Eddies: Fluid Dynamical Niches or Transporters?–A Case Study in the Western Baltic Sea

Fluid flows in the ocean have a strong impact on the growth and distribution of planktonic communities. In this case study, we applied a Lagrangian eddy detection and tracking tool and a transfer operator approach to data from a coupled hydrodynamical-chemical-biological model of the Western Baltic Sea and studied the effects of eddies on plankton in the blooming period March to October 2010. We investigated the residence times of water bodies inside these eddies, using a tracer analysis and found that eddies can act in two different ways: They can be transporters of an enclosed water body that embodies nutrients and the plankton community and export them from the coast to the open sea; and they can act as fluid dynamical niches that enhance the growth of certain species or functional groups by providing optimal temperature and nutrient composition

A trajectory-based loss function to learn missing terms in bifurcating dynamical systems

Missing terms in dynamical systems are a challenging problem for modeling. Recent developments in the combination of machine learning and dynamical system theory open possibilities for a solution. We show how physics-informed differential equations and machine learning—combined in the Universal Differential Equation (UDE) framework by Rackauckas et al.—can be modified to discover missing terms in systems that undergo sudden fundamental changes in their dynamical behavior called bifurcations. With this we enable the application of the UDE approach to a wider class of problems which are common in many real world applications. The choice of the loss function, which compares the training data trajectory in state space and the current estimated solution trajectory of the UDE to optimize the solution, plays a crucial role within this approach. The Mean Square Error as loss function contains the risk of a reconstruction which completely misses the dynamical behavior of the training data. By contrast, our suggested trajectory-based loss function which optimizes two largely independent components, the length and angle of state space vectors of the training data, performs reliable well in examples of systems from neuroscience, chemistry and biology showing Saddle-Node, Pitchfork, Hopf and Period-doubling bifurcations