Because different parts of the brain have rich interconnections, it is not possible to model small parts realistically in isolation. However, it is also impractical to simulate large neural systems in detail. This article outlines a new approach to multiscale modeling of neural systems that involves constructing efficient surrogate models of populations. Given a population of neuron models with correlated activity and with specific, nonrandom connections, a surrogate model is constructed in order to approximate the aggregate outputs of the population. The surrogate model requires less computation than the neural model, but it has a clear and specific relationship with the neural model. For example, approximate spike rasters for specific neurons can be derived from a simulation of the surrogate model. This article deals specifically with neural engineering framework (NEF) circuits of leaky-integrate-and-fire point neurons. Weighted sums of spikes are modeled by interpolating over latent variables in the population activity, and linear filters operate on gaussian random variables to approximate spike-related fluctuations. It is found that the surrogate models can often closely approximate network behavior with orders-of-magnitude reduction in computational demands, although there are certain systematic differences between the spiking and surrogate models. Since individual spikes are not modeled, some simulations can be performed with much longer steps sizes (e.g., 20 ms). Possible extensions to non-NEF networks and to more complex neuron models are discussed.
A Review of Finite Approximations, Archimedean and Non-Archimedean
