  Computer models play a crucial role in numerous scientific and engineering
domains. To ensure the accuracy of simulations, it is essential to properly
calibrate the input parameters of these models through statistical inference.
While Bayesian inference is the standard approach for this task, employing
Markov Chain Monte Carlo methods often encounters computational hurdles due to
the costly evaluation of likelihood functions and slow mixing rates. Although
variational inference (VI) can be a fast alternative to traditional Bayesian
approaches, VI has limited applicability due to boundary issues and local
optima problems. To address these challenges, we propose flexible VI methods
based on deep generative models that do not require parametric assumptions on
the variational distribution. We embed a surjective transformation in our
framework to avoid posterior truncation at the boundary. Additionally, we
provide theoretical conditions that guarantee the success of the algorithm.
Furthermore, our temperature annealing scheme can prevent being trapped in
local optima through a series of intermediate posteriors. We apply our method
to infectious disease models and a geophysical model, illustrating that the
proposed method can provide fast and accurate inference compared to its
competitors.
