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## Presentations

### Paradigm shift in the approach to brain modeling

Mysin I.E.

Institute of Theoretical and Experimental Biophysics of RAS

Modern neuroscience has accumulated a large amount of data about the brain. However, it was not possible to generalize the volume of modern data in the form of mathematical models. Big projects like the "Blue brain" or "Human brain project" have not produced the expected results, although they have significantly advanced our understanding of the brain. Thus, the problem of building models of neural networks that simulate the work of the brain is an urgent task.

We propose a solution to the problem based on combining two approaches. The first approach is population models. In this type of models, the behavior of not one neuron is reproduced, but the frequency of discharges of a large population of neurons. The most well-known is the population approach based on the Fokker-Planck equation. In our work, we used the method of modeling the refractory density distribution (CBRD) [1].

The second approach is the adjont state method [2]. This method allows us to estimate the gradient from the solution of a system of differential equations, according to the simulation parameters. Gradient estimation in turn gives two possibilities. Firstly, it allows you to evaluate the sensitivity of the simulation results in relation to the parameters. If the modulus of the partial derivative with respect to some parameter is large, then this means a high sensitivity to this parameter. Secondly, gradient estimation allows using gradient descent methods to find optimal parameters.

We applied our approach to the problem of modeling the phase relations between the inhibitory neurons of the hippocampal CA1 field during theta rhythm generation. Using gradient descent, we found the parameters of the network of inhibitory neurons that best describe experimental data on the phase relations of the discharges of neurons and theta rhythm. The solution of this problem shows the fundamental applicability of our approach. We are convinced that our approach to model construction can be scaled to be applied to problems with a large number of optimizable variables and the description of a larger number of experimental data.

The work was supported by a grant of RSF № 20-71-10109.

References

1. Chizhov A.V., Graham L.J. Population model of hippocampal pyramidal neurons, linking a refractory density approach to conductance-based neurons. // Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2007. Vol. 75, № 1 Pt 1. P. 011924.

2. Chen R.T.Q., Rubanova Y. Neural ordinary differential equations // Advances in neural Neural Information Processing Systems 31, 2018.

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