Fast emulation of two-point angular statistics for photometric galaxy surveys

Abstract

We develop a set of machine-learning based cosmological emulators, to obtain fast model predictions for the C( ) angular power spectrum coefficients characterising tomographic observations of galaxy clustering and weak gravitational lensing from multi-band photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving a speed-up O(10 3 ) in computing the required statistics for a given set of cosmological parameters, with respect to standard Boltzmann solvers, with an accuracy better than 0.175% (<0.1% for the weak lensing case). This corresponds to ∼ 2% or less of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through (i ) a specific pre-processing optimisation, ahead of the training phase, and (ii ) a more effective neural network architecture, compared to previous implementations. et al. ( 2020)).

Fast and robust Bayesian inference using Gaussian processes with GPry

“…X lie = X and y lie = y [11] repeat M times [12] find x add = argmax[a(x)] starting from n r,acq starting locations [13] X lie append x add and X new append x add [14] y lie append µ(x add ) Kriging believer [15] GP_fit(X lie , y lie ) [16] end [17] y true = log L(X new ) + log π(X new ) parallelizable [18] X append X new [19] y append y true [20] if is_converged (e.g. equation (4.4)) then break [21] end [22] Sample µ(x) with MC sampler [23] return MC sample [24] Function GP_fit(X, y) [25] Compute K −1 = k(X, X|θ MAP ) −1 matrix inversion [26] µ(x) = µ GP+SVM (x) equations (2.5) and (3.4) [27] σ(x) = Σ GP+SVM (x) equations (2.6) and (3.5)…”

Machine Learning for Observational Cosmology

“…We list large-scale cosmological simulation projects for emulators that interpolate summary statistics measured from simulations over the cosmological parameter space in Table 1. We note also that there are many other attempts to utilize emulators for different purposes, such as developing fast Boltzmann equation solvers or performing low-order perturbative calculations [323][324][325][326][327][328][329][330][331][332][333][334][335][336], to explore the galaxy-halo connection for fixed cosmology [337], to translate less costly, low-resolution simulations to mimic more expensive simulations. More specifically, the applications include incorporating baryonic effects to the dark-matter only simulations [338], predicting Lyman-α forest [339,340] or 21-cm power spectra [341,342], extrapolating the predictions in Λ-Cold Dark Matter ¶ Here, convergence means the change in the observed size of an object caused by gravitational lensing effect.…”

Machine learning for observational cosmology

“…We list large-scale cosmological simulation projects for emulators that interpolate summary statistics measured from simulations over the cosmological parameter space in table 1. We note also that there are many other attempts to utilize emulators for different purposes, such as developing fast Boltzmann equation solvers or performing low-order perturbative calculations [323][324][325][326][327][328][329][330][331][332][333][334][335][336], to explore the galaxy-halo connection for fixed cosmology [337], to translate less costly, low-resolution simulations to mimic more expensive simulations. More specifically, the applications include incorporating baryonic effects to the dark-matter only simulations [338], predicting Lyman-α forest [339,340] or 21 cm power spectra [341,342], extrapolating the predictions in Λ-cold dark matter (CDM) cosmology to alternative cosmological models Table 1.…”