## Accelerated simulation of a neuronal population via mathematical model order reduction

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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**Accelerated simulation of a neuronal population via mathematical model order reduction.** / Lehtimäki, Mikko; Seppälä, Ippa; Paunonen, Lassi; Linne, Marja-Leena.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

### Harvard

*2020 2nd IEEE International Conference on Artificial Intelligence Circuits and Systems (AICAS).*IEEE, pp. 118-122, IEEE International Conference on Artificial Intelligence Circuits and Systems, 1/01/00. https://doi.org/10.1109/AICAS48895.2020.9073844

### APA

*2020 2nd IEEE International Conference on Artificial Intelligence Circuits and Systems (AICAS)*(pp. 118-122). IEEE. https://doi.org/10.1109/AICAS48895.2020.9073844

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TY - GEN

T1 - Accelerated simulation of a neuronal population via mathematical model order reduction

AU - Lehtimäki, Mikko

AU - Seppälä, Ippa

AU - Paunonen, Lassi

AU - Linne, Marja-Leena

N1 - INT=bmte,"Seppälä, Ippa"

PY - 2020

Y1 - 2020

N2 - Mathematical modeling of biological neuronal networks is important in order to increase understanding of the brain and develop systems capable of brain-like learning. While mathematical analysis of these comprehensive, stochastic, and complex models is intractable, and their numerical simulation is very resource intensive, mean-field modeling is an effective tool in enabling the analysis of these models. The mean-field approach allows the study of populations of biophysically detailed neurons with some assumptions of the mean behaviour of the population, but ultimately requires numerical solving of highdimensional differential equation systems. Mathematical model order reduction methods can be employed to accelerate the analysis of high-dimensional nonlinear models with a purely softwarebased approach. Here we compare state-of-the-art methods for improving the simulation time of a neuronal mean-field model and show that a nonlinear Fokker-Planck-McKean-Vlasov model can be accurately approximated in low-dimensional subspaces with these methods. Using Proper Orthogonal Decomposition and different variations of the Discrete Empirical Interpolation Method, we improved the simulation time by over three orders of magnitude while achieving low approximation error.

AB - Mathematical modeling of biological neuronal networks is important in order to increase understanding of the brain and develop systems capable of brain-like learning. While mathematical analysis of these comprehensive, stochastic, and complex models is intractable, and their numerical simulation is very resource intensive, mean-field modeling is an effective tool in enabling the analysis of these models. The mean-field approach allows the study of populations of biophysically detailed neurons with some assumptions of the mean behaviour of the population, but ultimately requires numerical solving of highdimensional differential equation systems. Mathematical model order reduction methods can be employed to accelerate the analysis of high-dimensional nonlinear models with a purely softwarebased approach. Here we compare state-of-the-art methods for improving the simulation time of a neuronal mean-field model and show that a nonlinear Fokker-Planck-McKean-Vlasov model can be accurately approximated in low-dimensional subspaces with these methods. Using Proper Orthogonal Decomposition and different variations of the Discrete Empirical Interpolation Method, we improved the simulation time by over three orders of magnitude while achieving low approximation error.

U2 - 10.1109/AICAS48895.2020.9073844

DO - 10.1109/AICAS48895.2020.9073844

M3 - Conference contribution

SN - 978-1-7281-4923-3

SP - 118

EP - 122

BT - 2020 2nd IEEE International Conference on Artificial Intelligence Circuits and Systems (AICAS)

PB - IEEE

ER -