Bayesian Learning Machines for Fish Models

For fish models, a significant amount of uncertainty exists in the functional form of model equations, parameterizations, and even the state variables themselves. This is due to the complexity and lack of understanding of the processes involved, as well as to the very sparse measurements. These challenges motivate the objective of the present work, which is the simultaneous estimation of state variables, parameters, and model equations in dynamics-based Bayesian learning of high-dimensional coupled fish-biogeochemical-physical models using sparse observations. A rigorous PDE-based machine learning framework is used for the simultaneous nonlinear inference of all the learning objectives, with the ability to choose from existing models and even extrapolate into the space of models to discover newer ones. We also demonstrate selection of optimal observation locations for model learning and the concept of identifiability using mutual information. Results are showcased for varied ocean physical and ecosystem dynamics.