Machine Learning for Gravitational Lenses

We describe two scenarioes for Machine Learning for Gravitational Lenses.. The first one assumes a parametric lens model.
The second one uses the roulette formalism as a parameter-free model.

Parameter Recovery

The vanilla problem is to assume particular lens and source models, and aim to estimate the relevant parameters. For instance,

• The SIS lens model has a single parameter $R_E$ (Einstein radius),
• The spherical source model has three parameters, the size $\sigma$ and the position $(x,y)$.
• Additionally, there is a distance parameter $\chi$ which is the distance to the lens relative to the distance to the source (plane).

The machine learning problem is to estimate the columns chi, einsteinR, sigma, x, and y in the CSV file from the corresponding image files.

Roulette Amplitude Recovery

The roulette amplitudes can be thought of as coefficients of a Taylor expansion of the lens potential. Thus they give a local description of the lens potential in a single point. The hope is to use this as a parameter-free model, but the research is still in early stages.

The columns we want to estimate in this scenario are

• The roulette amplitudes alpha[$m$][$s$] and beta[$m$][$s$] up to a chosen maximum $m$. This is the local description of the lens potential $\psi$.
• The position of the reference point xiX and xiY relative to the centre of mass. This is the point where we have the local description of $\psi$.
• Possibly sigma if we want to resimulate.
  The position of the source is not required, as it is inferred from the roulette amplitudes.

Source information, including the position (x, y) are copied from the original dataset. Other colums of the CSV file are described under Roulette Formalism.