Optimization of the “mature” fields development in machine learning algorithms is one of the urgent problems nowadays. The task is set to extend the effective operation of wells, optimize production management at the late stage of field development. Based on the task set, the article provides an overview of possible solutions in waterflooding management problems. Production management technology is considered as an alternative to intensification of operation, which is associated with an increase in the produciton rate and involves finding solutions aimed at reducing the water cut of well production. The practical implementation of the “Neural technologies for production improvement” includes the following steps: evaluation, selection, predictive analytics. The result is a digital technological regime of wells that corresponds to the set goal and the solution of the optimization problem in artificial intelligence algorithms using the software and hardware complex “Atlas – Waterflood Management”. “Neural technologies for production improvement” have been successfully tested at the pilot project site of the productive formation of the Vatyeganskoe field. The article provides a thorough and detailed analysis of the work performed, describes the algorithms and calculation results of the proxy model using the example of the pilot area, as well as the integration of the “Atlas – Waterflood Management” and the organization of the workflow with the field professionals of the Territorial Production Enterprise Povkhneftegaz.

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In the present research, existence and stability of ring solutions to two-dimensional Amari neural field equation with periodic microstructure and Heaviside activation function are studied. Results on dependence of the inner and the outer radii of the ring solutions are obtained. Necessary conditions for existence and sufficient conditions for non-existence of radial travelling waves are formulated for homogeneous neural medium and neural media with mild periodic microstructure. Theoretical results obtained are illustrated with a concrete example based on a connectivity function commonly used in the neuroscience community.

We suggest a method allowing to investigate existence and the measure of proximity between the stationary solutions to continuous and discontinuous neural fields with microstructure. The present part involves results on proximity of the stationary solutions to specific homogenized neural field equations with continuous and discontinuous activation functions. The results of numerical investigation of radially symmetric stationary solutions (bumps) to the neural field with a discontinuous activation function and a given microstructure are presented.

The article is devoted to investigation of integro-differential equation with the Hammerstein integral operator of the following form: ∂_t u(t,x)=-τu(t,x,x_f )+∫_(R^2)▒〖ω(x-y)f(u(t,y) )dy, t≥0, x∈R^2 〗. The equation describes the dynamics of electrical potentials u(t,x) in a planar neural medium and has the name of neural field equation.We study ring solutions that are represented by stationary radially symmetric solutions corresponding to the active state of the neural medium in between two concentric circles and the rest state elsewhere in the neural field. We suggest conditions of existence of ring solutions as well as a method of their numerical approximation. The approach used relies on the replacement of the probabilistic neuronal activation function f that has sigmoidal shape by a Heaviside-type function. The theory is accompanied by an example illustrating the procedure of investigation of ring solutions of a neural field equation containing a typically used in the neuroscience community neuronal connectivity function that allows taking into account both excitatory and inhibitory interneuronal interactions. Similar to the case of bump solutions (i. e. stationary solutions of neural field equations, which correspond to the activated area in the neural field represented by the interior of some circle) at a high values of the neuronal activation threshold there coexist a broad ring and a narrow ring solutions that merge together at the critical value of the activation threshold, above which there are no ring solutions.