Preprints on Uncertainty Quantification for Neural Fields with random data

Daniele Avitabile, Francesca Cavallini, Svetlana Dubinkina, and Gabriel Lord have published two preprints analysing the problem of Forward Uncertainty Quantification in neural fields, which are models of brain dynamics.

In the first paper the group studies neural fields subject to random data in the synaptic kernel, firing rate function, external stimulation, and initial conditions. The well-posedness and regularity of the solutions is studied in abstract form for spatially continuous and spatially discrete formulations of the problem.

In the second paper they leverage the theory of the first paper to analyse a stochastic collocation scheme for the neural fields, proving that the scheme can be exponentially convergent in both the spatial variable, and in the parameter discretisation.

This work opens up the possibility of studying how uncertainties in the input data in the model are propagated forward and become uncertainties in the model prediction.