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.

翻译：基于条件神经密度估计器的仿真推断是解决科学中逆问题的强大方法。然而，这些方法通常将底层前向模型视为黑箱，无法利用等变性等几何性质。等变性在科学模型中普遍存在，但将其直接集成到表达性推理网络（如归一化流）中并非易事。我们在此描述一种替代方法，用于在参数和数据的联合变换下纳入等变性。我们的方法——称为群等变神经后验估计（GNPE）——基于在估计参数后验的同时，自洽地标准化数据的“位姿”。该方法与架构无关，既适用于精确等变性，也适用于近似等变性。作为实际应用，我们使用GNPE从引力波观测中推演天体物理双黑洞系统的摊销化估计。结果表明，GNPE在实现最先进精度的同时，将推理时间降低了三个数量级。