High-Performance Computing, Planet Formation & Searching for Extrasolar Planets

Transcription

1 High-Performance Computing, Planet Formation & Searching for Extrasolar Planets Eric B. Ford (UF Astronomy) Research Computing Day September 29, 2011 Postdocs: A. Boley, S. Chatterjee, A. Moorhead, M. Payne, D. Veras ( Cambridge), Graduate Students: K. Colon, R. Morehead, B. Nelson, J. Wang. Undergrads: T. Hettinger ( Michigan State U), L. Legel ( U Colorado), G. Marquez ( US Navy), R. Ruth ( ELISA Tech) CISE: Graduate Students: S. Dindar, A. Ganchha, J. Gao, Y.I. Yeo; Prof. Jorg Peters, External collaborators include M. Juric (Harvard-Smithsonian Center for Astrophysics) on GPUs, the California Planet Survey team & the entire NASA Kepler Science Team. Photo: Gabriel Pérez

2 Planet formation Models How did our solar system form? How can we the diversity of planetary systems in nature? Is our solar system special? Growing atoms into giant planets spans ~45 orders of magnitude in mass! At least 6 physical processes on timescales spanning ~23 orders of magnitude! Image credit: NASA/Ames/JPL-Caltech/T. Pyle

3 Where to Planet Initially Form? 3 GLS Illustration by E. Chiang

4 4 Orbital Migration through Disk? Illustration by E. Chiang

5 Planet Scattering 5 GLS Illustration by E. Chiang

6 Planetessimal Scattering 6 GLS Illustration by E. Chiang Ford & Chiang 2007 Goldreich et al 2004 Kenyon & Bromley 06 Thommes et al. 99, 02

7 What Determines Final Orbits? 7 GLS Difference in architectures of systems with: Giant planets only? Low-mass planets only? Both giant & low-mass planets? Illustration by E. Chiang

8 Exoplanet Discovery Techniques Marois et al.

9 Image of Star s s Spectrum on Detector Measure Shift of Absorption Lines to Determine the Radial Velocity of Star N.A.Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF

10 Census of Exoplanets (w/ Doppler observations) NASA

11 Two Planet System Discovered by Doppler Technique (24 Sextans) Johnson et al. 2011

12 Uncertainty in Orbital Periods (24 Sextans) Keplerian N-Body Keplerian N-Body Johnson et al Histogram Histogram

13 Computational Challenge Analyzing radial velocity (or other) observations of extrasolar planetary systems with multiple planets. parameter estimation via Markov chain Monte Carlo ~7xN planets model parameters ~ model evaluations Parallelized via Differential Evolution MCMC Also want to test models for long-term stability Ideally, automated, with estimates updated each time a new observation is obtained Need algorithms that efficiently explore highdimensional parameter space Conventionally use clusters w/ OpenMP Moving to Graphics Processing Units

14 Shadow of a Distant Planet Planet Velocity Time (hours) Change in Brightness Planet Size

15 Kepler Mission NASA, photometry of >150,000 stars Looking for Earth-like planets in transit 50μmag in 6 hours; 30 minute cadence First ~210 days went public last week NASA/Ames

16 Kepler s First Light NASA/Ames

17 NASA/Ames

18 NASA/Ames

19 NASA/Ames

20 Kepler s Abundance of Riches Kepler 9 b d Kepler 10b Kepler 11 b g

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22 NASA/Ames

23 NASA/Ames

24 A Simple CPU Implementation Initial conditions Sys 1 Compute accelerations, jerks Run for N timesteps Store output

25 CPU parallelization (trivial: run N=N cores jobs at a time) Initial conditions Sys 1 Initial conditions Sys 2 Compute accelerations, jerks Initial conditions Run for N timesteps Sys 3 Compute accelerations, jerks Initial conditions Run for N timesteps Sys 4 Store output Store output Compute accelerations, jerks Run for N timesteps Compute accelerations, jerks Run for N timesteps Store output Store output

26 What is in a Intel Core i7? Intel Corp. ~0.1% Devoted to Floating Point Arithmetic!

27 GPU: Massively Multi-core Processor NVIDIA Corp. Hundreds of simple cores (ALUs) Minimal program control logic Exposed memory hierarchy Zero overhead thread context switching

28 GPU Design: Graphics Processing Units Heritage All cores execute the same program on different data Process large streams of data with small, independent, arithmetic intensive, programs E.g., transforming the pixels of an image Transforming geometry in 3D games Shading polygons 3D games Lots of raw computational power 80% of GPU transistors are devoted to math Fast basic arithmetic Hardware implementation of common transcendental functions (e.g., sin, cos, exp, ln, ) Excellent overlap with needs of typical scientific codes NVIDIA Corp.

29 GPU Challenges Programming (human time overhead) Is problem highly parallelizable? Branching (special cases, collisions, binaries, etc.) Memory latency (want lots of computation on relatively few numbers) CPU <-> GPU Data Transfers Speed up kernel by x100, other parts of code become significant Keeping up with the times (new architectures)

30 Simiple GPU parallelization (slightly nontrivial: N~16 N cores jobs in 1 process) Initial conditions for N systems Upload to GPU Separate device All cores run the same program Easy to parallelize as 1 system/thread Pack N>4,000 jobs into 1 process to hide memory latency & achieve large speed ups Simple integration algorithms Sys 1 Sys 2 Sys M+1 1 MP 1 Compute accelerations, Sys Compute jerks Sys Compute M+2 2 Sys 12M+1 MP accelerations, Sys Compute jerks accelerations, M Sys Compute jerks Sys Compute 2M+2 Sys 1 accelerations, Compute jerks accelerations, Sys Compute jerksm 2M accelerations, Sys Compute jerks Sys Compute 2 Advance accelerations, x,v,t jerks accelerations, Compute jerks accelerations, Sys Compute jerksm 3M accelerations, Sys Compute jerks accelerations, Advance jerks x,v,t accelerations, Compute jerks accelerations, Sys Compute jerksm N accelerations, Advance jerks x,v,t accelerations, Compute jerks accelerations, jerks MP 2 Store intermediate output in GPU memory Download results from GPU to CPU [to disk] Analyze results (currently with CPU) MP N MP

31 GPUs keep getting better: Fermi Upto 8x faster double precision (750 GFLOPS) 512 (vs 240) cores 4 Special Function Units per multiprocessor (vs 1) Increase shared memory On GPU memory cache Atomic ops 5-20x faster Fewer registers per core Favors algorithms w/ finer grained parallelization NVIDIA Corp.

32 High Performance GPU parallelization (challenging: N~few N cores jobs in 1 process) NVIDIA Corp. All multiprocessors (MPs) run the same program, each for M systems Parallelize each step optimally, for finer parallelization Achieve large speed ups with only ~1,000 jobs More complex integration algorithms Initial conditions for N systems Upload to GPU Sys 1 M Load x, v, t MP 1 Compute Sys 1M+1 Load x, v, t MP 2 accelerations, jerks Sync 2M Compute Sys 12M+1 Load x, v, t MP 3 accelerations, jerks Sync Compute Sys 1 Compute accelerations, jerks 3M Sys Load 1 x, v, Nt MP accelerations, jerks Sync Load x, v, t MP N Compute MP Compute accelerations, jerks accelerations, jerks Compute Advance Sync x,v,t Sync Compute accelerations, jerks accelerations, jerks Sync Advance Sync x,v,t Advance & Store x,v,t Compute accelerations, jerks Advance Sync x,v,t Compute accelerations, jerks Sync Sync Sync Sync Store intermediate output in GPU memory Download results from GPU to CPU [to disk] Analyze results (currently with CPU)

33 A Moment of Zen About GPUs, this is NOT This is about CPUs, 5 years from now We must: (Re)learn how to code for 1000-core, shared memory machines Have the basic tools to efficiently use them (e.g., ODE and N-body solvers) Obtaining x speedup NOW doesn t hurt either For more about Swarm-NG

34 Example Application Characterizing (the very small) uncertainties in masses, radii and orbital parameters in systems with a transiting circumbinary planet NASA/JPL-Caltech/T. Pyle

35 Kepler-16 Doyle et al. 2011

36 Doyle et al. 2011

37 Doyle et al. 2011

38 Precise Masses & Radii Doyle et al. 2011

39 Exquisite Precision in Mass & Radius Winn et al. 2011

40 Questions NASA