  Simulation-based inference with conditional neural density estimators is a
powerful approach to solving inverse problems in science. However, these
methods typically treat the underlying forward model as a black box, with no
way to exploit geometric properties such as equivariances. Equivariances are
common in scientific models, however integrating them directly into expressive
inference networks (such as normalizing flows) is not straightforward. We here
describe an alternative method to incorporate equivariances under joint
transformations of parameters and data. Our method -- called group equivariant
neural posterior estimation (GNPE) -- is based on self-consistently
standardizing the "pose" of the data while estimating the posterior over
parameters. It is architecture-independent, and applies both to exact and
approximate equivariances. As a real-world application, we use GNPE for
amortized inference of astrophysical binary black hole systems from
gravitational-wave observations. We show that GNPE achieves state-of-the-art
accuracy while reducing inference times by three orders of magnitude.

Machine Learning;Instrumentation and Methods for Astrophysics;General Relativity and Quantum Cosmology;Machine Learning