Bayesian calibration of computer models and beyond

Bayesian calibration of computationally expensive computer models offers an established framework for quantification of uncertainty of model parameters and predictions. Traditional Bayesian calibration involves the emulation of the computer model and an additive model discrepancy term using Gaussian processes; inference is then carried out using Markov chain Monte Carlo. In this talk, I present a calibration framework where limited flexibility and scalability are addressed by means of compositions of Gaussian processes into Deep Gaussian processes and scalable variational inference techniques. This formulation can be easily implemented in development environments featuring automatic differentiation and exploiting GPU-type hardware. I then discuss identifiability issues and cases where the computer model implements ODEs/PDEs/SDEs. Finally, I draw connections with other inference frameworks, such as transfer learning, gradient matching for ODEs and SDEs, and Physics-informed priors for Bayesian deep learning.