  Neural field models represent neuronal communication on a population level
via synaptic weight functions. Using voltage sensitive dye (VSD) imaging it is
possible to obtain measurements of neural fields with a relatively high spatial
and temporal resolution. The synaptic weight functions represent functional
connectivity in the brain and give rise to a spatio-temporal dependence
structure. We present a stochastic functional differential equation for
modeling neural fields, which leads to a vector autoregressive model of the
data via basis expansions of the synaptic weight functions and time and space
discretization. Fitting the model to data is a pratical challenge as this
represents a large scale regression problem. By using a 1-norm penalty in
combination with localized basis functions it is possible to learn a sparse
network representation of the functional connectivity of the brain, but still,
the explicit construction of a design matrix can be computationally
prohibitive. We demonstrate that by using tensor product basis expansions, the
computation of the penalized estimator via a proximal gradient algorithm
becomes feasible. It is crucial for the computations that the data is organized
in an array as is the case for the three dimensional VSD imaging data. This
allows for the use of array arithmetic that is both memory and time
efficient.The proposed method is implemented and showcased in the R package
dynamo available from CRAN.
