## Abstrakti

In this thesis, we study the use of Model Order Reduction (MOR) methods for accelerating and reducing the computational burden of brain simulations. Mathematical modeling and numerical simulations are the primary tools of computational neuroscience, a ﬁeld that strives to understand the brain by combining data and theories. Due to the complexity of brain cells and the neuronal networks they form, computer simulations cannot consider neuronal networks in biologically realistic detail. We apply MOR methods to derive lightweight reduced order models and show that they can approximate models of neuronal networks. Reduced order models may thus enable more detailed and large-scale simulations of neuronal systems.

We selected several mathematical models that are used in neuronal network simulations, ranging from synaptic signaling to neuronal population models, to use as reduction targets in this thesis. We implemented the models and determined the mathematical requirements for applying MOR to each model. We then identiﬁed suitable MOR algorithms for each model and established eﬃcient implementations of our selected methods. Finally, we evaluated the accuracy and speed of our reduced order models. Our studies apply MOR to model types that were not previously reduced using these methods, widening the possibilities for use of MOR in computational neuroscience and deep learning. In summary, the results of this thesis show that MOR can be an eﬀective acceleration strategy for neuronal network models, making it a valuable tool for building large-scale simulations of the brain.

MOR methods have the advantage that the reduced model can be used to reconstruct the original detailed model, hence the reduction process does not discard variables or decrease morphological resolution. We identiﬁed the Proper Orthogonal Decomposition (POD) combined with Discrete Empirical Interpolation Method (DEIM) as the most suitable tool for reducing our selected models. Additionally, we implemented several recent advanced variants of these methods. The primary obstacle of applying MOR in neuroscience is the nonlinearity of neuronal models, and POD-DEIM can account for that complexity. Extensions of the Balanced Truncation and Iterative Rational Krylov Approximation methods for nonlinear systems also show promise, but have stricter requirements than POD-DEIM with regards to the structure of the original model.

Excellent accuracy and acceleration were found when reducing a high-dimensional mean-ﬁeld model of a neuronal network and chemical reactions in the synapse, using the POD-DEIM method. We also found that a biophysical network, which models action potentials through ionic currents, beneﬁts from the use of adaptive MOR methods that update the reduced model during the model simulation phase. We further show that MOR can be integrated to deep learning networks and that MOR is an eﬀective reduction strategy for convolutional networks, used for example in vision research.

Our results validate MOR as a powerful tool for accelerating simulations of nonlinear neuronal networks. Based on the original publications of this thesis, we can conclude that several models and model types of neuronal phenomena that were not previously reduced can be successfully accelerated using MOR methods. In the future, integrating MOR into brain simulation tools will enable faster development of models and extracting new knowledge from numerical studies through improved model eﬃciency, resolution and scale.

We selected several mathematical models that are used in neuronal network simulations, ranging from synaptic signaling to neuronal population models, to use as reduction targets in this thesis. We implemented the models and determined the mathematical requirements for applying MOR to each model. We then identiﬁed suitable MOR algorithms for each model and established eﬃcient implementations of our selected methods. Finally, we evaluated the accuracy and speed of our reduced order models. Our studies apply MOR to model types that were not previously reduced using these methods, widening the possibilities for use of MOR in computational neuroscience and deep learning. In summary, the results of this thesis show that MOR can be an eﬀective acceleration strategy for neuronal network models, making it a valuable tool for building large-scale simulations of the brain.

MOR methods have the advantage that the reduced model can be used to reconstruct the original detailed model, hence the reduction process does not discard variables or decrease morphological resolution. We identiﬁed the Proper Orthogonal Decomposition (POD) combined with Discrete Empirical Interpolation Method (DEIM) as the most suitable tool for reducing our selected models. Additionally, we implemented several recent advanced variants of these methods. The primary obstacle of applying MOR in neuroscience is the nonlinearity of neuronal models, and POD-DEIM can account for that complexity. Extensions of the Balanced Truncation and Iterative Rational Krylov Approximation methods for nonlinear systems also show promise, but have stricter requirements than POD-DEIM with regards to the structure of the original model.

Excellent accuracy and acceleration were found when reducing a high-dimensional mean-ﬁeld model of a neuronal network and chemical reactions in the synapse, using the POD-DEIM method. We also found that a biophysical network, which models action potentials through ionic currents, beneﬁts from the use of adaptive MOR methods that update the reduced model during the model simulation phase. We further show that MOR can be integrated to deep learning networks and that MOR is an eﬀective reduction strategy for convolutional networks, used for example in vision research.

Our results validate MOR as a powerful tool for accelerating simulations of nonlinear neuronal networks. Based on the original publications of this thesis, we can conclude that several models and model types of neuronal phenomena that were not previously reduced can be successfully accelerated using MOR methods. In the future, integrating MOR into brain simulation tools will enable faster development of models and extracting new knowledge from numerical studies through improved model eﬃciency, resolution and scale.

Alkuperäiskieli | Englanti |
---|---|

Julkaisupaikka | Tampere |

ISBN (elektroninen) | 978-952-03-2942-6 |

Tila | Julkaistu - 2023 |

OKM-julkaisutyyppi | G5 Artikkeliväitöskirja |

### Julkaisusarja

Nimi | Tampere University Dissertations - Tampereen yliopiston väitöskirjat |
---|---|

Vuosikerta | 817 |

ISSN (painettu) | 2489-9860 |

ISSN (elektroninen) | 2490-0028 |