Evaluating machine learning techniques for predicting power spectra from
  reionization simulations
  Upcoming experiments such as the SKA will provide huge quantities of data.
Fast modelling of the high-redshift 21cm signal will be crucial for efficiently
comparing these data sets with theory. The most detailed theoretical
predictions currently come from numerical simulations and from faster but less
accurate semi-numerical simulations. Recently, machine learning techniques have
been proposed to emulate the behaviour of these semi-numerical simulations with
drastically reduced time and computing cost. We compare the viability of five
such machine learning techniques for emulating the 21cm power spectrum of the
publicly-available code SimFast21. Our best emulator is a multilayer perceptron
with three hidden layers, reproducing SimFast21 power spectra $10^8$ times
faster than the simulation with 4% mean squared error averaged across all
redshifts and input parameters. The other techniques (interpolation, Gaussian
processes regression, and support vector machine) have slower prediction times
and worse prediction accuracy than the multilayer perceptron. All our emulators
can make predictions at any redshift and scale, which gives more flexible
predictions but results in significantly worse prediction accuracy at lower
redshifts. We then present a proof-of-concept technique for mapping between two
different simulations, exploiting our best emulator's fast prediction speed. We
demonstrate this technique to find a mapping between SimFast21 and another
publicly-available code 21cmFAST. We observe a noticeable offset between the
simulations for some regions of the input space. Such techniques could
potentially be used as a bridge between fast semi-numerical simulations and
accurate numerical radiative transfer simulations.
