Self-supervised Learning with Physics-aware Neural Networks I: Galaxy
  Model Fitting
  Estimating the parameters of a model describing a set of observations using a
neural network is in general solved in a supervised way. In cases when we do
not have access to the model's true parameters this approach can not be
applied. Standard unsupervised learning techniques on the other hand, do not
produce meaningful or semantic representations that can be associated to the
model's parameters. Here we introduce a self-supervised hybrid network that
combines traditional neural network elements with analytic or numerical models
which represent a physical process to be learned by the system. Self-supervised
learning is achieved by generating an internal representation equivalent to the
parameters of the physical model. This semantic representation is used to
evaluate the model and compare it to the input data during training. The
Semantic Autoencoder architecture described here shares the robustness of
neural networks while including an explicit model of the data, learns in an
unsupervised way and estimates, by construction, parameters with direct
physical interpretation. As an illustrative application we perform unsupervised
learning for 2D model fitting of exponential light profiles.
