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Compartment models are widely used in climate science, epidemiology, andphysics, among other disciplines. An important example of a compartment modelis susceptible-infected-recovered (SIR) model, which can describe diseasedynamics. Bayesian inference for SIR models is challenging because likelihoodevaluation requires solving expensive ordinary differential equations. Althoughvariational inference (VI) can be a fast alternative to the traditional Bayesapproaches, VI has limited applicability due to boundary issues and localoptima problems. To address these challenges, we propose flexible VI methodsbased on deep generative models that do not require parametric assumptions onthe variational distribution. We embed a surjective transformation in ourframework to avoid posterior truncation at the boundary. We provide theoreticalconditions that guarantee the success of the algorithm. Furthermore, ourtemperature annealing scheme can avoid being trapped in local optima through aseries of intermediate posteriors. We apply our method to variants of SIRmodels, illustrating that the proposed method can provide fast and accurateinference compared to its competitors.

Fast Compartment Model Calibration using Annealed and Transformed Variational Inference