C3NN-SBI: Learning hierarchies of N -point statistics from cosmological fields with physics-informed neural networks
6 affiliations
- 1Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität
- 2Center for Computational Astrophysics, Flatiron Institute
- 3Excellence Cluster ORIGINS
- 4Max-Planck-Institut für extraterrestrische Physik
- 5Steward Observatory, University of Arizona
- 6Fakultät für Physik, Universität Bielefeld
Abstract
Cosmological analyses are moving past the well-understood two-point statistics to extract more information from cosmological fields. A natural step in extending inference pipelines to other summary statistics is to include higher-order N-point correlation functions (NPCFs), which are computationally expensive and difficult to model. At the same time it is unclear how many NPCFs one would have to include to reasonably exhaust the cosmological information in the observable fields. An efficient alternative is given by learned and optimized summary statistics, largely driven by overparametrization through neural networks. This, however, largely abandons our physical intuition about the NPCF formalism, and information extraction becomes opaque to the practitioner. We designed a simulation-based inference pipeline that not only benefits from the efficiency of machine-learned summaries through optimization, but also holds on to the NPCF program. We employed the heavily constrained cosmological correlator convolutional neural network (C3NN), which extracts summary statistics that can be directly linked to a given order of NPCF. We present an application of our framework to simulated lensing convergence maps and study the information content of our learned summary at various orders in NPCFs for this idealized example. We view our approach as an exciting new avenue for physics-informed simulation-based inference.
Related
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BibTeX
@article{lehman2026c3nnsbi,
title = {{C3NN-SBI: Learning hierarchies of N -point statistics from cosmological fields with physics-informed neural networks}},
author = {Kai Lehman and Zhengyangguang Gong and David Gebauer and Stella Seitz and Jochen Weller},
journal = {Astronomy \& Astrophysics},
year = {2026},
month = oct,
doi = {10.1051/0004-6361/202660266},
url = {https://www.aanda.org/10.1051/0004-6361/202660266},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - C3NN-SBI: Learning hierarchies of N -point statistics from cosmological fields with physics-informed neural networks
AU - Kai Lehman
AU - Zhengyangguang Gong
AU - David Gebauer
AU - Stella Seitz
AU - Jochen Weller
PY - 2026
DA - 2026/10/28
JO - Astronomy & Astrophysics
DO - 10.1051/0004-6361/202660266
UR - https://www.aanda.org/10.1051/0004-6361/202660266
AB - Cosmological analyses are moving past the well-understood two-point statistics to extract more information from cosmological fields. A natural step in extending inference pipelines to other summary statistics is to include higher-order N-point correlation functions (NPCFs), which are computationally expensive and difficult to model. At the same time it is unclear how many NPCFs one would have to include to reasonably exhaust the cosmological information in the observable fields. An efficient alternative is given by learned and optimized summary statistics, largely driven by overparametrization through neural networks. This, however, largely abandons our physical intuition about the NPCF formalism, and information extraction becomes opaque to the practitioner. We designed a simulation-based inference pipeline that not only benefits from the efficiency of machine-learned summaries through optimization, but also holds on to the NPCF program. We employed the heavily constrained cosmological correlator convolutional neural network (C3NN), which extracts summary statistics that can be directly linked to a given order of NPCF. We present an application of our framework to simulated lensing convergence maps and study the information content of our learned summary at various orders in NPCFs for this idealized example. We view our approach as an exciting new avenue for physics-informed simulation-based inference.
SN - 0004-6361
SN - 1432-0746
ER -