# Performance¶

The default parameter settings in ARES are not necessarily optimal for all applications. In this section, we detail some tricks that may be useful if one can tolerate a small hit in accuracy.

## Time-stepping¶

For Simple Physical Models for the Global 21-cm Signal, the main parameters that control the speed of the calculation are epsilon_dt and max_timestep, which are described a bit more in Control Parameters. In short, epsilon_dt determines the largest fractional change allowed in any property of the intergalactic medium (IGM) – if a given timestep results in a larger fraction change than epsilon_dt allows, the iteration will be repeated with a smaller timestep. On the other hand, max_timestep governs the “global” timestep, i.e., the largest step we are allowed to take even in the limit where IGM quantities are evolving slowly, and thus are not restricted by epsilon_dt. This parameter is in some sense aesthetic, as it determines how frequently data is saved and as a result controls the smoothness in the time evolution of quantities of interest.

The default values for these parameters, epsilon_dt=0.05 and max_timestep=1 (the latter in Myr) are set so that they have no discernible impact on the evolution of the IGM. However, relaxing epsilon_dt by a factor of a few and increasing max_timestep to $$\sim 10$$ Myr can provide a factor of $$\sim 2-3$$ speed-up, with only a limited impact in the results (e.g., $$\sim 5\%$$ errors induced in global 21-cm signal). Their effects have not been studied exhaustively, so it is possible that for some combinations of parameters the impact of changing these parameters may be greater. Proceed with caution!

Time-stepping is controlled a little differently in models that properly solve for the evolution of the X-ray background (as in Mirocha (2014); see The Metagalactic X-ray Background). In this case, the time resolution is set to be logarithmic in $$1+z$$, which accelerates solutions to the radiative transfer equation. The key parameter is tau_redshift_bins, which is 1000 by default in the mirocha2017:dpl models (see Working with Data and Models From the Literature). Reducing this to 400 or 500 can result in a factor of $$\sim 2$$ speed-up. Just note that you will need to re-generate a lookup table for the IGM optical depth of that resolution – see Initial Conditions & Lookup Tables for a few notes about how to do that (the relevant adjustment is re-setting Nz in the \$ARES/examples/generate_optical_depth_tables.py script).

## Avoiding Overhead: Halo Mass Function and Stellar Population Synthesis Models¶

Most ARES calculations spend $$\sim 10-30\%$$ of the run-time simply reading in some necessary look-up tables – this sounds like a lot but is of course much faster than re-generating them on-the-fly. However, for most applications, these tables are always the same, so you can read them into memory once and pass them along to subsequent calculations for a speed-up.

The two most common lookup tables are those for the halo mass function (HMF) and stellar population synthesis (SPS) models. The following example grabs instances of the HMF and SPS classes that are attached to an initial ARES simulation, and then supplies those objects to a subsequent model which then does not need to read them in for itself:

import ares
import time

# First, setup a UVLF-calibrated model for the global signal.
pars = ares.util.ParameterBundle('mirocha2017:base')

# Time it
t1 = time.time()
sim = ares.simulations.Global21cm(**pars)
sim.run()
t2 = time.time()

# Grab the HMF and SPS model instances from the first source population
# and pass them to the next model via parameters that exist solely for
# this purpose.
pars['hmf_instance'] = sim.pops[0].halos
pars['pop_src_instance{0}'] = sim.pops[0].src

# Time the new run.
t3 = time.time()
sim = ares.simulations.Global21cm(**pars)
sim.run()
t4 = time.time()

print("Sim 1 done in {} sec.".format(t2 - t1))
print("Sim 2 done in {} sec.".format(t4 - t3))


This should provide a $$\sim 20\%$$ speed-up.

Note

The HMF speed-up applies also to the simplest global signal models, but the pop_src_instance trick used above does not, as such models do not initialize stellar population synthesis models.

Note

These tricks are built-in to the ModelGrid and ModelFit machinery in ARES. Simply set the save_hmf and save_psm attributes of each class to True before running.

There are two main differences between the so-called $$f_{\mathrm{coll}}$$ models and the 'mirocha2017' UVLF-calibrated models relevant to the performance of the code: (i) the UVLF-calibrated models generate an entire population of galaxies, rather than linking the star formation rate density to $$\dot{f}_{\mathrm{coll}}$$, which is slightly slower, and (ii) by default, the 'mirocha2017:base' models will solve the cosmological radiative transfer equation in detail, as mentioned above in the “Time Stepping” section. The accuracy of this calculation can be reduced to achieve a speed-up (see above), but you can also just turn this off if you’d like – just beware that if performing inference, this will bias your constraints on any X-ray-related parameters.

To turn off the advanced RTE machinery, do the following:

pars = ares.util.ParameterBundle('mirocha2017:base')

# X-rays are emitted by population #1: turn off RTE solution
pars['pop_solve_rte{1}'] = False

# Must also switch to a simpler, energy-independent scheme for
# depositing photo-electron energies in the IGM.
pars['secondary_ionization] = 1


Setting secondary_ionization=1 will revert to using the Shull & van Steenberg (1985) approach to secondary ionization and heating, which is an asymtoptic high-energy limit. By default, secondary_ionization=3, which corresponds to the energy-dependent results of Furlanetto & Johnson-Stoever (2010).