Model Order Reduction in Neuroscience

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)

arXiv comment14 pages, no figures

References in corpus (28)

• The structure and function of complex networks
• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
• Chaos as an Intermittently Forced Linear System
• Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition
• Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
• Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations
• A Novel Model Order Reduction Approach for Navier-Stokes Equations at High Reynolds Number
• Pod-Galerkin Reduced Order Methods for CFD Using Finite Volume Discretisation: Vortex Shedding Around a Circular Cylinder
• Sparse Identification for Nonlinear Optical Communication Systems: SINO Method
• The Randomized Dependence Coefficient
• Prediction of frequencies in thermosolutal convection from mean flows
• pyMOR - Generic Algorithms and Interfaces for Model Order Reduction
• State-space model identification and feedback control of unsteady aerodynamic forces
• Digital Twin: Values, Challenges and Enablers
• Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks
• Sparse Identification of Nonlinear Dynamics with Control (SINDYc)
• Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: applications to Coanda effect in cardiology
• On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics
• Model Order Reduction by Proper Orthogonal Decomposition
• TurboMOR: an Efficient Model Order Reduction Technique for RC Networks with Many Ports
• Data-Driven Combined State and Parameter Reduction for Extreme-Scale Inverse Problems
• High-order accurate difference schemes for the Hodgkin-Huxley equations
• Should You Derive, Or Let the Data Drive? An Optimization Framework for Hybrid First-Principles Data-Driven Modeling
• Reduced Order Modeling of Diffusively Coupled Network Systems: An Optimal Edge Weighting Approach
• Digital Twins
• Automatic rational approximation and linearization of nonlinear eigenvalue problems

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