7 Model order reduction in neuroscience

The human brain contains approximately 109 neurons, each with approximately 103 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 have been developed for recording large numbers of neurons either sequentially or simultaneously. Increases in computational power and algorithmic developments have enabled advanced analyses of the 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 the accurate and fast prediction of patterns and their propagation in different areas of the brain. Spatiotemporal features of brain activity are identified on low-dimensional subspaces with methods such as dynamic mode decomposition, proper orthogonal decomposition, the discrete empirical interpolation method, and combined parameter and state reduction. In this chapter, we give an overview of the currently used dimensionality reduction and model order reduction techniques in neuroscience.