# Cosmic Inference: Constraining Parameters With Observations and Highly Limited Number of Simulations

## TL;DR

This paper introduces a novel statistical framework that combines limited cosmological simulations with observational data using Gaussian process emulators and Bayesian optimization, enabling accurate parameter inference in complex cosmological models.

## Contribution

The paper presents an adaptive Gaussian process emulator framework that reduces the number of required simulations for cosmological parameter inference, improving efficiency and robustness.

## Key findings

- Requires fewer simulations than traditional methods
- More robust in reconstructing parameters and credible intervals
- Effective for small-scale structure observations like Lyman alpha forest

## Abstract

Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern cosmological probes increasingly rely on measurements of the small-scale structure, and the only way to accurately model physical behavior on those scales, roughly 65 Mpc/h or smaller, is via expensive numerical simulations. In this paper, we provide a detailed description of a novel statistical framework for obtaining accurate parameter constraints by combining observations with a very limited number of cosmological simulations. The proposed framework utilizes multi-output Gaussian process emulators that are adaptively constructed using Bayesian optimization methods. We compare several approaches for constructing multi-output emulators that enable us to take possible inter-output correlations into account while maintaining the efficiency needed for inference. Using Lyman alpha forest flux power spectrum, we demonstrate that our adaptive approach requires considerably fewer --- by a factor of a few in Lyman alpha P(k) case considered here --- simulations compared to the emulation based on Latin hypercube sampling, and that the method is more robust in reconstructing parameters and their Bayesian credible intervals.