The goal of this project is to develop computationally efficient Bayesian inference methods for mixed-effects stochastic models, in particular we consider models with time-dynamics, with a focus on stochastic differential equations (SDE). Existing inference methods for these models are computationally intensive, which proves to be a computational bottleneck when the size of the data set increases. We develop a simulation-based inference method training mixture models to provide surrogates of the intractable likelihood and posterior.