Machine Learning and Colliders, Lecture notes of Optics

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Machine Learning and Colliders

Elena Fol

R. Tomás, G. Franchetti

CERN

Goethe-University Frankfurt

Part I. Introduction to Machine Learning

• Tasks that are extremely easy and obvious for us are difficult to program in traditional ways
• Impossible to learn every possible rule to perform a task ➢ learn from examples instead Teaching machines to learn from experience

• Tasks that are extremely easy and obvious for us are difficult to program in traditional ways
• Impossible to learn every possible rule to perform a task ➢ learn from examples instead Teaching machines to learn from experience Cat?

High Energy Physics

• ML is used in dark matter search, jets recognition, particle tracking, neutrino classification, shower simulations Ben Nachman, CERN Data Science Seminars Medical Research: COVID- 19

• 1000 articles no arxiv.org related to ML applications to COVID19 research.

• Mostly image processing (x-ray images) and modeling of transmission.

Relevant ML concepts and definitions Supervised Learning Unsupervised Learning Reinforcement Learning

• Input/output pairs available
• Make prediction for unknown input based on experience from given examples - Only input data is given - Learn structures and patterns - No training data - Interact with an environment - Trying to learn optimal sequences of decisions

• Thomas M. Mitchell. Machine Learning. McGraw-Hill, Inc., New York, 1997. Object detection in computer vision, speech recognition, predictive control Anomaly detection, pattern recognition, clustering, dimensionality reduction Robotics, industrial automation, dialog systems "… computer programs and algorithms that automatically improve with experience by learning from examples with respect to some class of task and performance measure, without being explicitly programmed ." *

Supervised Learning Training input data Function with adjustable parameters (weights, bias) Model output Training output data Compute the loss (approximation error ): example 1^ e.g. MSE, MAE example 2 example 3 . . . 𝒚 = 𝒇 ෍ 𝒙𝒊𝒘𝒊 + 𝒃 Neural Network as an example: ➢ Weights w of the inputs x ➢ Activation function f ➢ Output y of a single neuron: 𝑦 = 𝑓 σ^ 𝑥𝑖𝑤 + 𝑏 How does the learning work in practice? Universal Approximation Theorem: A simple neural network including only a single hidden layer can approximate any bounded continuous target function with arbitrary small error. (Cybenko, 1989, for sigmoid activation functions) w w w x x x Input Activation function Σ^ f Weighted sum b

Supervised Learning Training input data Function with adjustable parameters (weights, bias) Model output Training output data Compute the loss (approximation error ): example 1^ e.g. MSE, MAE example 2 example 3 . . . 𝒚 = 𝒇 ෍ 𝒙𝒊𝒘𝒊 + 𝒃 Neural Network as an example: ➢ Weights w of the inputs x ➢ Activation function f ➢ Output y of a single neuron: 𝑦 = 𝑓 σ^ 𝑥𝑖𝑤 + 𝑏 How does the learning work in practice? Universal Approximation Theorem: A simple neural network including only a single hidden layer can approximate any bounded continuous target function with arbitrary small error. (Cybenko, 1989, for sigmoid activation functions) w w w x x x Input Activation function Σ^ f Weighted sum Adjust parameters Minimizing the loss e.g. Gradient Descent b

• Regression and Classification Models: resolve correlation between input variables and dependent target variables - Simple Linear Regression, Multivariate Regression, Logistic regression, Support Vector Machine
• Dimensionality reduction techniques: reduce the number of independent variables (features) without significant decrease on prediction accuracy - Independent Component Analysis, Principle Component Analysis, Features Importance Analysis
• Decision Trees : split the input data based on a sequence of variables (thresholds) to estimate the target output value or to separate data points into regions - Ensemble methods: Train several slightly different models and take majority vote/ average of the prediction
• Clustering: grouping or separating data objects into clusters
  • Identify hidden patterns in the data, similarities and differences ML is more than Neural Networks…

• Regression and Classification Models: resolve correlation between input variables and dependent target variables - Simple Linear Regression, Multivariate Regression, Logistic regression, Support Vector Machine
• Dimensionality reduction techniques: reduce the number of independent variables (features) without significant decrease on prediction accuracy - Independent Component Analysis, Principle Component Analysis, Features Importance Analysis
• Decision Trees : split the input data based on a sequence of variables (thresholds) to estimate the target output value or to separate data points into regions - Ensemble methods: Train several slightly different models and take majority vote/ average of the prediction
• Clustering: grouping or separating data objects into clusters
  • Identify hidden patterns in the data, similarities and differences ML is more than Neural Networks… Machine Learning is about learning from the data, not about application of a particular “intelligent” technique.

Adapting typical ML tasks to accelerator-specific problems

Image processing using Convolutional

Neural Networks is a very common

approach in ML research.

→ Image-based prediction of multiple beam parameters

"First steps toward incorporating image based diagnostics

into particle accelerator control systems using Convolutional

Neural Network", A.L. Edelen et al. NAPAC16 (TUPOA51)

• CNN and fully-connected ANN are used to incorporate

image-based and non-image-based data into the model to

predict multiple beam parameters via regression.

Predict the probability of an object present in a picture

Adapting typical ML tasks to accelerator-specific problems Reinforcement Learning is widely applied in robotics in control systems in general. (Coherent Synchrotron Radiation) (Radiofrequency cavities) → Automatic sub-systems tuning to achieve optimal machine performance

T. Boltz et al. “Feedback Design for Control of the Micro-Bunching Instability based

on Reinforcement Learning”, IPAC’19 (MOPGW017)

• Instabilities resulting from self-interaction of the bunch with its own radiation

field limits stable operation.

• Fast and adaptive feedback system to stabilize the dynamics is required.

→ Reinforcement Learning model based on “actions” = modifications in RF

and CSR signal as “reward”.

Learn how to walk/ jump/ avoid obstacles

ML for Beam Optics Measurements and Corrections at the LHC Importance of Beam Optics Control in Colliders:

• Control of the beam size in Interaction Points (IPs) to increase the chances of a collision.

→ Luminosity: the ratio of the number of collisions in a certain time to the interaction cross-section area.

• Beam Optics imperfections can lead to machine safety issues. Courtesy of J. Jowett

• Optics measurements are based on the signal of Beam Position Monitors : record the position of the beam

at several thousands of turns.

• Corrections aim to minimize the difference between the measured and design optics by changing the

strength of quadrupole magnets installed around the ring.

ML for Beam Optics Measurements and Corrections at the LHC

Detection of BPM failures

• Robust optics measurements

rely on BPMs integrity.

• Applying traditional

techniques, few faulty BPMs

remain in the data.

→ Detection of BPM failures prior to

optics computation using

unsupervised learning.

Magnetic field errors

• The deviations from design

optics are caused by magnetic

field errors.

→ Estimation of field errors

currently present in the machine

based on measured optics.

Missing or noisy measurements

• In case of BPMs failures the

signal and the optics function

computation at the location is

missing.

→ Denoising and reconstruction of

optics measurements using Neural

Networks.

→ Tasks to be (potentially) solved using Machine Learning