  This work uses a combination of a variational auto-encoder and generative
adversarial network to compare different dark energy models in light of
observations, e.g., the distance modulus from type Ia supernovae. The network
finds an analytical variational approximation to the true posterior of the
latent parameters in the models, yielding consistent model comparison results
with those derived by the standard Bayesian method, which suffers from a
computationally expensive integral over the parameters in the product of the
likelihood and the prior. The parallel computational nature of the network
together with the stochastic gradient descent optimization technique leads to
an efficient way to compare the physical models given a set of observations.
The converged network also provides interpolation for a dataset, which is
useful for data reconstruction.
