The z -Vertex Trigger for Belle II Sebastian Skambraks Technische - - PowerPoint PPT Presentation

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The z -Vertex Trigger for Belle II Sebastian Skambraks Technische - - PowerPoint PPT Presentation

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion The z -Vertex Trigger for Belle II Sebastian Skambraks Technische Universit at M unchen July 3, 2015 1 / 15 Introduction Multi Layer Perceptron - MLP

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

The z-Vertex Trigger for Belle II

Sebastian Skambraks

Technische Universit¨ at M¨ unchen

July 3, 2015

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Outline

Introduction Motivation Signal Flow Multi Layer Perceptron - MLP Theory Setup Preprocessing Least Square fit - LS Results MLP and LS results Conclusion

Neuro Team

  • F. Abudinen (LMU), Y. Chen (TUM), M. Feindt (KIT), R. Fr¨

uhwirth (HEPHY),

  • M. Heck (KIT), C. Kiesling (MPI), A. Knoll (TUM), S. Neuhaus (TUM),
  • S. Paul (TUM), T. R¨
  • der (TUM), J. Schieck (HEPHY), S. Skambraks (TUM)

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Introduction

Goals

◮ build a z-vertex track trigger ◮ achieve high precision

(spatial resolution ∆z ≈ 2 cm)

◮ get a fast decision (< 1 µs)

Method

◮ Input:

◮ CDC Track Segment data

[IDs & clock cycle (2 ns timing)]

◮ Algorithms:

  • 1. Bayes Classifier / Hough Transformation

(pattern recognition)

  • 2. LS - Least Square fit

(linear estimation)

  • 3. MLP - Multi Layer Perceptron

(nonlinear correction)

z (cm)

  • 40
  • 30
  • 20
  • 10

10 20 30 40 # of events / 5 mm 200 400 600 800 1000 Z distribution

Offline z distribution in the Belle Experimenta.

a) T. Abe et al., Belle II Technical Design Report, KEK-REPORT-2010-1, arXiv:1011.0352v1 [physics.ins-det] (2010). 3 / 15

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Main approach

Pattern recognition - Bayes Classifier / Hough Transform

sectorize Input in the track parameters (pT, ϕ, ϑ) P(Sector|Hits) = P(Hits|Sector) · P(Sector) P(Hits) (1)

Fitter - Least Squares

  • n = (XTX)−1XT

y (2) X and y contain the hits, n defines a track parameter sector

Neural Network - MLP

z(Hits, pT, ϕ, ϑ) = NN(f (Hits, pT, ϕ, ϑ)) (3)

◮ output float value interpreted as scaled z-position ◮ NN input transformation (function f ) requires preprocessing

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Signal flow in the CDC Trigger

CDC Digitizer Merger Axial TSF Stereo TSF 2D Finder Pattern Recognition 3D Trigger

  • 1. 2D Fit
  • 2. 3D Fit

NeuroTrigger

  • 1. Preprocessing:

HHimprove (pT, ϕ) & HHsectorize phase space

  • 2. MLP

HHoutput: improved z Global Decision Logic t < 5 µs TSaxial TSaxial, pT, ϕ TSstereo z

→ The neural network trigger will be implemented on a Virtex 7 FPGA

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Signal flow in the CDC Trigger

CDC Digitizer Merger Axial TSF Stereo TSF 2D Finder Pattern Recognition 3D Trigger

  • 1. 2D Fit
  • 2. 3D Fit

NeuroTrigger

  • 1. Preprocessing:

HHimprove (pT, ϕ) & HHsectorize phase space

  • 2. MLP

HHoutput: improved z Global Decision Logic t < 5 µs TSaxial TSaxial, pT, ϕ TSstereo z

→ The neural network trigger will be implemented on a Virtex 7 FPGA

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

MLP - Multi Layer Perceptron

Properties

◮ supervised machine learning ◮ function approximation ◮ short deterministic runtime ◮ one neuron:

y = tanh(

  • i=1

wi · xi + w0)

Input

3 nodes per SL (t, ϕrel, µ) with t: drift time, ϕrel: relative wire position, µ: 2D arc length z . . . . . . wkj wji ti ϕreli µi ti ϕreli µi ti ϕreli µi ti ϕreli µi ti ϕreli µi

input layer hidden layer

  • utput

layer

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

MLP - Setup

Sectorization

◮ the track parameter space is sectorized in (pT, ϕ, ϑ) ◮ for each sector an expert MLP is trained ◮ asymmetry in ϑ, and pT can be taken into account ◮ preprocessing selects the proper MLP

Two different sectors in (pT, ϕ) (left) and in ϑ (right).

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

“Expert” MLP - Capabilities

a) b)

Figure: z-vertex prediction with an “expert” MLP for a small sector in two pT regions with φ ∈ [0, 360]◦, θ ∈ [56, 62]◦ and z ∈ [−10, 10] cm. a) pT ∈ [0.3, 0.317] GeV. b) pT ∈ [3.5, 9.625] GeV.

! high accuracy on the z-vertex within a small sector

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Preprocessing

TSF 2D Finder Preprocessing MLP z TSaxial, TSstereo pT, ϕ NN input

Figure: Information flow in the NeuroTrigger

Tasks

  • 1. match Track Segments to tracks
  • 2. improve (pT, ϕ) estimate (2D fit)

→ Least Squares fit including drift times

  • 3. provide 3D estimate (ϑ, z)
  • 4. prepare Neural Net Input (& choose sector)

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Preprocessing - Least Square fit

solve the linear equation y = X · n by: n = (XTX)−1XT y

2D fit

circle fit; center at c; track from origin. pT, ϕ ← cx, cy xi, yi: cartesian coordinates of axial hits in the (r, ϕ) plane. (x2

i + y 2 i ) = 2cx · xi + 2cy · yi

x y ϕ

  • c

3D fit

line fit in the (µ, z) plane. µi, zi: stereo hits transformed by 2D fit result. zi = cot(ϑ) · µi + z0 µ z z-vertex

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Results - 2D LS Fit (ϕ, pT) 90% RMS

pT [GeV] 1 2 3 4 5 ∆ϕ [◦] 1 2 3 4 nonlinear xt inner detector no background pT [GeV] 1 2 3 4 5 ∆pT pT [%] 1 2 3 4 5 6 7 8 9 nonlinear xt inner detector no background pT ∈ [0.3, 5] GeV ϕ ∈ [0, 90]◦ ϑ ∈ [35, 123]◦ z ∈ [−50, 50] cm

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Results - 3D LS Fit (ϑ, z) 90% RMS

pT [GeV] 1 2 3 4 5 ∆θ [◦] 1 2 3 4 5 6 7 8 9 10 11 12 13 nonlinear xt inner detector no background pT [GeV] 1 2 3 4 5 ∆z [cm] 1 2 3 4 5 6 7 8 9 10 11 12 13 nonlinear xt inner detector no background pT ∈ [0.3, 5] GeV ϕ ∈ [0, 90]◦ ϑ ∈ [35, 123]◦ z ∈ [−50, 50] cm

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

LS Fitter efficiency

Cuts lead to efficiency decrease

◮ min 3 axial hits in different layers ◮ max 10 axial hits total ◮ min 2 stereo hits in different layers ◮ max 8 stereo hits total ◮ min 5 hits total

pT [GeV] 1 2 3 4 5 ε [%] 50 60 70 80 90 100 nonlinear xt inner detector no background

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

z-90% RMS with LS fit and MLP

pT [GeV] 1 2 3 4 5 ∆z [cm] 1 2 3 4 5 6 7 8 9 MLP, inner detector, nonlinear xt LS Fit, inner detector, nonlinear xt MLP, small (pT, ϑ) sectors no inner detector, nonlinear xt sector 1 sector 2 pT ∈ [0.3, 5] GeV ϕ ∈ [0, 90]◦ ϑ ∈ [35, 123]◦ z ∈ [−50, 50] cm

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Introduction Multi Layer Perceptron - MLP Preprocessing Results Conclusion

Conclusion

MLP

◮ MLP requires preprocessing ◮ MLP can improve z-RMS in low pt region ◮ Sectorization improves MLP prediction

Preprocessing

◮ LS fit useful for preprocessing ◮ LS fit achieves good z-RMS for high pT tracks

Outlook

◮ MLP optimization for low pT tracks ◮ further preprocessing studies ◮ hardware implementation on Virtex 7 FPGA

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