Data Assimilation and Kernel Reconstruction for Nonlocal Field Dynamics
Data assimilation is concerned with state estimation in dynamical systems. Methods such as three-dimensional or four-dimensional variational data assimilation have a long history and are used with large success in operational centers. Today, ensemble data assimilation and particle filters are methods which attract a lot of attention.
The reconstruction of unknown parts of some dynamical system such as structural functions or connectivity is a basic task of inverse problems, medical imaging and nondestructive testing. Here, we study the reconstruction of the neural connectivity kernel within a neural field given the full dynamical evolution. Kernels are non-local and model both short-range and long-range signal processing in living neural tissue.
We formulate an iterative data assimilation inversion method, where the activity fields of of some neural tissue is reconstructed from non-local measurements and the kernel is reconstructed given the reconstruction of the activity. This approach is iterated in the sense that the first guess for the state reconstruction can be improved based on the kernel reconstruction of step two. We provide a description of the method, numerical examples and also the basic elements of a convergence proof of the iteration when the measurement error tends to zero.
Prof. Roland Potthast Deutscher Wetterdienst