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We develop an approach for fully Bayesian learning and calibration ofspatiotemporal dynamical mechanistic models based on noisy observations.Calibration is achieved by melding information from observed data withsimulated computer experiments from the mechanistic system. The joint meldingmakes use of both Gaussian and non-Gaussian state-space methods as well asGaussian process regression. Assuming the dynamical system is controlled by afinite collection of inputs, Gaussian process regression learns the effect ofthese parameters through a number of training runs, driving the stochasticinnovations of the spatiotemporal state-space component. This enables efficientmodeling of the dynamics over space and time. Through reduced-rank Gaussianprocesses and a conjugate model specification, our methodology is applicable tolarge-scale calibration and inverse problems. Our method is general,extensible, and capable of learning a wide range of dynamical systems withpotential model misspecification. We demonstrate this flexibility throughsolving inverse problems arising in the analysis of ordinary and partialnonlinear differential equations and, in addition, to a black-box computermodel generating spatiotemporal dynamics across a network.

Dynamic Bayesian Learning and Calibration of Spatiotemporal Mechanistic Systems