Efficient sparse matrix-delayed vector multiplication for discretized neural field model

Abstract

Computational models of the human brain provide an important tool for studying the principles behind brain function and disease. To achieve whole-brain simulation, models are formulated at the level of neuronal populations as systems of delayed differential equations. In this paper, we show that the integration of large systems of sparsely connected neural masses is similar to well-studied sparse matrix-vector multiplication; however, due to delayed contributions, it differs in the data access pattern to the vectors. To improve data locality, we propose a combination of node reordering and tiled schedules derived from the connectivity matrix of the particular system, which allows performing multiple integration steps within a tile. We present two schedules: with a serial processing of the tiles and one allowing for parallel processing of the tiles. We evaluate the presented schedules showing speedup up to \(2\,\times \) on single-socket CPU, and \(1.25\,\times \) on Xeon Phi accelerator.