pdet

This package defines ready-to-use neural network emulators for the LIGO-Virgo-KAGRA compact binary selection function. Specifically, this package can be used to compute detection probabilities for compact binary parameters with a wide range of parameters.

The following table describes available emulators.

Name	Observing run	Instruments	Valid Parameter Space
pdet_O3	O3 (includes both O3a and O3b)	LIGO-Hanford, LIGO-Livingston, Virgo	pdet_O3

How to use

Once installed, detection probability calculations can be used in one of two ways, (1) the predict method and (2) directly calling the neural network via the __call__ method

1. predict()

The predict method allows for the evaluation of detection probabilities based on straightforward user-defined parameters. An example is the following:

from pdet import pdet_O3

# Create an emulator
p = pdet_O3()

# Define data
# As an example, consider parameters for three compact binaries
params = {'mass_1': [2.5, 20.0, 50.0],  # Primary source-frame mass (units Msun)
          'mass_2': [1.2, 20.0, 10.0],   # Secondary source-frame mass (units Msun)
          'a_1': [0.0, 0.2, 0.3],       # Primary dimensionless spin
          'a_2': [0.1, 0.4, 0.2],       # Secondary dimensionless spin
          'redshift': [0.1 ,0.4, 1.0]   # Redshift
          }

# Compute detection probabilities
p.predict(params)

Output

Array([[2.03875096e-14],
       [1.52368634e-02],
       [4.16787806e-14]], dtype=float64)

Compact binary parameters can be passed through any structure with key/value pairs, such as a dictionary as above, pandas DataFrame, or other structured array.

Required parameters. The following binary parameters are required:

• mass_1: Primary source-frame mass (units of solar masses)
• mass_2: Secondary source-frame mass (units of solar masses)
• a_1: Primary dimensionless spin
• a_2: Secondary dimensionless spin
• One of the following:
  • redshift: Redshift
  • luminosity_distance: Luminosity distance in Gpc
  • comoving_distance: Comoving distance in Gpc

Optional parameters. The following parameters are, in contrast, optional. Note that, if not provided, they will be generated randomly for each binary according to the default distributions listed below.

• cos_theta_1: Spin-orbit tilt of primary. If not provided, drawn uniformly between $[-1,1]$.
• cos_theta_2: Spin-orbit tilt of secondary. If not provided, drawn uniformly between $[-1,1]$.
• phi_12: Azimuthal angle between primary and secondary spin vectors (units of radians). If not provided, drawn uniformly between $[0,2\pi]$.
• right_ascension: Right ascension of binary on the sky (units of radians). If not provided, drawn uniformly between $[0,2\pi]$.
• cos_inclination: Cosine inclination of the binary's orbit with respect to our line of sight. If not provided, drawn uniformly between $[-1,1]$. The parameter inclination can equivalently be provided (units of radians)
• polarization_angle: Binary polarization angle. If not provided, drawn uniformly between $[0,2\pi]$.

2. Direct evaluation via __call__()

The predict() method above is not amenable to compilation and/or autodifferentiation in jax. An alternative JIT-compileable and differentiable method is the p.__call__() function:

from pdet import pdet_O3
import jax

# Instantiate trained emulator
p = pdet_O3()

# JIT compile
jitted_pdet_O3 = jax.jit(p)

# Define binary parameters.
m1 = [20., 30.]
m2 = [15., 29.]
a1 = [0.5, 0.9]
a2 = [0.3, 0.]
cost1 = [0.2, -0.7]
cost2 = [0.9, 0.]
z = [0.2, 0.5]
cos_inclination = [0.7, 1.]
pol = [0., 2.9]
phi12 = [1.2, 0.]
ra = [3.2, 0.5]
sin_dec = [-1.1, -0.7]
params = jnp.array([m1, m2, a1, a2, cost1, cost2, z, cos_inclination, pol, phi12, ra, sin_dec])

# Compute detection probabilities
jitted_pdet_O3(params)

Output

Array([[0.55567697],
       [0.27248132]], dtype=float64)

Range of validity

Networks were trained using data spanning the ranges described below:

pdet_O3

Primary masses

• $$1 M_\odot \leq m_1 \leq 100 M_\odot$$

Secondary masses

• $$m_2 \geq 1 M_\odot$$ ($$1 M_\odot \leq m_1 \leq 60 M_\odot$$)
• $$m_2 \geq 2 M_\odot$$ ($$60 M_\odot \leq m_1 \leq 100 M_\odot$$)
• Note: Although real pipeline injections were available only in the above intervals, auxiliary "hopeless" training data were generated with $$m_2 \geq 1 M_\odot$$ across the full range of primary masses, and so the network has learned some information outisde these ranges.

Spin magnitudes

• $$a<0.4$$ (component masses below $$2 M_\odot$$)
• $$a<0.998$$ (component masses above $$2 M_\odot$$)
• Note: Although real pipeline injections were available only in the above intervals, auxiliary "hopeless" training data were generated with $$a<0.998$$ across the full range of component masses.