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Surrogate Modeling Solutionsfor Cosmological Parameter Inference
of Hydrogen Intensity Mapping Surveys
Nick KernUC Berkeley
NASA Machine Learning WorkshopAugust 30th, 2017
Overview
1. ScienceRadio intensity mapping of cosmic hydrogen and the quest to
detect the Epoch of Reionization (EoR)
Nick Kern NASA ML Workshop 8/30/2017
2. Machine LearningCosmological parameter inference and how surrogate modeling
enables for more robust constraints
3. ApplicationForecast of future constraints from the Hydrogen Epoch of
Reionization Array1 (HERA), a $15M international project to build a radio telescope capable of detecting the EoR
1reionization.orgKern et al. 2017
arXiv:1705.04688
Science
Nick Kern NASA ML Workshop 8/30/2017
Cosmic History Timeline
Nick Kern NASA ML Workshop 8/30/2017
13.7 Gyr
Cosmic History Timeline
Nick Kern NASA ML Workshop 8/30/2017
Cosmic Microwave Background
Sloan Digital Sky Survey
what happened here?
13.7 Gyr
Cosmic History Timeline
Nick Kern NASA ML Workshop 8/30/2017
Cosmic Microwave Background
Sloan Digital Sky Survey
what happened here?
13.7 GyrAlvarez et al. 2009
Hydrogen’s 21cm “Spin Flip” Transition
Nick Kern NASA ML Workshop 8/30/2017
Nick Kern NASA ML Workshop 8/30/2017
21cm “Spin Flip” Transition for 3D Tomographic Mapping
Nick Kern NASA ML Workshop 8/30/2017
21cm “Spin Flip” Transition for 3D Tomographic Mapping
Nick Kern NASA ML Workshop 8/30/2017
21cm “Spin Flip” Transition for 3D Tomographic Mapping
Nick Kern NASA ML Workshop 8/30/2017
21cm “Spin Flip” Transition for 3D Tomographic Mapping
21cm “Spin Flip” Transition for 3D Tomographic Mapping
Nick Kern NASA ML Workshop 8/30/2017
redshift
frequency
z = 7z = 9z = 11
Radio Intensity Mapping Experiments
Nick Kern NASA ML Workshop 8/30/2017
21cm power spectrum
Machine Learning
Nick Kern NASA ML Workshop 8/30/2017
The last step: How do we interpret our data?• We want to constrain cosmological models:
Nick Kern NASA ML Workshop 8/30/2017
data
Ali et al. 2015
The last step: How do we interpret our data?• We want to constrain cosmological models:
Nick Kern NASA ML Workshop 8/30/2017
data model
Ali et al. 2015
The last step: How do we interpret our data?• We want to constrain cosmological models:
Nick Kern NASA ML Workshop 8/30/2017
data model
Ali et al. 2015
The last step: How do we interpret our data?• Maximize likelihood for parameter constraints
Nick Kern NASA ML Workshop 8/30/2017
data
model
observational error
Problem: what if our models are sophisticated & expensive simulations?— performing MCMC directly with the simulation is not practical (or even feasible) with limited time and resources
Solution:— use surrogate models to describe the simulation output over the space of its input parameters
— example: tRUN ~ 24 hours, NRUN ~ 104, tMCMC > 6 years on 100-core cluster
Surrogate Modeling aka Emulation
Nick Kern NASA ML Workshop 8/30/2017
Surrogate Modeling aka Emulation
Nick Kern NASA ML Workshop 8/30/2017
Surrogate Modeling aka Emulation
Nick Kern NASA ML Workshop 8/30/2017
emulatorcross validation set
training set
Surrogate Modeling aka Emulation
Nick Kern NASA ML Workshop 8/30/2017
Considerations:• training set sampling• choice of regression model• cross validation• error propagation
Benefits:• parameter constraints
with complex simulations• orders of magnitude faster
Costs:• approximate• bound by training set
Kern et al. 2017arXiv:1705.04688
github.com/nkern/emupy
Gaussian Process Regression
Nick Kern NASA ML Workshop 8/30/2017
Forecasting HERA Constraints
Nick Kern NASA ML Workshop 8/30/2017
Hydrogen Epoch of Reionization Array (HERA)
Nick Kern NASA ML Workshop 8/30/2017
PI: Parsons
Training an Emulator on an EoR Simulation
Nick Kern NASA ML Workshop 8/30/2017
Mesinger et al. 2011
• start with an eleven parameter model- six astrophysical : flat priors- five cosmological : Planck CMB priors
Training an Emulator on an EoR Simulation
Nick Kern NASA ML Workshop 8/30/2017
• generate Gaussian training set
• emulate 21cm power spectra
• cross validate
• HERA instrumental simulation
Joint Posterior Distribution
Nick Kern NASA ML Workshop 8/30/2017
Marginalized Posterior Distribution
Nick Kern NASA ML Workshop 8/30/2017
cosmologicalparameters
astrophysicalparameters
Summary
• Radio intensity mapping surveys are poised to make a first detection of primordial hydrogen at the EoR and subsequently produce strong
constraints on astrophysical parameters
• Challenges of MCMC with complex numerical simulations can be overcome by developing surrogate models that approximate the input-
output mapping of the simulation, which can then be used to accelerate MCMC sampling
• Surrogate modeling can be used to extract information from the data (i.e., parameter constraints) but, viewed the other way, can also be
used to extract information from the simulation (i.e., model calibration)
Nick Kern NASA ML Workshop 8/30/2017
Comparison against brute-force MCMC
Nick Kern NASA ML Workshop 8/30/2017
