Detecting Model Misspecification in Cosmology with Scale-Dependent Normalizing Flows

TL;DR

This paper introduces a new method combining scale-dependent neural summary statistics and normalizing flows to detect when cosmological models do not fit observational data, helping validate theoretical models in high-dimensional cosmological datasets.

Contribution

The paper presents a novel framework that uses scale-dependent neural networks and normalizing flows for model validation in cosmology, enabling data-driven detection of model misspecification.

Findings

Successfully applied to CAMELS simulations with different physics.

Identifies breakdown points of theoretical models at various scales.

Provides a systematic way to validate complex cosmological models.

Abstract

Current and upcoming cosmological surveys will produce unprecedented amounts of high-dimensional data, which require complex high-fidelity forward simulations to accurately model both physical processes and systematic effects which describe the data generation process. However, validating whether our theoretical models accurately describe the observed datasets remains a fundamental challenge. An additional complexity to this task comes from choosing appropriate representations of the data which retain all the relevant cosmological information, while reducing the dimensionality of the original dataset. In this work we present a novel framework combining scale-dependent neural summary statistics with normalizing flows to detect model misspecification in cosmological simulations through Bayesian evidence estimation. By conditioning our neural network models for data compression and evidence estimation on the smoothing scale, we systematically identify where theoretical models break down in a data-driven manner. We demonstrate a first application to our approach using matter and gas density fields from three CAMELS simulation suites with different subgrid physics implementations.