Bayesian Deep Gaussian Processes for Correlated Functional Data: A Case Study in Cosmological Matter Power Spectra

TL;DR

This paper introduces a Bayesian deep Gaussian process model to estimate and predict correlated functional matter power spectra in cosmology, providing uncertainty quantification and improved predictions for unobserved cosmologies.

Contribution

It extends Bayesian DGPs to handle correlated functional outputs and integrates this with a Gaussian process emulator for cosmological predictions.

Findings

Model performs well on synthetic data

Outperforms benchmark cosmological emulator

Provides effective uncertainty quantification

Abstract

Understanding the structure of our universe and the distribution of matter is an area of active research. As cosmological surveys grow in complexity, the development of emulators to efficiently and effectively predict matter power spectra is essential. We are particularly motivated by the Mira-Titan Universe simulation suite that, for a specified cosmological parameterization (termed a "cosmology"), provides multiple response curves of various fidelities, including correlated functional realizations. Our objective is two-fold. First, we estimate the underlying true matter power spectra, with appropriate uncertainty quantification (UQ), from all of the provided curves. To this end, we propose a novel Bayesian deep Gaussian process (DGP) hierarchical model which synthesizes all the simulation information to estimate the underlying matter power spectra while providing effective UQ. Our model extends previous work on Bayesian DGPs from scalar responses to correlated functional outputs. Second, we leverage our predicted power spectra from various cosmologies in order to accurately predict the entire matter power spectra for an unobserved cosmology. For this task, we use basis function representations of the functional spectra to train a separate Gaussian process emulator. Our method performs well in synthetic exercises and against the benchmark cosmological emulator (Cosmic Emu).