  Predictive dynamical models for marine ecosystems are used for a variety of
needs. Due to sparse measurements and limited understanding of the myriad of
ocean processes, there is however significant uncertainty. There is model
uncertainty in the parameter values, functional forms with diverse
parameterizations, level of complexity needed, and thus in the state fields. We
develop a Bayesian model learning methodology that allows interpolation in the
space of candidate models and discovery of new models from noisy, sparse, and
indirect observations, all while estimating state fields and parameter values,
as well as the joint PDFs of all learned quantities. We address the challenges
of high-dimensional and multidisciplinary dynamics governed by PDEs by using
state augmentation and the computationally efficient GMM-DO filter. Our
innovations include stochastic formulation and complexity parameters to unify
candidate models into a single general model as well as stochastic expansion
parameters within piecewise function approximations to generate dense candidate
model spaces. These innovations allow handling many compatible and embedded
candidate models, possibly none of which are accurate, and learning elusive
unknown functional forms. Our new methodology is generalizable, interpretable,
and extrapolates out of the space of models to discover new ones. We perform a
series of twin experiments based on flows past a ridge coupled with
three-to-five component ecosystem models, including flows with chaotic
advection. The probabilities of known, uncertain, and unknown model
formulations, and of state fields and parameters, are updated jointly using
Bayes' law. Non-Gaussian statistics, ambiguity, and biases are captured. The
parameter values and model formulations that best explain the data are
identified. When observations are sufficiently informative, model complexity
and functions are discovered.

Computational Engineering, Finance, and Science;Machine Learning;Geophysics