Bayesian Learning of Stochastic Dynamical Model Formulation

Pierre Lermusiaux, Massachusetts Institute of Technology
November 13th, 2013 at 3:30PM–4:30PM in 939 Evans Hall [Map]

In this presentation, we first highlight recent results by our MSEAS group, including high-order Finite-Element schemes for biogeochemical ocean dynamics and exact path planning for swarms of ocean vehicles using level-set equations. We then address a holistic challenge in ocean Bayesian estimation: i) predict the probability distribution functions (pdfs) of large nonlinear ocean systems using stochastic partial differential equations, ii) assimilate data using Bayes' law with these pdfs, iii) predict the future data that optimally reduce uncertainties and rank the known and learn the new model formulations themselves. Overall, we allow the joint inference of the state, equations, geometry, boundary conditions and initial conditions of dynamical models. Examples are provided using time-dependent ocean and fluid flows, including cavity, double-gyre and sudden-expansion flows with jets and eddies. The Bayesian model inference is illustrated by the estimation of obstacle shapes and of biogeochemical reaction equations based on very limited observations. This is joint work with our MSEAS group.