Bayesian emulator optimisation for cosmology: application to the Lyman-alpha forest

Abstract

The Lyman-alpha forest provides strong constraints on both cosmological parameters and intergalactic medium astrophysics, which are forecast to improve further with the next generation of surveys including eBOSS and DESI. As is generic in cosmological inference, extracting this information requires a likelihood to be computed throughout a high-dimensional parameter space. Evaluating the likelihood requires a robust and accurate mapping between the parameters and observables, in this case the 1D flux power spectrum. Cosmological simulations enable such a mapping, but due to computational time constraints can only be evaluated at a handful of sample points; "emulators" are designed to interpolate between these. The problem then reduces to placing the sample points such that an accurate mapping is obtained while minimising the number of expensive simulations required. To address this, we introduce an emulation procedure that employs Bayesian optimisation of the training set for a Gaussian process interpolation scheme. Starting with a Latin hypercube sampling (other schemes with good space-filling properties can be used), we iteratively augment the training set with extra simulations at new parameter positions which balance the need to reduce interpolation error while focussing on regions of high likelihood. We show that smaller emulator error from the Bayesian optimisation propagates to smaller widths on the posterior distribution. Even with fewer simulations than a Latin hypercube, Bayesian optimisation shrinks the 95% credible volume by 90% and, e. g., the 1σ error on the amplitude of small-scale primordial fluctuations by 38%. This is the first demonstration of Bayesian optimisation applied to large-scale structure emulation, and we anticipate the technique will generalise to many other probes such as galaxy clustering, weak lensing and 21cm.

Massive neutrinos and degeneracies in Lyman-alpha forest simulations

“…This allows for the use of Bayesian optimisation to distribute the hydrodynamical simulations more efficiently throughout parameter space, minimising the total number of simulations required and helping to ensure convergence to the true posterior distribution. [24].…”

Revealing Reionization with the Thermal History of the Intergalactic Medium: New Constraints from the Lyα Flux Power Spectrum

“…These bounds (including our own) can be weakened when considering the case where ULAs do not make up all the dark matter [31], but we defer analysis of these mixed a [8], by accessing wavenumbers 2.5 times larger, we can probe axion masses about eight times heavier. Second, we model the simulated flux power spectra using a Bayesianoptimized Gaussian process emulator, which explicitly tests for convergence in parameter estimation with respect to the accuracy of the emulator model [32,33,38]. This contrasts with previous simulation interpolation methods [e. g., 29, 36, 37] which have relied on a Taylor expansion around a fiducial point and which we have shown in prior work can bias power spectrum estimation and weaken parameter constraints [33].…”

On the road to per cent accuracy – II. Calibration of the non-linear matter power spectrum for arbitrary cosmologies

“…The results presented here should be regarded as conservative, as other emulation schemes, such as sparse polynomial chaos expansion (Blatman & Sudret 2011;Euclid Collaboration et al 2018), and further design optimisation (Rogers et al 2019;Caron et al 2019) could help overcome the shortcomings of Gaussian process regression. Furthermore, we have only considered departures from ΛCDM on scales of k > 10 −3 h/Mpc.…”