Applications

Abstract

The human brain contains approximately $10^9$ neurons, each with approximately $10^3$ connections, synapses, with other neurons. Most sensory, cognitive and motor functions of our brains depend on the interaction of a large population of neurons. In recent years, many technologies are developed for recording large numbers of neurons either sequentially or simultaneously. An increase in computational power and algorithmic developments have enabled advanced analyses of neuronal population parallel to the rapid growth of quantity and complexity of the recorded neuronal activity. Recent studies made use of dimensionality and model order reduction techniques to extract coherent features which are not apparent at the level of individual neurons. It has been observed that the neuronal activity evolves on low-dimensional subspaces. The aim of model reduction of large-scale neuronal networks is an accurate and fast prediction of patterns and their propagation in different areas of the brain. Spatiotemporal features of the brain activity are identified on low dimensional subspaces with methods such as dynamic mode decomposition (DMD), proper orthogonal decomposition (POD), discrete empirical interpolation (DEIM) and combined parameter and state reduction. In this paper, we give an overview of the currently used dimensionality reduction and model order reduction techniques in neuroscience. This work will be featured as a chapter in the upcoming Handbook on Model Order Reduction,(P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W. H. A. Schilders, L. M. Silveira, eds, to appear on DE GRUYTER)