神经科学中的模型降阶
Model Order Reduction in Neuroscience
摘要：
人脑包含大约$10^9$神经元，每个神经元与其他神经元具有大约$10^3$连接、突触。我们大脑的大多数感觉、认知和运动功能都依赖于大量神经元的相互作用。近年来，许多技术被开发用于顺序地或同时地记录大量神经元。随着计算能力的提高和算法的发展，神经元群体的高级分析与所记录的神经元活动的数量和复杂性的快速增长并行。最近的研究利用降维和模型降阶技术来提取在单个神经元水平上不明显的相干特征。已经观察到，神经元活动在低维子空间上演化。大规模神经网络模型简化的目的是准确快速地预测模式及其在大脑不同区域的传播。采用动态模式分解（DMD）、本征正交分解（POD）、离散经验插值（DEIM）和参数与状态联合约简等方法在低维子空间上识别脑活动的时空特征。本文综述了神经科学中常用的降维和模型降阶技术。这项工作将在即将出版的《模型降阶手册》中作为一个章节。Grivet-Talocia，A.夸特罗尼湾Rozza，W. H. A.席尔德斯湖M. Silveira，编辑，出现在DE GRUYTER）
英文摘要：
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)
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