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https://tuni.zoom.us/j/64993452348
Mikko Lehtimäki,
Marja-Leena Linne,
Lassi PaunonenIn computational neuroscience there is a great demand to incorporate more molecular and cellular level detail into mathematical models of neuronal networks. This is deemed necessary in order to recreate phenomena such as learning, memory and behavior in silico. However, numerical simulation of such multi-scale models is resource intensive, if not impossible. This problem has been partially overcome by using simplified synapse, neuron and population models that replace biological variables and mechanisms from the models with phenomenological descriptions. While useful, this approach causes information loss that might diminish the value of such models, as the variables might lack biological meaning.
In this study we present approximation as an alternative to simplification. By using mathematical model order reduction (MOR) methods approximations can be derived algorithmically. Here we compute reduced models with the Discrete Empirical Interpolation Method (DEIM) [1] algorithm along with its advanced variants. The appeal of these methods is that there is no need to linearize the model, make assumptions of the system behavior or discard any variables. A reduced model can be simulated efficiently in a low-dimensional subspace where a smaller number of equations needs to be solved. An approximation of the original high-dimensional model can be reconstructed at any time (Fig 1). The acceleration in simulation time gained this way requires no special hardware and can be readily implemented in any programming language.
We discuss results from approximating three nonlinear systems; chemical reactions in the synapse, a compartmental neuronal network and a multi- dimensional mean-field model [2-4]. We have made the code to approximate the mean-field model open source [5]. We demonstrate the value of reduced models in computational neuroscience and explain the pros and cons of several different reduction methods with regards to the above models. Especially implementation of mathematical model order reduction algorithms in neuronal simulators and using reduced models in neuromorphic hardware are potential applications of these methods for enabling multi-scale simulations of brain activity.
Acknowledgements
M.L. is supported by TUNI Graduate School, M.-L.L by Academy of Finland grant 297893 and L.P. by grants 298182 and 310489. This research has received funding from the European Union’s Horizon 2020 Framework Programme for Research and Innovation under the Specific Grant Agreement No. 785907 (Human Brain Project SGA2).
References
1 S. Chaturantabut and D. Sorensen, “Nonlinear model reduction via discrete empirical interpolation,” SIAM Journal on Scientific Computing, vol. 32, no. 5, pp. 2737–2764, 2010.
2 M. Lehtimäki, L. Paunonen, S. Pohjolainen, and M.-L. Linne, “Order reduction for a signaling pathway model of neuronal synaptic plasticity,” IFAC- PapersOnLine, vol. 50, no. 1, pp. 7687–7692, 2017.
3 M. Lehtimäki, L. Paunonen, and M.-L. Linne, “Projection-based order reduction of a nonlinear biophysical neuronal network model,” 2019 Proceedings of the IEEE Conference on Decision and Control (CDC). IEEE, 2020 (in press).
4 M. Lehtimäki, I. Seppälä, L. Paunonen, and M.-L. Linne. Accelerated simulation of a neuronal population via mathematical model order reduction. Proceedings of the IEEE International Conference on Artificial Intelligence Circuits and Systems, 2020 (in press).
5 https://github.com/Mikkolehtimaki/neuro-mor
