Bayesian Inference of Coupled Biogeochemical-Physical Models

The present study deals with the joint estimation of states, parameters and parameterizations in dynamics-based Bayesian learning of biogeochemical model equations. The joint Bayesian inference is based on stochastic Dynamically Orthogonal (DO) partial differential equations (PDEs) for reduced-dimension probabilistic prediction, and on Gaussian Mixture Model DO filtering and smoothing for nonlinear inference of state variables and parameters. The Bayesian model inference is then completed by parallelized and analytical computation of marginal likelihoods for multiple candidate biogeochemical models. The classes of models considered correspond to competing scientific hypotheses and differ in complexity and in the representation of specific biogeochemical processes. Within each model class, model equations have unknown parameters and uncertain parameterizations, all of which are estimated by the joint Bayesian inference. For each model class, the result is a Bayesian update of the joint distribution of the state, parameters and parameterizations. The combined multi-model scientific result is a rigorous Bayesian inference of the marginal distribution of biogeochemical model equations. The examples illustrate how such PDE-based machine learning could rigorously guide the selection and discovery of ecosystem models. This is joint work with our MSEAS group at MIT.