EiffL / herculens

Auto-differentiable strong lens modelling with JAX

Herculens: differentiable gravitational lensing

Analysis of strong lensing imaging data

The primary purpose of herculens is to provide flexible modeling methods to model current and future observations of strong gravitational lenses. Currently, it supports various degrees of model complexity, ranging from standard smooth analytical profiles to pixelated models combined with machine learning approaches.

Currently, herculens supports several of the most widely-used analytical profiles, as well as multi-scale pixelated models regularized with wavelets. Future updates will include the support of point source modeling, new regularization techniques, and more expressive models based on neural networks.

JAX-based automatic differentiation and code compilation

herculens is based on the powerful framework of differentiable programming. The code is entirely based on the automatic differentiation and compilation features of JAX. This simply means that you have access, analytically, to all partial derivatives of your model with respect to any of its parameters. This enables faster convergence to the solution, more efficient exploration of the parameter space including the sampling of posterior distributions, and new ways to mitigate degeneracies that affect gravitational lensing.

This highly modular framework offers a way to merge all modeling paradigms explored in the literature, into a single tool:

• analytical: model components are described by analytical functions with few parameters and clear physical meaning, but that may be insufficient to fit all observations;
• pixelated: regular or irregular grid of pixels are used as individual parameters, which offer higher flexibility, but requires well-motivated regularization strategies;
• deep learning: neural networks (among others) are by construction fully differentiable, regardless of being pre-trained or not. It is therefore effortless to plug-in any deep learning-based model component to herculens.

Example notebooks

Below you can find a few examples of synthetic problems that can be tackled with herculens:

• Starting guide: Lens modeling with gradient descent, Fisher analysis and Hamiltonian sampling
• Reconstruction of a complex lensed galaxy with wavelets (and analytical profiles)
• Detection of a dark satellite as a localized deviation to the smooth lens potential

New notebooks will be added soon in order to showcase other features of the package and apply those in different situations.

Installation

Manual installation

The package will be soon available through PyPi directly, but it is as easy to install it manually.

Good practice is to create a new python environment:

conda create -n herculens-env python=3.7
conda activate herculens-env

Download the package cd into the directory. Then install the local herculens package (or use -e for a development install) as follows:

pip install (-e) .

The following dependencies will be installed automatically.

External package requirements

We tested herculens with the versions mentioned in parenthesis. It does not mean that it breaks for newer versions though.

Necessary

• jax (0.2.13)
• jaxlib (0.1.67)
• numpy (1.20.3)
• scipy (1.6.3)

Optional

• optax (0.0.9), for advanced gradient descent algorithms
• numpyro (0.7.1), for HMC sampling
• blackjax (0.7.1), for jax-based HMC sampling integrated with
• dynesty (1.1), for nested sampling
• jaxns (1.1), for jax-based nested sampling
• emcee (3.0.2), for Ensemble MCMC sampling
• lenstronomy (1.9.3), for particle swarm optimization
• palettable (3.3.0), for nicer colormaps for plots

To run the notebooks, jupyter and matplotlib are also necessary.

Attribution

Citation

If you make use of herculens, please cite Galan et al. 2022. This work presents the global architecture of the tool, and applies it to reconstruct a pixelated lens potential with wavelets.

@article{Galan:2022:herculens,
    author        = "Galan, Aymeric and Vernardos, Georgios and Peel, Austin and Courbin, Fr\'ed\'eric and Starck, Jean-Luc",
    title         = "{Using wavelets to capture deviations from smoothness in galaxy-scale strong lenses}",
    eprint        = "2207.05763",
    archivePrefix = "arXiv",
    primaryClass  = "astro-ph.CO",
    year          = "2022"
}

Special mention regarding Lenstronomy

Part of the herculens code originates from the open-source lens modeling software package lenstronomy, described in Birrer et al. 2021 (and references therein). In every source file, proper credits are given to the specific developers and contributors to both the original lenstronomy (up to version 1.9.3) and herculens.

Contributors

The list of people that contributed to Herculens and credits to original lenstronomy contributors, is in this document.