(KAVLI IPMU) Cosmology with Subaru HSC survey. A large number of cosmological N-body simulations. Parameter space exploration and the Gaussian process

Transcription

1 ,, (KAVLI IPMU) Cosmology with Subaru HSC survey A large number of cosmological N-body simulations Parameter space exploration and the Gaussian process

2 Observa(onal data and forward modeling (SDSS

3 COSMOLOGICAL PARAMETER DEPENDENCE

4 COSMOLOGICAL PARAMETER DEPENDENCE

5 COSMOLOGICAL PARAMETER DEPENDENCE

6 HSC GALAXY-GALAXY LENSING cluster region 1 cluster region 2 N-th cluster region Π R clusters with z R Known lens objects host halo properties well known photo-z accuracy not important can measure Σ as a function of scale R instead of angle on the sky

7 ωb = Ωbh 2 : ±5% ωc = Ωch 2 : ±10% ΩΛ: ±20% ln(10 10 As): ±20% ns: ±5% w: ±20%

8 cosmological parameter 1 cosmological parameter 1 cosmological parameter 1 G-G LENSING SIMULATIONS EFFICIENT SAMPLING IN MULTI DIMENSIONAL SPACE: LATIN HYPERCUBE Each sample is the only one in each axisaligned hyperplane containing it One can find many realizations of such design (ex. diagonal design) Impose additional condition such as the sum of the distances to the nearest design point is maximal (maximin distance) cosmological parameter 2 cosmological parameter 1 cosmological parameter 2 cosmological parameter 2 cosmological parameter 2

9 EFFICIENT SAMPLING IN MULTI DIMENSIONAL SPACE: LATIN HYPERCUBE Simulation spec N of particles: Size: 5 billion lightyears 21 outputs per model 5 Tbyte data per model ωb = Ωbh 2 : ±5% ωc = Ωch 2 : ±10% ΩΛ: ±20% ln(10 10 As): ±20% ns: ±5% w: ±20% 84 sims are already available parameter space sweep sliced LH design (Ba, Brenneman & Myers 15) generate >100 sample eventually maxi-min distance LH design for each 20 model set (e.g., red/blue points) two suites of runs keep the initial random number seed (20 done) different seeds (40) red: emulator blue: validation

10 SUPERCOMPUTING AND BIG DATA 理研 三好チーム プレゼンより

11 EFFICIENT SAMPLING IN MULTI DIMENSIONAL SPACE: LATIN HYPERCUBE fiducial model PLANCK15 (flat ΛCDM) 24 realizations done assess statistical error emulator accuracy check parameter space sweep sliced LH design (Ba, Brenneman & Myers 15) generate >200 sample eventually maxi-min distance LH design for each 20 model set (e.g., red/blue points) ωb = Ωbh 2 : ±5% ωc = Ωch 2 : ±10% ΩΛ: ±20% ln(10 10 As): ±20% ns: ±5% w: ±20% 119 sims are already available two suites of runs keep the initial random number seed (20 done) different seeds (40) red: emulator blue: validation

12 SIMULATION SPEC N of particles: box size: 1h -1 Gpc resolve a h -1 M solar halo with ~100 particles 2nd-order Lagrangian PT initial z in =59 (vary slightly for different cosmologies to keep the RMS displacement about 25% of the inter-particle separation) Tree-PM force by L-Gadget2 (w/ PM mesh) 21 outputs in 0 z 1.5 (equispaced in linear growth factor) Data compression (256GB -> 48GB par snapshot) positions -> displacement (16 bits par dimension; accuracy ~1h -1 kpc) velocity: discard after halo identification ID: rearrange the order of particles by ID and then discard already consuming ~200TB in half a year (~observational data)

13 SIMULATIONS SIMULATION PIPELINE ~2TB, 2+2days / 1 run IC generator create universes time evolution Gadget2 FOF (on the fly) rockstar subfind object identification on supercomputer using 648 cores) on-the-fly analysis stream density estimate data analysis mass/profile determination prediction final catalog locations of cluster-size halos

14 GAUSSIAN PROCESS A machine-learning technique to do inference in function space non-parametic Bayesian inference nonlinear regression analysis Basic quantities f(x) ~ P [μ (x), k(x, x')] mean function (cf. mean) covariance function (cf. variance) covariance function is characterized by a simple function with several hyper parameters ex. "length scale" r i for each x i (x 1, t 1 ) P (t N+1 t N ) exp [ 1 2 infer hyper parameters θ from training data (x i, t i ) [ ] [ ] Given a point x N+1, infer t N+1 [ from θ and (x i, t i ) answer: (x 2, t 2 ) (x 5, t 5 ) (x 3, t 3 ) (x 6, t 6 ) (x 4, t 4 ) [ ]] [ ] tn t N+1 C 1 tn N+1. t N+1 ˆt N+1 = k T C 1 N t N σ 2ˆt N+1 = κ k T C 1 N k.

15 GAUSSIAN PROCESS A machine-learning technique to do inference in function space non-parametic Bayesian inference nonlinear regression analysis Basic quantities f(x) ~ P [μ (x), k(x, x')] mean function (cf. mean) covariance function (cf. variance) covariance function is characterized by a simple function with several hyper parameters ex. "length scale" r i for each x i (x 1, t 1 ) P (t N+1 t N ) exp [ 1 2 infer hyper parameters θ from training data (x i, t i ) [ ] [ ] Given a point x N+1, infer t N+1 [ from θ and (x i, t i ) answer: (x 2, t 2 ) (x 5, t 5 ) (x 3, t 3 ) (x 6, t 6 ) (x 4, t 4 ) [ ]] [ ] tn t N+1 C 1 tn N+1. t N+1 ˆt N+1 = k T C 1 N t N σ 2ˆt N+1 = κ k T C 1 N k.

16 OUR ΔΣ EMULATOR DEMONSTRATIONS [2x10 14, 4x10 14 ] M sun [5x10 13, 1x10 14 ] M sun

17 GAUSSIAN PROCESS ACCURACY training with 20 models (red) validation with 20 other models (blue) realizations with different random # seeds

18 HMF EMULATOR PERFORMANCE N of halos in bin PLANCK cosmology

19 HMF EMULATOR PERFORMANCE N of halos in bin PLANCK cosmology

20 HMF EMULATOR PERFORMANCE N of halos in bin PLANCK cosmology

21 Read out pre-computed PCA basis function + GP Prepare a table for 3D spline Inputs: scale factor number density (or halo mass) projected distance give your cosmological params ~5s and redshifts ~600ms; HMF GP called inside convert M_min to n_h ~50μs Evaluate!! ~1ms

22 SUMMARY + FUTURE Modeling the halo mass function and galaxygalaxy lensing signal Latin hypercube design + fitting/gp/spline handy emulator in python ready accuracy test undergoing, aimed at 5% accuracy To come scikit-learn george RSD emulator to combine g-g lensing and 3D clustering (needs bigger volume) further extension under discussion e.g., non-flat, w0-wa cosmologies other dependence (time, scale, mass, ) (6++)-D cosmological parameter space

23 Don't forget, however, the effect of baryons Dark ma'er + adiaba-c gas +gal. model MF V 0 adiaba(c SF Osato, Shirasaki, NY, 2015

24 Need for accurate templates dark energy EoS mean density Parameter bias with respect to naive es-mate from dark ma'er only simula-ons Osato, Shirasaki, NY, 2015