occurs is employed but can currently not provide any information about its location. Simulations with a detailed P-spice model including the entire RF infrastructure from the amplifier, the combiner station, the waveguide system, and the rather big cyclotron with a diameter of 18 meters will provide the necessary information whether the location of a spark in the system can be located. The evaluated signals are the rate of change of the falling DEE voltage and the RF signals in different locations of the RF system. These results and actual measurements of sparks in the system can then in the future be used to train a Machine Learning model to implement a real time spark detection and reaction system. Such a system provides fast diagnostics and enables preventative maintenance during scheduled maintenance times and hence can reduce the machine downtime significantly.

At a heavy-ion linac facility, such as ATLAS at Argonne National Laboratory, a new ion beam is tuned once or twice a week. The use of artificial intelligence can be leveraged to streamline the tuning process, reducing the time needed to tune a given beam and allowing more beam time for the experiment. After establishing the required automatic data collection procedures, we have developed and deployed machine learning models to tune and control the machine. We have successfully trained online different Bayesian Optimization (BO)-based models for different sections of the linac, including the commissioning of a new beamline. We have also demonstrated transfer learning from one ion beam to another allowing fast tune switching between different ion beams. And more importantly, we have demonstrated transfer learning from the simulation to the online machine model using Neural Networks as the kernel for the BO optimization instead of Gaussian Processes (GP). This latest development allowed fast convergence even when including a multitude of variable parameters. We have also explored Reinforcement Learning (RL)-based models which showed some promising results but will require more development. These models will be later generalized for the whole ATLAS linac and can, in principle, be adapted to control other heavy-ion linacs and accelerators with modern control systems.

The use of artificial intelligence (AI) has the potential to significantly reduce the time required to tune particle accelerators, such as the Argonne Tandem Linear Accelera-tor System (ATLAS). Bayesian optimization with Gauss-ian processes is a suitable AI technique for this purpose, it allows the system to learn from past observations to make predictions without explicitly learning representations of the data. In this paper, we present a Bayesian optimiza-tion method with deep kernel learning that combines the representational power of neural networks with the reliable uncertainty estimates of Gaussian processes. The kernel is first trained with physics simulations, then the model is deployed online in a real machine, in this case a subsec-tion of the ATLAS linac, to perform the optimization. In addition to the kernel, we also modelled the mean of the Gaussian process using a neural network trained with simulation data and later with experimental data. The results show that the model not only converges quickly to an optimal tune, but it also requires very little initial data to do so. These approaches have the potential of signifi-cantly improving the efficiency of particle accelerator tuning, and could have important applications in a wide range of settings.

We present an approach for detection of anomalous behavior of magnet power supplies (PSs) in storage rings, which may serve as an early indication of an impending PS trip. In this new method, we train a Long Short-Term Memory (LSTM) neural network to predict the temperature of several components of a PS (transistors, capacitors) based on the PS current, PS voltage, room temperature, and cooling water temperature. For training and testing, years of historical data are used from the Advanced Photon Source (APS). The neural network is trained on the data corresponding to the normal operation of the PSs. Anomalous behavior of a PS can be detected when the observed PS temperature starts to deviate significantly from the LSTM prediction. This may allow for preemptive action by the operators or PS group.

After the upcoming upgrade, the storage ring in the Advanced Photon Source (APS-U) will have over two thousand magnet power supplies. They will be constantly monitored in order to prevent impeding failures, when possible. The new data acquisition system (DAQ) will deliver 22600 samples of each power supply’s current per second. The data can be saved at this rate for a short period of time around a suspected anomaly. However, continuous data logging is more feasible at a smaller rate. In this contribution, we present (1) a statistical plug-in for the DAQ, which allows to reduce the data rate for logging, while capturing the most important statistical properties of the raw data, (2) a number of machine learning models for anomaly detection in the compressed data, and (3) an application with a graphical user interface to review the detected anomalies.

Particle accelerators require continuous adjustment to maintain beam quality. Several machine learning (ML) approaches are being explored for this task. At the Advanced Photon Source (APS), we have recently proposed the adaptive Bayesian optimization (ABO) algorithm and have shown it to be effective experimentally in the APS injector complex. Further testing has suggested several improvements, on which we report here. We introduce dynamic kernel switching, deep kernel learning, and surrogate model prior means, resulting in improved robustness. We also extend our code with multi-dimensional time kernel support and predictive constraint avoidance to make it applicable to a wider range of systems. These changes also improve the general ABO performance, but more importantly expand ABO applicability to systems with rapid or unexpected changes in either optimization parameters or time properties. Notably, this allows for rapid and automated fallback to conservative parameters when optimizer confidence degrades, with alarms raised for further operator review. These features will permit further operational ML adoption at APS.

The 3rd ICFA Beam Dynamics Mini-Workshop on Machine Learning (ML) Applications for Particle Accelerators was held in Chicago, Il, USA, on November 1-4, 2022. This was an in-person workshop focused on ML techniques as applied to accelerator operations, design, and simulations. There were 76 attendees representing 26 institutions from around the world. A total of 59 abstracts were submitted allowing us to build a diverse program with both oral and poster presentations. The workshop was sponsored by the Center for Bright Beams (CBB), with support from the National Science Foundation and by RadiaSoft, an industry leader in high-level research and design and scientific consulting for beamline physics and machine learning. CBB supported eight graduate students for this meeting. The workshop was approved as a mini workshop by the International Committee for Future Accelerators (ICFA) Beam Dynamics Panel. We will provide a summary of the work presented at the workshop and the outlook for future efforts.

The ionization profile monitors (IPMs) are used to measure the transverse profiles of the beams accelerated at the Brookhaven National Laboratory (BNL) AGS. These devices use multi-channel plates (MCP) to collect electrons generated by ionization of the residual gas to get an image of the beam projection onto the two transverse planes. The gains of each of the 64 channels in the MCP can vary from channel to channel due to both initial fabrication variations and over time as the channel exposed to more signal degrade and become less sensitive. There are also systematic errors associated with varying delays in the digitization paths for different groups of channels. We describe a reinforcement learning approach to accounting for and calibrating these errors using historical data from the Brookhaven AGS IPMs.

The Collider Accelerator Complex at Brookhaven National Lab (BNL) contains millions of control points. Monitoring tolerances for these control points is crucial for the system and is a challenging task. Catching early signs of failures in those systems will be very beneficial as they can save extensive downtime. Anomaly detection in particle accelerators has been highlighted and can significantly impact the system. Autoencoder is one of the most commonly used techniques for detecting anomalies. In this contribution, we apply an autoencoder method to analyze the historical data for runs 21 and 22 to find precursors for trips (and actual trips) of Air Conditioning (AC) systems based on local thermostat readbacks. Results from the existing system are presented, showing that the new method can catch early signs of AC trips so that advance notices can be sent for the operators to take prompt action.

To harness the full potential of the ultrafast electron diffraction (UED) and microscopy (UEM), we need to know accurately the electron beam properties, such as emittance, energy spread, spatial-pointing jitter, and shot-to-shot energy fluctuation. Owing to the inherent fluctuations in UED/UEM instruments, obtaining such detailed knowledge requires real-time characterization of the beam properties for each electron bunch. While diagnostics of these properties exist, they are often invasive, and many of them cannot operate at a high repetition rate. Here, we present a technique to overcome such limitations. Employing a machine learning (ML) strategy by training a model on a small set of fully diagnosed bunches, we can accurately predict electron beam properties for every shot using only parameters that are easily recorded at high repetition rate by the detector while the experiments are ongoing. Applying ML as real-time non-invasive diagnostics could enable some new capabilities, such as online optimization of the long-term stability and fine single-shot quality of the electron beam, filtering the events and making online corrections of the data for time-resolved UED, fully realizing the potential of high repetition rate UED and UEM for life science and condensed matter physics applications.

The CERN SPS Beam Dump System (SBDS) is responsible for disposing the beam in the SPS in case of any machine malfunctioning or end of cycled operation. This is achieved by the actuation of kicker magnets with predefined pulses, which aim to: i) deviate the beam towards the absorber block (TIDVG); ii) dilute the particle density. Evidently, a malfunction of this system may have negative consequences, such as the absorber block degrading if the beam is not sufficiently diluted, unwanted activation of the surroundings or even damage to the vacuum chamber in case of complete failure. By leveraging a combination of real images from a beam screen device and data from simulations, we train an online monitoring system to identify potential failures of the SBDS from real-time images. This work improves the safety of the operation of the SPS and contributes towards the goal of automating the operation of accelerators.

The Alternating Gradient Synchrotron (AGS) is a particle accelerator at Brookhaven National Laboratory (BNL) that accelerates protons and heavy ions using the strong focusing principle. In this work, we perform simulation studies on the AGS ring of a machine error detection method by comparing simulated and measured orbit response matrices (ORMs). We also present preliminary results of building two machine learning (ML) surrogate models of the AGS system. The first ML model is a surrogate model for the ORM, which describes mapping between orbit distortions and corrector settings. Building a self-adaptive model of ORM eliminates the need to re-measure ORM using the traditional time-consuming procedure. The second ML model is an error identification model, which maps the correlation between measurement errors (differences between measurement and model) and sources of such errors. The most relevant error sources for the error model are determined by performing sensitivity studies of the ORM.

Longitudinal beam diagnostics are a useful aid during tuning of particle accelerators, but acquiring them usually requires destructive and time intensive measurements. In order to provide such diagnostics non-destructively, computational methods allow for the development of virtual diagnostics. Existing Fourier-based reconstruction methods for longitudinal current reconstruction, tend to be slow and struggle to reliably reconstruct phase information. We propose using an artificial neural network trained on data from a start-to-end beam dynamics simulation to combine scalar and spectral information in order to infer the longitudinal phase space of the electron beam. We demonstrate that our method can reconstruct longitudinal beam diagnostics accurately and provide the reconstructed data with adaptive resolution. Deployed to control rooms today, our method can help human operators reduce tuning times, improve repeatability and achieve pioneering working points. In the future, ML-based virtual diagnostics will help the deployment of feedbacks and autonomous tuning methods, working toward the ultimate goal of autonomous particle accelerators.

The use of fast computational tools is important in the operation of X-ray free electron lasers, in order to predict the output of diagnostics when they are either destructive or unavailable. Physics-based simulations can be computationally intensive to provide estimates on a real-time basis. This proposed work explores the use of machine learning to provide operators with estimates of key photon pulse characteristics related to beam pointing. A data pipeline is set up and the method is applied to the SASE1 undulator line at the European XFEL. This case study evaluates the performance of the model for different amounts of training data.

For any linear accelerator, a thorough understanding of the Longitudinal Phase Space (LPS) of the beam is a great advantage. At the synchrotron light source MAX IV the two storage rings are injected with electrons using a 3 GeV linear accelerator, which also serves to provide beam for a short pulse facility (SPF). A newly commissioned Transverse Deflecting Cavity (TDC) is used to reconstruct the full LPS in a separate branch in the SPF after the second bunch compressor. This diagnostic performs a destructive measurement to extract the LPS and can not be used simultaneously with the beamline in the other branch in the SPF. In this paper we present a new virtual diagnostics which utilizes machine learning methods to extract the LPS information from other, non-destructive signals in the MAX IV linac. This involves simulations of the linac including the TDC response, as well as the collection of real data from the new TDC, for use in training artificial neural networks to predict the full LPS.

Reinforcement learning (RL) algorithms are investigated at KIT as an option to control the beam dynamics at storage rings. These methods require specialized hardware to satisfy throughput and latency constraints dictated by the timescale of the relevant phenomena. The KINGFISHER platform, based on the novel Xilinx Versal Adaptive Compute and Acceleration Platform, is an ideal candidate to deploy RL-on-a-chip thanks to its ability to execute computationally intensive and low latency feedback loops in the order of tens of microseconds. In this publication, we will present the integration of the KINGFISHER system at the Karlsruhe Research Accelerator (KARA), as a proof-of-principle turn-by-turn control feedback loop, to control induced transversal oscillations of an electron beam.

Parameter tuning is a regular task and takes considerable time for daily operations at FEL facilities. In this contribution, we demonstrate SASE pulse energy optimization at the European XFEL with Bayesian optimization (BO) as an alternative approach to the widely used simplex method. Preliminary experimental results show that BO could reach a comparable performance as the simplex method, even with an out-of-the-box implementation. Compared to previous attempts, our version of BO does not require setting hyperparameters via additional measurements, thus effectively reducing the required effort for machine operators to use it during operation. On the other hand, BO has the potential to be further improved by introducing prior physical knowledge about the task and fine-tuning the algorithm to specific tasks. This makes BO a promising candidate for routine tuning tasks at particle accelerators in the future.

In recent work, it has been shown that reinforcement learning (RL) is capable of outperforming existing methods on accelerator tuning tasks. However, RL algorithms are difficult and time-consuming to train and currently need to be retrained for every single task. This makes fast deployment in operation difficult and hinders collaborative efforts in this research area. At the same time, modern accelerators often reuse certain structures within or across facilities such as transport lines consisting of several magnets, leading to similar tuning tasks. In this contribution, we use different methods, such as domain randomization, to allow an agent trained in simulation to easily be deployed for a group of similar tasks. Preliminary results show that this training method is transferable and allows the RL agent to control the beam trajectory at similar lattice sections of two different real linear accelerators. We expect that future work in this direction will enable faster deployment of learning-based tuning routines, and lead towards the ultimate goal of autonomous operation of accelerator systems and transfer of RL methods to most accelerators.

The energy consumption in accelerator structures during beam downtimes is a significant fraction of the overall energy budget. Accurate prediction of downtime duration could inform actions to reduce this energy consumption. The LCAPE project started in 2020 and develops artificial intelligence to improve operations in the FNAL control room by reducing the time to identify the cause of a beam outage, improving the reproducibility of labeling it, predicting their duration and forecasting their occurrence. We present our solution for incorporating information from ~2.5k monitored devices in near-real time to distinguish between dozens of different causes of down time. We discuss the performance of different techniques for modeling the state of health of the facility and we compare unsupervised clustering techniques to distinguish between different causes of down time.

The temporal profile of the electron bunch is of critical importance in accelerator areas such as free-electron lasers and novel acceleration. In FELs, it strongly influences factors including efficiency and the profile of the photon pulse generated for user experiments, while in novel acceleration techniques it contributes to enhanced interaction of the witness beam with the driving electric field. Work is in progress at the CLARA facility at Daresbury Laboratory on temporal shaping of the ultraviolet photoinjector laser, using a fused-silica acousto-optic modulator. Generating a user-defined (programmable) time-domain target profile requires finding the corresponding spectral phase configuration of the shaper; this is a non-trivial problem for complex pulse shapes. Using a physically informed machine learning model, we demonstrate accurate and rapid shaping of the photo-injector laser to a wide range of arbitrary target temporal intensity profiles on the CLARA PI laser. Additionally, we discuss the utility of this expanded range of laser pulse shapes to potential applications in FELs and novel acceleration.

Magnetic field errors pose a limitation in the performance of circular accelerators, as they excite non-systematic resonances, reduce dynamic aperture and may result in beam loss. Their effect can be compensated assuming knowledge of their location and strength. Procedures based on orbit response matrices or resonance driving terms build a field error model sequentially for different accelerator sections, whereas a method detecting field errors in parallel yields the potential to save valuable beamtime. We introduce deep Lie map networks, which enable construction of an accelerator model including multipole components for the magnetic field errors by linking charged particle dynamics with machine learning methodology in a data-driven approach. Based on simulated beam-position- monitor readings for the example case of SIS18 at GSI, we demonstrate inference of location and strengths of quadrupole and sextupole errors for all accelerator sections in parallel. The obtained refined accelerator model may support set up of corrector magnets in operations to allow precise control over tunes, chromaticities and resonance compensation.

One of the Grand Challenges in beam physics relates to the use of virtual particle accelerators for beam prediction and optimization. Useful virtual accelerators rely on efficient and effective methodologies grounded in theory, simulation, and experiment. This work extends the application of the Sparse Identification of Nonlinear Dynamical systems (SINDy) algorithm, which we have previously presented at the North American Particle Accelerator Conference. The SINDy methodology promises to simplify the optimization of accelerator design and commissioning by discovery of underlying dynamics. We extend how SINDy can be used to discover and identify underlying differential systems governing the beam’s sigma matrix evolution and corresponding invariants. We compare discovered differential systems to theoretical predictions and numerical results. We then integrate the discovered differential system forward in time to evaluate model fidelity. We analyze the uncovered dynamical system and identify terms that could contribute to the growth(decay) of (un)desired beam parameters. Finally, we propose extending our methodology to the broader community's virtual and real experiments.

Presently, superconducting radio frequency (SRF) cavities with high intrinsic quality factors are used in particle accelerators, as a high intrinsic quality factor allows for increased energy efficiency. As such, this technology benefits new research into light source linacs such as in the new LCLS-II system. However, due to the narrow bandwidth attributed to large quality factors, the use of these SRF cavities requires more accurate control to mitigate the effects of vibrations within the cavity and maintain a fixed frequency. In a paper by Banerjee et al., it was proposed that the current practice of actively suppressing such vibrations using fast tuners may be improved through the implementation of a narrowband active noise control algorithm (NANC) that makes use of gradient descent. It is the aim of this research to explore which gradient descent methods work best for active resonance control

Reinforcement learning (RL) is a promising direction in machine learning for the control and optimisation of particle accelerators since it learns directly from experience without needing a model a-priori. However, RL generally suffers from low sample efficiency and thus training from scracth on the machine is often not an option. RL agents are usually trained or pre-tuned on simulators and then transferred to the real environment. In this work we propose a model-based RL approach based on Gaussian processes (GPs) to overcome the sample efficiency limitation. Our RL agent was able to learn to control the trajectory at the CERN AWAKE (Advanced Wakefield Experiment) facility, a problem of 10 degrees of freedom, within a few interactions only. To date, numerical optimises are used to restore or increase and stabilise the performance of accelerators. A major drawback is that they must explore the optimisation space each time they are applied. Our RL approach learns as quickly as numerical optimisers for one optimisation run, but can be used afterwards as single-shot or few-shot controllers. Furthermore, it can also handle safety and time-varying systems and can be used for the online stabilisation of accelerator operation.This approach opens a new avenue for the application of RL in accelerator control and brings it into the realm of everyday applications.

Accelerator physics simulators accurately predict the propagation of a beam in a particle accelerator, taking into account the particle interactions (a.k.a. space charge) inside the beam. A precise estimation of the space charge is required to understand the potential errors causing the difference between simulations and reality. Unfortunately, the space charge is computationally expensive, needing the simulation of a few dozen thousand particles to obtain an accurate prediction. This paper presents a Machine Learning-based approximation of the simulator output, a.k.a. surrogate model. Such an inexpensive surrogate model can support multiple experiments in parallel, allowing the wide exploration of the simulator control parameters. While the state of the art is limited to considering a few such parameters with a restricted range, the proposed approach, LinacNet, scales up to one hundred parameters with wide domains. LinacNet uses a large-size particle cloud to represent the beam and estimates the particle behavior using a dedicated neural network architecture reflecting the architecture of a Linac and its different physical regimes.