Cosmological Analysis with Calibrated Neural Quantile Estimation and Approximate Simulators

A major challenge in analyzing data from upcoming cosmological surveys (e.g. DESI, Euclid, Rubin and Roman) is the limited availability of costly high-fidelity simulations. We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) algorithm that can be trained on numerous inexpensive, approximate simulations and calibrated with a small set (~100) of high-fidelity simulations. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. After calibration, NQE is guaranteed to be unbiased, although it may be suboptimal if the cheap simulator used to generate training data notably lacks accuracy. As a proof-of-concept, we demonstrate that NQE can be trained using fast Particle-Mesh (PM) simulations with post-processing corrections and calibrated with Particle-Particle (PP) simulations, ensuring unbiased posterior predictions on mock data generated from PP simulations. This approach offers a more cost-effective solution while retaining similar constraining power to an estimator trained directly with a significantly larger number of PP simulations. Furthermore, we can calibrate NQE with multiple baryonic models, allowing us to explicitly marginalize over uncertainties stemming from the incomplete understanding of baryonic physics.