HOLISMOKES -- IV. Efficient mass modeling of strong lenses through deep learning

Modelling the mass distributions of strong gravitational lenses is often necessary to use them as astrophysical and cosmological probes. With the high number of lens systems ($>10^5$) expected from upcoming surveys, it is timely to explore efficient modeling approaches beyond traditional MCMC techniques that are time consuming. We train a CNN on images of galaxy-scale lenses to predict the parameters of the SIE mass model ($x,y,e_x,e_y$, and $θ_E$). To train the network, we simulate images based on real observations from the HSC Survey for the lens galaxies and from the HUDF as lensed galaxies. We tested different network architectures, the effect of different data sets, and using different input distributions of $θ_E$. We find that the CNN performs well and obtain with the network trained with a uniform distribution of $θ_E$ $>0.5"$ the following median values with $1σ$ scatter: $Δx=(0.00^{+0.30}_{-0.30})"$, $Δy=(0.00^{+0.30}_{-0.29})"$, $Δθ_E=(0.07^{+0.29}_{-0.12})"$, $Δe_x = -0.01^{+0.08}_{-0.09}$ and $Δe_y = 0.00^{+0.08}_{-0.09}$. The bias in $θ_E$ is driven by systems with small $θ_E$. Therefore, when we further predict the multiple lensed image positions and time delays based on the network output, we apply the network to the sample limited to $θ_E>0.8"$. In this case, the offset between the predicted and input lensed image positions is $(0.00_{-0.29}^{+0.29})"$ and $(0.00_{-0.31}^{+0.32})"$ for $x$ and $y$, respectively. For the fractional difference between the predicted and true time delay, we obtain $0.04_{-0.05}^{+0.27}$. Our CNN is able to predict the SIE parameters in fractions of a second on a single CPU and with the output we can predict the image positions and time delays in an automated way, such that we are able to process efficiently the huge amount of expected lens detections in the near future.

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