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COSMORPH

Julian Merten � Marie Skłodowska-Curie fellow | INAF-OAS Bologna

AstroFIt2 annual meeting | INAF-headquarters Roma | 23.10.2018

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The standard model of cosmology

The standard model | Data representation and processing | Mass mapping | Learning structure

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Big problems

Hikage et al. (2018); arXiv:1809.09148

The standard model | Data representation and processing | Mass mapping | Learning structure

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Intermediate (cluster) problems

The standard model | Data representation and processing | Mass mapping | Learning structure

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Small problems

The standard model | Data representation and processing | Mass mapping | Learning structure

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What could it all mean

  • New physics
    • Massive neutrinos
    • Modified gravity
    • Self-interacting dark matter�
  • Insufficient modelling of baryonic physics
    • Subgrid physics not enough
    • Wrong parameters�
  • Unaccounted systematics in the observations�
  • Wrong interpretation of the data
    • Projection effects
    • Selection effects
    • Apples to oranges comparisons

The standard model | Data representation and processing | Mass mapping | Learning structure

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The era of galaxy redshift surveys

The data to improve our understanding of nonlinear structure is coming

on-going

soon (2020’ish)

future (2025’ish)

Together with Planck, JWST, eRosita (space); DESI, PFS (ground-spec); CMB stage 3.5 and 4

The standard model | Data representation and processing | Mass mapping | Learning structure

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Data representation

Then you would probably not represent such data via e.g. 1-d functional forms of the density profile in the halo regime or 2pt correlation functions on larger scales.

The goal is then to find a more complete representation of the simulated data, ideally with minimal compression.

Let’s accept for a moment that all our reference theoretical model derive from numerical simulations

The standard model | Data representation and processing | Mass mapping | Learning structure

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Learning simulations

data {x}

mechanism {f(x)}

labels {y}

image preparation

image characterisation

(representation)

(compression)

classification / regression

training {g(x,y)}

(fitting)

(learning)

prediction

Disclaimer: x does not have to be a mass map, but it will be the focus of this talk.

The standard model | Data representation and processing | Mass mapping | Learning structure

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(Big) Data processing

  • Scope
    • Mass mapping (this work)
    • Dark matter characterisation using CNNs
    • Galaxy image simulations using GANs
  • Grant
    • 2 x NVIDIA Titan Xp
    • 3840 streaming cores @ 1.582 GHz
    • 12 GB memory
    • 12 TFLOPS (sp); 6 TFLOPS (dp)

This work is supported by an NVIDIA academic grant:

The standard model | Data representation and processing | Mass mapping | Learning structure

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Exploiting many-core architectures

NVIDIA CUDA C �programming guide

https://docs.nvidia.com/

The standard model | Data representation and processing | Mass mapping | Learning structure

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My project

Image data

Cosmology

I Optimal shape catalogues for weak lensing

II Mapping all structure in the sky

III Understand how structure organises itself

The standard model | Data representation and processing | Mass mapping | Learning structure

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Euclid PSF modelling

with Lance Miller, Chris Duncan and the Euclid PSF team

The standard model | Data representation and processing | Mass mapping | Learning structure

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Measuring shapes with deep learning

Springer et al. (2018) | arXiv:1808.07491

The standard model | Data representation and processing | Mass mapping | Learning structure

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Introduction to mass mapping

Clowe et al. (2006); arXiv:0608407

The conversion of observational measurements into an actual map of the distribution of matter in the sky.

Why mass maps?

  • If it’s a good one: Peaks, troughs, mass profiles, magnifications
  • Combination of different mass tracers into a joint reconstruction
  • Comparison of different tracers to learn about astrophysics
  • Higher-order topological analyses
    • Machine and deep learning applications (talk to me about that)

The standard model | Data representation and processing | Mass mapping | Learning structure

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Wide fields - adaptive resolution - multi-tracer

Perfectly adaptive method in the Euclid era, which interactively incorporates all data where available into a single reconstruction

  • Lensing (with K. Huber, J. Wagner)
    • Reduced shear (2nd order in \psi)
    • Flexion (3rd)
    • Point-like multiple images (1st)
    • Extended sources (1st)
    • Critical line tracers (2nd)
    • Magnification input (Type 1a SNe) (2nd)
    • Convergence ratios etc. (see J. Wagner’s talk) (2nd and up)�
  • ICM (with K. Huber, C. Tchernin, M. Bartelmann)
    • X-ray via Richardson-Lucy (0th)
    • SZ via Richardson-Lucy (0th)�
  • Galaxy kinematics (with A. Biviano, B. Sartoris)
    • Potential tracers (2nd and higher)
    • Reconstruction templates (any you want)

Input data

5deg

The standard model | Data representation and processing | Mass mapping | Learning structure

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Mass mapping challenges

Combination

  • Different probes may trace different physical properties of the system
    • One must find a common ground for all of them
  • Signal to noise properties between different tracers might be quite different
  • Validation e.g. via simulations can be more difficult since more properties have to be considered

Topology

  • Different probes may trace largely different length scales
    • One needs to find a reconstruction domain that is adaptive
  • Data coverage of the field of interest might be sparse in some, dense in other tracers
  • In the age of wide surveys, masks and other artefacts become very significant

Runtime

  • Many surveys are or will be all-sky or close to it
    • Fairly large computational challenge esp. for a sophisticated method
    • Many surveys will deliver this at high resolution
  • Meaningful error bars may only be derived from resampling of input data

The standard model | Data representation and processing | Mass mapping | Learning structure

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Inhomogeneous input

Real CLASH data field

Real KiDS data field

The standard model | Data representation and processing | Mass mapping | Learning structure

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Mesh-free domain via RBFs

In reality slightly more complicated due to polynomial support

JMM (2016) | arXiv:1412.5182

Fornberg & Flyer (2015) | A primer on radial basis

functions with applications to the geosciences

The standard model | Data representation and processing | Mass mapping | Learning structure

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Results -- cluster lensing

Tested via ray-tracing through a full hydro cluster simulation

JMM (2016) | arXiv:1412.5182

WL: 25 gal arcmin^-2

SL: 10 systems 1 < z < 3.6

Special thanks to:

M. Meneghetti, E. Rasia, �S. Borgani

The standard model | Data representation and processing | Mass mapping | Learning structure

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Results -- multi-tracer

  • Based on Richardson-Lucy deprojection
    • Assumes spherical symmetry but generalisation is possible

  • Produces lensing potential profiles from X-ray observations�
  • Introduces simple additional term into the minimisation process
    • Includes an azimuthal averaging operator�
  • This can work for SZ constraints in a similar fashion

With Korbinian Huber in Munich, as well as Celine Tchernin and Matthias Bartelmann in Heidelberg

Huber et al. (in prep.)

The standard model | Data representation and processing | Mass mapping | Learning structure

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Results -- Runtime

SawLens2

ks93_raw

task

speed-up

Invert dense matrices

5-10

Find optimal shapes for RBF-FD nodes

500

Build B_lk = a_i*b_j*A_ij*B_il*C_jk

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Total

200-400

This is actually significantly better than the naive

40 GFLOPS (1 XEON core) vs. 6000 GFLOPS (NVIDIA Pascal)

real

G15: 10deg x 6deg, HH blind

Currently: 3 x 3 deg^2 with 1 arcmin mean resolution at O(1sec)

Example Euclid: Full field in 30 mins; lots of bootstraps possible

The standard model | Data representation and processing | Mass mapping | Learning structure

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Where to go from here

  • Application of the method to current surveys �and Euclid-like simulations
  • Inclusion of more tracers into the framework

The standard model | Data representation and processing | Mass mapping | Learning structure

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A worked example: Dustgrain-pathfinder

‘Observationally’ degenerate cosmological models of f(R) modified gravity with massive neutrinos.

Dustgrain pathfinder simulations

with M. Baldi, C. Giocoli

  • f4
  • f4_03eV
  • f5

  • f5_01eV
  • f5_015eV
  • f6

  • f6_006eV
  • f6_01eV
  • lcdm

Light-cone realisations with MapSim deliver convergence maps for different source redshift.

Giocoli et al. (2018), arXiv:1806.04681

The standard model | Data representation and processing | Mass mapping | Learning structure

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Classic Dustgrain-pathfinder

Peel et al. (2018), arXiv:1805.05146

The standard model | Data representation and processing | Mass mapping | Learning structure

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Semi-classic Dustgrain-pathfinder

Merten et al. (2018), to be submitted

Classification

Fully-connected neural network

Characterisation

99 ‘common’ features: �14 bins for Power spectrum, Peak counts and first three Minkowski functions

PDF, eleven percentiles, mean, variance, skewness, kurtosis

The standard model | Data representation and processing | Mass mapping | Learning structure

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Convolutional neural networks

AlexNet, Krizhevsky et al. (2012); NIPS 25, 1097­1105

Zeiler et al. (2013); arXiv:1311.2901

The standard model | Data representation and processing | Mass mapping | Learning structure

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Convnets in practice

high-level

Python

rigid

low-level

Python / CUDA

flexible

bit-level

libcuDNN / CUDA

Merten et al. (2018) submitted

The standard model | Data representation and processing | Mass mapping | Learning structure

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Dissecting Dustgrain-pathfinder

Merten et al. (2018), to be submitted

The standard model | Data representation and processing | Mass mapping | Learning structure

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Dreaming of mass maps

Merten et al. (2018) to be submitted

The standard model | Data representation and processing | Mass mapping | Learning structure

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Where to go from here

  • We are working on a similar approach to characterise cluster simulations
  • Learn also ‘vanilla’ LCDM from mass maps
  • Trained GANs will deliver fast creation of new simulations
  • We recently started a collaboration in order to filter radio-observations to perform 21cm studies

The standard model | Data representation and processing | Mass mapping | Learning structure

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  • The aim of this proposal is to study nonlinear structure formation and cosmology with the help of gravitational lensing, the latest computer hardware and machine learning techniques.�
  • Our mass mapping software is ready to be released. Many applications to follow.�
  • Deep learning seems to be an optimal way to interpret simulated data and compare it to observations.�
  • Work remains in order to show that current simulations are good enough as training sets. �
  • Work on Euclid prepatorial work has been slow. Too political and undefined.

Summary