Efficient exploration and calibration of a semi-analytical model of galaxy formation with deep learning

TL;DR

This paper presents a deep learning-based emulator for semi-analytical galaxy formation models, enabling rapid parameter exploration, sensitivity analysis, and calibration against observational data with high efficiency and accuracy.

Contribution

The authors develop a sample-efficient deep learning emulator for galaxy formation models, facilitating fast exploration, sensitivity analysis, and automatic calibration, outperforming previous methods in efficiency.

Findings

Achieved a mean absolute error of 0.06 dex at the K-band luminosity function's knee.

Emulator requires fewer than 1000 model evaluations, significantly reducing computational cost.

Successfully calibrated model parameters to observational constraints, discovering improved fits.

Abstract

We implement a sample-efficient method for rapid and accurate emulation of semi-analytical galaxy formation models over a wide range of model outputs. We use ensembled deep learning algorithms to produce a fast emulator of an updated version of the GALFORM model from a small number of training examples. We use the emulator to explore the model's parameter space, and apply sensitivity analysis techniques to better understand the relative importance of the model parameters. We uncover key tensions between observational datasets by applying a heuristic weighting scheme in a Markov chain Monte Carlo framework and exploring the effects of requiring improved fits to certain datasets relative to others. Furthermore, we demonstrate that this method can be used to successfully calibrate the model parameters to a comprehensive list of observational constraints. In doing so, we re-discover previous GALFORM fits in an automatic and transparent way, and discover an improved fit by applying a heavier weighting to the fit to the metallicities of early-type galaxies. The deep learning emulator requires a fraction of the model evaluations needed in similar emulation approaches, achieving an out-of-sample mean absolute error at the knee of the K-band luminosity function of 0.06 dex with less than 1000 model evaluations. We demonstrate that this is an extremely efficient, inexpensive and transparent way to explore multi-dimensional parameter spaces, and can be applied more widely beyond semi-analytical galaxy formation models.