HEP Experiments: Fixed-Target and Collider

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1 HEP Experiments: Fixed-Target and Collider Beam Beam Beam Target Inelastic collisions Signal events High energy = high density + high rate CBM (FAIR/GSI) Magnet PID ALICE (CERN) TPC Inner Tracker Muon Chambers HEP Experiments: select interesting physics on-line 11 September 2012, GSI Ivan Kisel, Uni-Frankfurt, FIAS, GSI

2 Stages of Data Reconstruction 1 Track finding 2 Track fitting Time consuming!!! Conformal Mapping Hough Transformation Track Following + Kalman Filter Cellular Automaton + Kalman Filter Kalman Filter 3 Ring finding (Particle ID) Combinatorics D 0 4 Particles finding K - π + Hough Transformation Elastic Neural Net Kalman Filter 11 September 2012, GSI Ivan Kisel, Uni-Frankfurt, FIAS, GSI

3 Global Methods: Conformal Mapping + Histogramming Global methods are especially suitable for fast tracking in projections Example: Collider experiment with a solenoid, where tracks are circular trajectories Triggers Simple Conformal Mapping: Transform circles into straight lines u = x/(x 2 +y 2 ) v = -y/(x 2 +y 2 ) Histogram: Collect a histogram of azimuth angles φ Find peaks in the histogram Collect hits into tracks Fast φ y v x u φ

4 Global Methods: Conformal Mapping + Histogramming Advantages: Impressive visual simplification of the problem Each step is easy to implement in hardware This results in a fast algorithm Disadvantages: Non-obvious complications of the problem Reverse order of the hits (last <-> first) Measurement errors are now no more uniform Geometry of detectors must be transformed Geometry of material walls must also be transformed What with the alignment constants? A (non-uniform) magnetic field (map) must be transformed What with the Lorentz force: F = q(e+vxb)? Needs to know exact position of the interaction point Finds only primary tracks Does not find secondary tracks Is it possible to build a trigger on primary tracks only? In fact, histogramming provides only track parameters No errors of track parameters estimates (covariance matrix) No hits grouping into track candidates Therefore, no possibility to refit tracks Histogramming needs access to main memory (slow) Conclusion: Useful implemented in hardware and for very simple event topologies only

5 Global Methods: Hough Transformation Measurement Space Parameter Space y = a*x + b b = -x*a + y y b x a

6 Global Methods: Hough Transformation Advantages: Generalization of the histogramming method Easy to implement in hardware This results in a fast algorithm Disadvantages: Needs a global track model Therefore, appropriate for simple magnetic fields only Does not include multiple scattering Finds only fast tracks (not MF and MS dependent) Histogramming provides only track parameters No errors of track parameters estimates (covariance matrix) No hits grouping into track candidates Therefore, no possibility to refit tracks Not possible competition between track candidates Therefore, relatively large percentage of wrong tracks Histogramming needs access to main memory -> slow 5D histogramming (x, y, tx, ty, q/p) needs a lot of memory Precise tracking requires even more memory -> swapping? Memory initialization for every event Conclusion: Useful implemented in hardware and for simple event and trigger topologies

7 Local Methods: Kalman Filter for Track Finding KF Fit KF Find Seeding Planes

8 Local Methods: Kalman Filter for Track Finding Advantages: Psychologically easy to accept hit by hit track finding Combined track finder and fitter based on KF Development of a new experiment starts with an ideal MC track finder and a realistic KF track fitter, therefore the next step to a realistic track finder is obvious KF... Disadvantages: Track finding a combinatorial (NP) problem, can not be solved directly using methods suitable for single track Repeats the same calculations many times, when discarding track candidates Works at the hit level Needs seeding (starting short track segments) Final efficiency is always limited by seeding efficiency It is limited also by the efficiency of the seeding chambers Therefore needs a lot of seeds -> even larger combinatorics How many inefficient detectors can be tolerated in general? How to include missing hits into the Kalman filter? How to calculate chi^2 in this case? Too early competition between track candidates --- Conclusion: Useful for relatively simple event topologies and as initial (second after the ideal) track finder

9 Cellular Automaton (CA) as Track Finder Track finding: Which hits in detector belong to the same track? Cellular Automaton (CA) 0. Hits (CBM) 0. Hits Detector layers Hits 1. Segments 1000 Hits 2. Counters Cellular Automaton: 1. Build short track segments. 2. Connect according to the track model, estimate a possible position on a track. 3. Tree structures appear, collect segments into track candidates. 4. Select the best track candidates. Cellular Automaton: local w.r.t. data intrinsically parallel extremely simple very fast Perfect for many-core CPU/GPU! 3. Track Candidates 4. Tracks 4. Tracks (CBM) 1000 Tracks

10 Cellular Automaton (CA) as Track Finder Advantages: Local relations -> simple calculations Local relations -> parallel algorithm Staged implementation: hits -> segments -> tracks Polynomial (2nd order?) combinatorics Track competition at the global level Includes the KF fitter, if necessary, for high track densities Detector inefficiency problem outside the combinatorics... Disadvantages: Not easy to understand a parallel algorithm (Game of Life) Currently implementations on sequential computers Parallel hardware is coming now... Conclusion: Useful for complicated event topologies with large combinatorics and for parallel hardware

11 Kalman Filter (KF) based Track Fit Track fit: Estimation of the track parameters at one or more hits along the track Kalman Filter (KF) Hits 3 Correction Detector layers 1 Initialising π (r, C) Precision r Track parameters C Precision KF Block-diagram 1 2 Prediction State vector Position, direction and momentum r = { x, y, z, p x, p y, p z } 2 3 Kalman Filter: 1. Start with an arbitrary initialization. 2. Add one hit after another. 3. Improve the state vector. 4. Get the optimal parameters after the last hit. KF as a recursive least squares method Nowadays the Kalman Filter is used in almost all HEP experiments

12 Coming now: Many-core Era of HPC (240) (128) (128) (128) (24) (4) (4) (16) (24) S. Borkar et al. (Intel), "Platform 2015: Intel Platform Evolution for the Next Decade", Cores HW Threads SIMD width On-line event selection Mathematical and computational optimization Optimization of the detector Heterogeneous systems of many cores Uniform approach to all CPU/GPU families Similar programming languages (CUDA, ArBB, OpenCL) Parallelization of the algorithm (vectors, multi-threads, many-cores)

13 Many-Core HPC: Cores, Threads and SIMD HEP experiments work with high data rates, therefore need High Performance Computing (HPC)! Cores and Threads realize the task level of parallelism 2015 Process Thread1 Thread2 exe r/w r/w exe exe r/w CPU 2010 Threads Cores Thread Thread Scalar D Core Vector S S S S HPC Vectors Vectors (SIMD) = data level of parallelism SIMD = Single Instruction, Multiple Data Fundamental redesign of traditional approaches to data processing is necessary

14 Many-Core CPU/GPU Architectures Intel/AMD CPU 4x8 cores NVIDIA/AMD GPU 512 cores Optimized for low-latency access to cached data sets Control logic for out-of-order and speculative execution Optimized for data-parallel, throughput computation More transistors dedicated to computation Intel MIC >50 cores IBM Cell 1+8 cores Many Integrated Cores architecture announced at ISC10 (June 2010) Based on the x86 architecture Many-cores + 4-way multithreaded bit wide vector unit General purpose RISC processor (PowerPC) 8 co-processors (SPE, Synergistic Processor Elements) 128-bit wide SIMD units Future systems are heterogeneous

15 CPU/GPU Programming Frameworks Intel Ct (C for throughput), ArBB (Array Building Blocks) Extension to the C language Intel CPU/GPU specific SIMD exploitation for automatic parallelism NVIDIA CUDA (Compute Unified Device Architecture) Defines hardware platform Generic programming Extension to the C language Explicit memory management Programming on thread level OpenCL (Open Computing Language) Open standard for generic programming Extension to the C language Supposed to work on any hardware Usage of specific hardware capabilities by extensions Vector classes (Vc) Overload of C operators with SIMD/SIMT instructions Uniform approach to all CPU/GPU families Uni-Frankfurt/FIAS/GSI ArBB, Vector classes: Cooperation with Intel

16 Kalman Filter Track Fit on Cell Intel P x faster on any PC Cell Comp. Phys. Comm. 178 (2008) The KF speed was increased by 5 orders of magnitude Böblingen: 2 Cell Broadband Engines, 256 kb LS, 2.4 GHz Motivated by, but not restricted to Cell!

17 CBM Cellular Automaton Track Finder Top view 770 Tracks Front view Efficiency Reliability 11 September 2012, GSI Highly efficient and reliable event reconstruction Ivan Kisel, Uni-Frankfurt, FIAS, GSI

18 Track Finding at Low Track Multiplicity Top view Front view Side view 3D view Au+Au mbias events at 25 AGeV, 8 STS, 0 x 7,5 strip angles A minimum bias event: average reconstructed track multiplicity 109 Ivan Kisel, Uni-Frankfurt, FIAS, GSI 2nd CBM Software Workshop, Ebernburg, /09

19 Track Finding at Medium Track Multiplicity Top view Side view Front view 3D view Au+Au mbias events at 25 AGeV, 8 STS, 0 x 7,5 strip angles A central event: average reconstructed track multiplicity 572 Ivan Kisel, Uni-Frankfurt, FIAS, GSI 2nd CBM Software Workshop, Ebernburg, /09

20 Track Finding at High Track Multiplicity Top view Side view Front view 3D view Au+Au mbias events at 25 AGeV, 8 STS, 0 x 7,5 strip angles A group with 100 minimum bias events: average reconstructed track multiplicity Ivan Kisel, Uni-Frankfurt, FIAS, GSI 2nd CBM Software Workshop, Ebernburg, /09

21 CA Track Finder: Efficiency and Time vs. Track Multiplicity Stable reconstruction efficiency and time as a second order polynomial up to 100 minimum bias events in a group Ivan Kisel, Uni-Frankfurt, FIAS, GSI 2nd CBM Software Workshop, Ebernburg, /09

22 KFParticle: Reconstruction of Vertices and Decayed Particles K - State vector Position, direction, momentum and energy D 0 r = { x, y, z, p x, p y, p z, E } π + x, y, z, p x, p y, p z, E, m, L, cτ AliKFVertex PrimVtx( ESDPrimVtx ); // Set primary vertex // Set daughters AliKFParticle K( ESDp1, -321 ), pi( ESDp2, 211 ); AliKFParticle D0( K, pi ); PrimVtx += D0; // Construct mother // Improve the primary vertex D0.SetProductionVertex( PrimVtx ); // D0 is fully fitted K.SetProductionVertex( D0 ); pi.setproductionvertex( D0 ); // K is fully fitted // pi is fully fitted KFParticle provides uncomplicated approach to physics analysis

23 KFParticle Finder for Physics Analysis and Selection Tracks: e ±, µ ±, π ±, K ±, p ± secondary and primary Open-charm: D 0 π + K - D 0 π + π + π - K - D 0 π - K + D 0 π - π - π + K + D + π + π + K - D - π - π - K + D s + π + K + K - D s - π - K + K - Λ c π + K - p Open-charm resonances: D *0 D + π - D *0 D - π + D *+ D 0 π + D *- D 0 π - Multi-strange hyperons: Ξ - Λ π - Ξ + Λ π + Ω - Λ K - Ω + Λ K + Multi-strange resonances: Ξ *0 Ξ - π + Ξ *0 Ξ + π - Ω *- Ξ - π + K - Ω *+ Ξ + π - K + Strange particles: K 0 s π+ π - Λ p π - Λ π + p - Strange and multi-strange resonances: Σ *+ Λ π + Σ *+ Λ π - Σ *- Λ π - Σ *- Λ π + K *- K 0 s π- K *+ K 0 s π+ Ξ *- Λ K - Ξ *+ Λ K + Gamma: γ e - e + Strange resonances: K *0 K + π - K *0 π + K - Λ * p K - Λ * p - K + Light vector mesons: ρ e - e + ρ µ - µ + ω e - e + ω µ - µ + φ e - e + φ µ - µ + φ K - K + Charmonium: J/Ψ e - e + J/Ψ µ - µ + 11 September 2012, GSI Ivan Kisel, Uni-Frankfurt, FIAS, GSI

24 Standalone First Level Event Selection (FLES) Package Geometry Hits FLES CA Track Finder KF Track Fitter KFParticle Finder Particle Selection Quality Check MC ASCII Files Efficiencies ROOT Histograms The first version of the FLES package is portable, efficient, vectorized and parallelized

25 FLES Package Scalability Given n threads each filled with 1000 events, run them on specified n logical cores, 1 thread per 1 core. The FLES package shows strong scalability on up to 80 cores

26 Consolidate Efforts: Common Reconstruction Package Uni-Frankfurt/FIAS: Vector classes CPU/GPU implementation HEPHY (Vienna)/Uni-Gjovik: Kalman Filter track fit Kalman Filter vertex fit GSI: Algorithms development Many-core optimization Common Reconstruction Package CBM (FAIR/GSI) OpenLab (CERN): Many-core optimization Benchmarking Intel: ArBB/OpenCL implementation Many-core optimization Benchmarking ALICE (CERN) Host Experiments PANDA (FAIR/GSI) 11 September 2012, GSI STAR (BNL) Ivan Kisel, Uni-Frankfurt, FIAS, GSI

27 Consolidate Efforts: International Workshops International Workshop for Future Challenges in Tracking and Trigger Concepts 1st 2nd 3rd 4th 11 September 2012, GSI GSI, Darmstadt, Germany, ; CERN, Geneva, Switzerland, ; FIAS, Frankfurt, Germany, ; CERN, Geneva, Switzerland, Ivan Kisel, Uni-Frankfurt, FIAS, GSI

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