Reconstructing the Universe with Variational self-Boosted Sampling

Forward modeling approaches in cosmology seek to reconstruct the initial conditions at the beginning of the Universe from the observed survey data.However the high dimensionality of the parameter space poses a challenge to explore the full posterior with traditional algorithms such as Hamiltonian Monte Carlo (HMC) and variational inference (VI).Here we develop a hybrid scheme called variational self-boosted sampling (VBS)that learns a variational approximation for the proposal distribution of HMC with samples generated on the fly, and in turn generates independent samples as proposals for MCMC chain to reduce their auto-correlation length. We use a normalizing flow with Fourier space convolutions as our variational distribution to scale to high dimensions of interest.We show that after a short initial warm-up and training phase, VBS generates better quality of samples than simple VI and reduces the correlation length in the sampling phase by a factor of 10-50 over using only HMC.