Differentiable strong lensing: uniting gravity and neural nets through differentiable probabilistic programming
Open accessAbstract
Since upcoming telescopes will observe thousands of strong lensing systems, creating fully automated analysis pipelines for these images becomes increasingly important. In this work, we make a step towards that direction by developing the first end-to-end differentiable strong lensing pipeline. Our approach leverages and combines three important computer science developments: (i) convolutional neural networks (CNNs), (ii) efficient gradient-based sampling techniques, and (iii) deep probabilistic programming languages. The latter automatize parameter inference and enable the combination of generative deep neural networks and physics components in a single model. In the current work, we demonstrate that it is possible to combine a CNN trained on galaxy images as a source model with a fully differentiable and exact implementation of gravitational lensing physics in a single probabilistic model. This does away with hyperparameter tuning for the source model, enables the simultaneous optimization of nearly 100 source and lens parameters with gradient-based methods, and allows the use of efficient gradient-based posterior sampling techniques. These features make this automated inference pipeline potentially suitable for processing a large amount of data. By analysing mock lensing systems with different signal-to-noise ratios, we show that lensing parameters are reconstructed with per cent-level accuracy. More generally, we consider this work as one of the first steps in establishing differentiable probabilistic programming techniques in the particle astrophysics community, which have the potential to significantly accelerate and improve many complex data analysis tasks.
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Chianese et al. (2020) main novelty is that thanks to the differentiable programming framework, it becomes possible to compute the derivatives of the likelihood function with respect to both the parameters of the source and the lens, allowing for fast inference.
“The main novelty, is that thanks to the differentiable programming framework, it becomes possible to compute the derivatives of the likelihood function with respect to both the parameters of the source and the lens, allowing for fast inference (Figure 26).”
From The Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys (2023) · cites this paper as Chianese et al. (2020)
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Coogan, A., Edwards, T., Chia, H. S., George, J., Katherine Freese, B., Messick, C., Setzer, C. N., Weniger, C., & Zimmerman, A. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.122001 · Cited by 19 · see citing works
Self-citationThe effect of the perturber population on subhalo measurements in strong gravitational lenses
Coogan, A., Montel, N. A., Karchev, K., Grootes, M. W., Nattino, F., & Weniger, C. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad2925 · Cited by 19 · see citing works
Self-citationStrong-lensing source reconstruction with variationally optimized Gaussian processes
Karchev, K., Coogan, A., & Weniger, C. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac311 · Cited by 18 · see citing works
Self-citationFinding strong gravitational lenses through self-attention
Thuruthipilly, H., Zadrożny, A., Pollo, A., & Biesiada, M. (2022) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202142463 · Cited by 17 · see citing works
Kernel Phase and Coronagraphy with Automatic Differentiation
Pope, B. J. S., Pueyo, L. A., Xin, Y., & Tuthill, P. (2021) · Cited by 16 · see citing works
Zubieta, E., Missel, R., Fiscella, V. S., Loustó, C. O., del Palacio, S., Armengol, F. G. L., García, F., Combi, J. A., Wang, L., Combi, L., et al. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad723 · Cited by 16 · see citing works
Dark Matter Subhalos, Strong Lensing and Machine LearningPreprint
Varma, S., Fairbairn, M., & Figueroa, J. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2005.05353 · Cited by 16 · see citing works
Kernel Phase and Coronagraphy with Automatic Differentiation
Pope, B. J. S., Pueyo, L. A., Xin, Y., & Tuthill, P. G. (2021) · The Astrophysical Journal · doi:10.3847/1538-4357/abcb00 · Cited by 15 · see citing works
Vernardos, G., Tsagkatakis, G., & Pantazis, Y. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa3201 · Cited by 14 · see citing works
Machine Learning and CosmologyPreprint
Dvorkin, C., Mishra-Sharma, S., Nord, B., Villar, V., Avestruz, C., Bechtol, K., Ciprijanovic, A., Connolly, A. J., Garrison, L., Narayan, G., et al. (2022) · arXiv.org · doi:10.48550/arxiv.2203.08056 · Cited by 21 · see citing works
Modeling lens potentials with continuous neural fields in galaxy-scale strong lenses
Biggio, L., Vernardos, G., Galan, A., Peel, A., & Courbin, F. (2023) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202245126 · Cited by 11 · see citing works
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Targeted Likelihood-Free Inference of Dark Matter Substructure in Strongly-Lensed GalaxiesPreprint
Coogan, A., Karchev, K., & Weniger, C. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2010.07032 · Cited by 10 · see citing works
Self-citationCaustics: A Python Package for Accelerated Strong Gravitational Lensing Simulations
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Self-citationVela pulsar: single pulses analysis with machine learning techniques
Loustó, C. O., Missel, R., Prajapati, H. S., Fiscella, S. V. S., Armengol, F. G. L., Gyawali, P., Wang, L., Cahill, N. D., Combi, L., del Palacio, S., et al. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab3287 · Cited by 5 · see citing works
Transformers as strong lens detectors - From simulation to surveys
Thuruthipilly, H., Grespan, M., & Zadrożny, A. (2024) · AIP conference proceedings · doi:10.1063/5.0203317 · Cited by 4 · see citing works
Analytic auto-differentiable ΛCDM cosmography
Karchev, K. (2023) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2023/07/065 · Cited by 3 · see citing works
A compact group lens modeled with GIGA-Lens: Enhanced inference for complex systems
Urcelay, F., Jullo, E., Barrientos, L. F., Huang, X., & Hernandez, J. (2025) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202449261 · Cited by 2 · see citing works
CSST strong lensing preparation: fast modelling of galaxy–galaxy strong lenses in the big data era
Cao, X., Li, R., Li, N., Chen, Y., Li, R., Shan, H., & Li, T. (2025) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staf891 · Cited by 2 · see citing works
Silvestri, G., Fertig, E., Moore, D., & Ambrogioni, L. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.06021 · Cited by 1 · see citing works
Determining the Dark Matter distribution in galaxies with Deep LearningPreprint
Rios, M. D. L., Petač, M., Zaldívar, B., Bonaventura, N., Calore, F., & Fabio Iocco, A. (2021) · arXiv (Cornell University) · doi:10.1093/mnras/stad2614
Differentiable probabilistic programming for strong gravitational lensingPreprint
Chianese, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.06617
Self-citation
- Authors
- Chianese, M., Coogan, A., Hofma, P., Otten, S., & Weniger, C.
- Affiliations
- Delta Institute for Theoretical Physics (NL)
- Radboud University Nijmegen (NL)
- Corresponding author
- Chianese, Marco
- Coogan, Adam
- Hofma, Paul
- Venue
- Monthly Notices of the Royal Astronomical Society
- Publisher
- Oxford University Press (OUP)
- Published
- 2020-05-28
- Volume
- 496
- Issue
- 1
- Pages
- 381-393
- ISSN
- 0035-8711 (ISSN-L)
- 1365-2966
- OpenAlex
- W2979416954
- Cited by
- 36
- References
- 84
- Citations by year
- 2025: 2 · 2024: 5 · 2023: 8 · 2022: 7 · 2021: 9 · 2020: 4 · 2019: 1
- FWCI
- 3.12
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Monthly Notices of the Royal Astronomical Society (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- UvA-DARE (University of Amsterdam) (submittedVersion, other-oa)
- Radboud Repository (Radboud University) (submittedVersion)
- Radboud Repository (Radboud University) (submittedVersion, other-oa)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- NWO (680-47-532)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astrophysical Phenomena and Observations
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- strong gravitational lensing, convolutional neural networks, automated image analysis, signal-to-noise ratio
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