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Accelerating Brain Simulations with the Fast Multipole Method

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Euro-Par 2022: Parallel Processing (Euro-Par 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13440))

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Abstract

The brain is probably the most complex organ in the human body. To understand processes such as learning or healing after brain lesions, we need suitable tools for brain simulations. The Model of Structural Plasticity offers a solution to that problem. It provides a way to model the brain bottom-up by specifying the behavior of the neurons and using structural plasticity to form the synapses. However, its original formulation involves a pairwise evaluation of attraction kernels, which drastically limits scalability. While this complexity has recently been decreased to \(O(n \cdot \log ^2 n)\) after reformulating the task as a variant of an n-body problem and solving it using an adapted version of the Barnes–Hut approximation, we propose an even faster approximation based on the fast multipole method (FMM). The fast multipole method was initially introduced to solve pairwise interactions in linear time. Our adaptation achieves this time complexity, and it is also faster in practice than the previous approximation.

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Acknowledgments

We acknowledge the support of the European Commission and the German Federal Ministry of Education and Research (BMBF) under the EuroHPC Programme DEEP-SEA (955606, BMBF Funding No. 16HPC015). The EuroHPC Joint Undertaking (JU) receives support from the European Union’s Horizon 2020 research and innovation programme and GER, FRA, ESP, GRC, BEL, SWE, UK, CHE. This research was also supported by the EBRAINS research infrastructure, funded by the European Union’s Horizon 2020 Framework Programme for Research and Innovation under the Specific GA No. 945539 (Human Brain Project SGA3), and is partly funded by the Federal Ministry of Education and Research (BMBF) and the state of Hesse as part of the NHR Program. The authors gratefully acknowledge having conducted a part of this study on the Lichtenberg high-performance computer of TU Darmstadt.

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Authors and Affiliations

  1. Laboratory for Parallel Programming, Technical University of Darmstadt, Darmstadt, Germany

    Hannah Nöttgen, Fabian Czappa & Felix Wolf

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  1. Hannah Nöttgen
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  2. Fabian Czappa
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Correspondence to Fabian Czappa .

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  1. University of Glasgow, Glasgow, UK

    José Cano

  2. University of Glasgow, Glasgow, UK

    Phil Trinder

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Nöttgen, H., Czappa, F., Wolf, F. (2022). Accelerating Brain Simulations with the Fast Multipole Method. In: Cano, J., Trinder, P. (eds) Euro-Par 2022: Parallel Processing. Euro-Par 2022. Lecture Notes in Computer Science, vol 13440. Springer, Cham. https://doi.org/10.1007/978-3-031-12597-3_24

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  • DOI: https://doi.org/10.1007/978-3-031-12597-3_24

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