Comparing sampling techniques to chart parameter space of 21 cm Global signal with Artificial Neural Networks

TL;DR

This paper compares different sampling techniques for training neural networks to analyze the 21cm global signal, finding that Hammersley sequence sampling offers superior robustness in modeling complex, high-dimensional parameter spaces.

Contribution

It evaluates and compares random, Latin hypercube, and Hammersley sampling methods for training ANNs in 21cm signal analysis, highlighting the effectiveness of quasi-Monte Carlo sampling.

Findings

Hammersley sequence sampling yields more robust ANN models.

Sample size depends on data complexity and number of parameters.

All sampling methods require sufficient samples for accurate training.

Abstract

Understanding the first billion years of the universe requires studying two critical epochs: the Epoch of Reionization (EoR) and Cosmic Dawn (CD). However, due to limited data, the properties of the Intergalactic Medium (IGM) during these periods remain poorly understood, leading to a vast parameter space for the global 21cm signal. Training an Artificial Neural Network (ANN) with a narrowly defined parameter space can result in biased inferences. To mitigate this, the training dataset must be uniformly drawn from the entire parameter space to cover all possible signal realizations. However, drawing all possible realizations is computationally challenging, necessitating the sampling of a representative subset of this space. This study aims to identify optimal sampling techniques for the extensive dimensionality and volume of the 21cm signal parameter space. The optimally sampled training set will be used to train the ANN to infer from the global signal experiment. We investigate three sampling techniques: random, Latin hypercube (stratified), and Hammersley sequence (quasi-Monte Carlo) sampling, and compare their outcomes. Our findings reveal that sufficient samples must be drawn for robust and accurate ANN model training, regardless of the sampling technique employed. The required sample size depends primarily on two factors: the complexity of the data and the number of free parameters. More free parameters necessitate drawing more realizations. Among the sampling techniques utilized, we find that ANN models trained with Hammersley sequence sampling demonstrate greater robustness compared to those trained with Latin hypercube and Random sampling.