# Detecting Model Misspecification in Cosmology with Scale-Dependent Normalizing Flows

arXiv: https://arxiv.org/abs/2508.05744 · HTML: https://mlsanity.com/paper/2508.05744/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 10 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [A brief review of contrastive learning applied to astrophysics](https://mlsanity.com/paper/2306.05528/) (2023)
- [SimBIG: Field-level Simulation-Based Inference of Galaxy Clustering](https://mlsanity.com/paper/2310.15256/) (2023)

## Built on by (most cited first, 2 of 2)

- [Generative Models and Statistical Validation](https://mlsanity.com/paper/2605.30453/) (2026)
- [Hybrid Physical-Neural Simulator for Fast Cosmological Hydrodynamics](https://mlsanity.com/paper/2510.26593/) (2025)

## Abstract (arXiv)

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.