StatClimatol: Pierre Lermusiaux

Bayesian Inference of Dynamical Model Formulation In this presentation, we address a holistic set of challenges in ocean Bayesian nonlinear 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 (iv) 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 fluid and ocean flows, including cavity, double-gyre and sudden-expansion/Strait flows with jets and eddies. The Bayesian model inference, based on very limited observations, is illustrated by the estimation of obstacle shapes and positions, of biogeochemical reaction equations and of multiscale bottom gravity current dynamics. This last multiscale inference is motivated in part by classic overflows and dense water formation sites and their relevance to climate monitoring and dynamics. Time permitting, we may also highlight recent results by our group, including high-order Finite-Element schemes for biogeochemical ocean dynamics and exact path planning for coordinated swarms of ocean vehicles. This is joint work with our MSEAS group.